Gonzaga Law Review
*325 CALCULATING TORT DAMAGES FOR LOST FUTURE EARNINGS: THE PUZZLES OF TAX,
INFLATION AND RISK
Michael I. Krauss [FNa1]
Robert A. Levy [FNaa1]
Copyright © 1996 by the Gonzaga Law Review Association; Michael I. Krauss and
Robert A. Levy
TABLE OF CONTENTS
I. SYNOPSIS ....................................................... 326
II. OVERVIEW ....................................................... 328
III. SELECTION OF A RISK-FREE DISCOUNT RATE ......................... 330
A. The Problem of a Constant Discount Rate ..................... 330
B. Reinvestment Rate Risk on Government Bonds .................. 332
IV. THE IMPACT OF INCOME TAXES ON AWARDS FOR LOST FUTURE EARNINGS .. 334
A. Subtraction of Income Taxes from Forecasted Earnings ........ 335
B. Adjustment for the Taxability of Income on the Award ........ 337
V. IMPLICATIONS OF INFLATION ON AWARDS FOR LOST FUTURE EARNINGS ... 341
A. Three Modern Approaches ..................................... 341
B. The Differential Discount Rate Approach ..................... 345
VI. RISK-ADJUSTMENT VIA THE CAPITAL ASSET PRICING MODEL ............ 348
A. Risk Measurement and CAPM ................................... 349
B. Employment Risk Versus Common Stocks ........................ 351
VII. RISK-ADJUSTMENT VIA HYPOTHETICAL INSURANCE LOADING ............. 353
A. Basing Risk-Adjustment on the Loading Factor ................ 354
B. The Percentage Impact of Loading Factors and Loss Periods ... 356
C. Determining the "Correct" Loading Factor .................... 358
D. Food for Thought ............................................ 361
VIII. SUMMARY AND CONCLUSIONS ........................................ 364
A. Selection of a Risk-Free Discount Rate ...................... 364
B. Income Taxes ................................................ 365
C. Inflation ................................................... 365
D. Risk-Adjustment Via the Capital Asset Pricing Model ......... 366
E. Hypothetical Insurance Loading .............................. 366
IX. APPENDIX A: EMPLOYMENT RISK VERSUS COMMON STOCKS ............... 368
X. APPENDIX B: ILLUSTRATIVE ADJUSTMENT FOR CERTAINTY EQUIVALENTS .. 370
XI. APPENDIX C: EFFECT OF CERTAINTY EQUIVALENTS ADJUSTMENTS ........ 372
The tort system typically requires that damages be assessed at the time liability is assigned. Therefore, unless the victim has fully recovered, a forecast of uncertain future events will usually be required. [FN1] Among the elements of damages that call for a look into the future is recovery for a disabled victim's lost earning capacity. If, for example, the victim of an automobile accident would have earned a projected $100,000 in the year 1999, the court will include that amount, after some important adjustments, as part of the award.
One of the adjustments to the $100,000 starting amount is likely to be for mortality risk, i.e., the probability that the accident victim would have died [FN2] by 1999 even if the accident had not occurred. Assuming a mortality risk of, *327 say, 20%, the victim's expected earnings in 1999 are only $80,000, and the damage award would be correspondingly reduced. [FN3]
It is important to note, however, that even an award of $80,000 overcompensates this hypothetical victim. Most persons are averse to significant risk, [FN4] and would thus prefer a sum certain of $80,000 to an 80% chance of receiving $100,000, coupled with a 20% chance of receiving nothing.
This paper establishes a framework by which the extent of possible over- compensation for lost future income can be measured. Part II sets the stage for our examination of this problem. Part III deals with selection of a risk-free discount rate. Part IV addresses income taxes, and Part V examines the implications of inflation. While these topics are peripheral to the risk- adjustment theme just alluded to, they are necessary to a complete discussion of the subject of lost future earnings. Parts VI and VII are directed at *328 assessing the potential for over-compensation of risk-averse plaintiffs when converting probabilistic outcomes into certainty equivalents.
Part VI approaches the problem from a traditional risk-adjustment perspective using the "capital asset pricing model." The appropriateness of this model to the calculation of damages for lost future earnings is then criticized. Part VII introduces a new approach which views damage awards for lost future income as the linkage of probabilistic future earnings and a non-loaded term insurance contract.
Part VIII recapitulates the recommendations contained in Parts III through VII and reiterates jurisprudential concerns raised throughout the paper.
Awards to accident victims should include the present value of the victim's lost future wages. [FN5] Simply adding up the projected earnings would unfairly burden the defendant. [FN6] Because damages are awarded as a lump sum, the defendant would in effect be paying unearned interest to the plaintiff.
In establishing the present value of lost future wages, a court will typically undertake the following steps: [FN7] (1) wages are forecasted based upon an assumed growth rate; (2) if the injured victim is still employable, wages from an alternative occupation should be subtracted, [FN8] but if the victim is *329 deceased, [FN9] amounts attributable to foregone personal consumption should be subtracted; [FN10] (3) income taxes are subtracted; [FN11] (4) each year's remaining amount is then multiplied by the probability that the victim would still have been working if the accident had not occurred; [FN12] (5) and finally, the residual is discounted to present value at a risk-free rate of interest. [FN13]
There are numerous questions in regard to each of these steps. Three of these questions will be analyzed in Parts III through V respectively. What risk-free rate should be used? Should it be pre-tax or post-tax? How should inflation be estimated, and should it impact the discount rate? [FN14]
*330 III. SELECTION OF A RISK-FREE DISCOUNT RATE
If the period between the date of a disabling accident and the date the victim would otherwise likely have retired from work is 20 years, the yield to maturity on a 20-year United States Government bond might seem to be a good proxy for the risk-free discount rate. The contention is that an investor buying such a bond and holding it until maturity is guaranteed to earn the quoted yield, since the risk of default would be zero for all practical purposes. But this proposition fails to grasp two important concepts. First, as Section A points out, it is incorrect to use a constant rate for the full period. Second, as Section B points out, the yield to maturity on a coupon- paying government bond cannot be guaranteed due to fluctuating interest rates. As such, the return on reinvested coupons will be unpredictable.
A. The Problem of a Constant Discount Rate
Assume that yields to maturity on 1-year and 20-year government bonds are 3% and 7% respectively. [FN15] Assume further that the forecasted wages of an accident victim are $1,000 at the end of year 1 and $100 at the end of year 20, with no earnings in years 2 through 19. (The absurdity of the wage model does not bear on the validity of the analysis; it is adopted solely to simplify calculations.)
Discounting the two wage payments at 7% per annum produces a present value of $961.42. [FN16] But when the sum of $961.42 is invested for the first *331 year, it does not earn 7%; it earns only about 3%, the yield on 1-year instruments. [FN17] The amount available at the end of the first year is thus $990.26 [FN18]--not even enough to cover the initial $1,000 wage. Bonds do not earn interest at a constant rate. If a constant rate is assumed, and the sums to be discounted vary widely from year to year, the problem is exacerbated.
There are two phenomena that will create wide variation in lost future earnings cases:
. The first, discussed in Part V, is the acceleration of wages due to inflation and increases in productivity. If a worker is earning $20,000 at age 20, and we add 6% annually for inflation and productivity increases, then that worker's forecasted wages at age 65 will be over $275,000. [FN19]
. The second phenomenon is the sharp increase in mortality rates that accompanies advancing age. Mortality rates for a 20-year-old are only 0.19% to age 21, but reach 25% to age 65. [FN20] Morbidity rates used to determine the likelihood disability, follow a similar pattern. [FN21] Reduction of wages for risk of death and disability reduce the amounts in later years to a far greater extent than in earlier years. These reductions offset increases due to inflation and productivity, but not uniformly and perfectly.
*332 To compensate for these phenomena, the risk-free rate must be set with reference to the yield curve. [FN22] That is, the rate must be revised from year to year, consonant with the yield to maturity on United States Government bonds of varying lengths. Lost future earnings assignable to the 20th year must be discounted by the rate on 20-year risk-free instruments; earnings assignable to the first year must be discounted at the rate on 1-year instruments; etc. [FN23]
B. Reinvestment Rate Risk on Government Bonds
The "risk-free" investment process appears deceptively easy: buy government bonds with a yield to maturity equal to the required yield and a term to maturity equal to the desired time horizon. There is, however, no guarantee that a 10-year bond yielding 7% will produce a 7% return over the 10-year period, even assuming that all payments are made as scheduled.
Yield to maturity calculations assume that coupons generated by a bond can be reinvested at the same rate over the life of the issue. But what would happen if interest rates rose or declined? Principal would still be repaid after 10 years, but all coupons received in the interim would be reinvested at higher or lower rates, thus producing more or less than a 7% overall return. The uncertainty of return is known as the "reinvestment rate risk." Any attempt to hedge against the reinvestment rate risk by investing in shorter-term maturities will only make matters worse. The coupon payments will vary as each short-term issue is rolled over, and the proceeds received from each sale will be reinvested at an interest rate not known in advance. [FN24]
*333 There are two ways to neutralize the reinvestment rate risk. One is to invest in zero coupon bonds, which eliminate reinvestment. [FN25] The second is to invest in issues whose term to maturity exceeds the time horizon. If interest rates should decline, the return on reinvested coupons will be lower than expected, but there will be a capital gain upon sale of the bond prior to its maturity. If interest rates should increase, the return on reinvested coupons will be higher, but there will be a capital loss upon sale of the bond before term. The key is to find the appropriate term of the bond so that any change in interest rates will generate offsetting rate of return effects. A recently rediscovered financial measure called "duration" [FN26] facilitates this calculation.
Duration is the weighted average timing of the receipt of cash flows from a bond, expressed in years. [FN27] If a bond is held to its duration, the yield to *334 maturity will be "immunized" against interest rate fluctuations. Capital gains or losses arising from interest rate variations are counterbalanced by lower or higher returns on reinvested coupons. In practice, this means holding bonds whose maturities are longer than one's time horizon, since duration will always be less than years to maturity for a coupon-paying bond. For purposes of setting a risk-free discount rate, one must use either zero coupon bonds or bonds with a duration (not maturity) equal to the time horizon over which the yield is to be locked in.
IV. THE IMPACT OF INCOME TAXES ON AWARDS FOR LOST FUTURE EARNINGS
The Internal Revenue Code provides that compensatory damages received on account of personal injuries are not taxable. [FN28] However, income earned on the damage award is subject to normal tax rules. [FN29] The general rule regarding deductibility of compensatory damage awards by tortfeasors is that multiple taxpayers associated as a business entity are allowed to deduct losses they actually pay against taxable income. [FN30] If the tortfeasor is an individual, deductibility is conditioned on incurring the loss in a trade or business. [FN31] Accordingly, the federal government (i.e., taxpayers at large) "absorbs" [FN32] a portion of compensatory damages, which are deductible when paid, yet non-taxable when received. [FN33]
*335 This section will address three questions pertaining to the impact of tax issues on compensation for forecasted lost earnings. [FN34] Part A discusses whether the present value of these earnings should be reduced by the income taxes that the victim would have paid. Part B raises the question of whether the present value of lost earnings should be increased to allow for the taxability of income to be earned on the damage award and whether courts should ignore both adjustments on the grounds that they are offsetting.
A. Subtraction of Income Taxes from Forecasted Earnings
One reason for using pre-tax as opposed to post-tax earnings as the basis for lump sum present values is that, given the unpredictability of changes in the Internal Revenue Code, future tax liability is speculative. [FN35] It has also been suggested that injection of an abstruse issue like income taxes would unduly complicate trials. [FN36] The plaintiff's tax liability, it is sometimes asserted, is an issue between him and his government (i.e., if the government chooses not to tax damage awards, the victim and not the tortfeasor should reap the benefits). [FN37] Using pre-tax income would assign to the injured party the gains attributable to the government's decision not to tax damage awards. [FN38] Finally, the choice of pre-tax income is sometimes justified by analogy to the common law "collateral benefits" doctrine, which declares that compensation from a source wholly independent of the tortfeasor should not reduce damages payable. [FN39]
*336 The contention that taxes are too conjectural to be used in determining the quantum of tort awards has been repudiated, in part because the actual burden of individual income taxes has been remarkably stable. [FN40] To paraphrase Benjamin Franklin, the only rate certain to be incorrect is a rate of zero--the implicit assumption when taxes are ignored. The "undue complexity" argument has also been rejected. The Supreme Court in 1980 held, in the context of the Federal Employers' Liability Act, that juries should reduce damage awards for income taxes the decedent would have paid notwithstanding the complexity of the issue. [FN41] Decisions under state tort law are largely similar. A New Jersey court, for example, has declared that the projection of tax liability is no more complex than many of the other factors associated with damages for future losses (e.g., interest rates, inflation and forecasted earnings). [FN42]
The counter-arguments to our collateral benefits doctrine analogy are fourfold:
. First, this doctrine condones multiple recovery and violates a principal objective of tort law which is to place the victim in as favorable of a position as he would have been absent the injury, but no more favorable. [FN43]
*337 . Second, with respect to the wrongdoer, pre-tax income recovery transforms the tort system's compensatory nature creating, in effect, a punitive regime.
. Third, liability in excess of compensatory amounts will, by encouraging over-deterrence, be economically inefficient.
. Fourth, it is possible that the law establishing non-taxability of damage awards was enacted specifically to avoid double taxation. In other words, legislators may have expected the courts to use after-tax earnings rather than pre-tax earnings.
B. Adjustment for the Taxability of Income on the Award
Even though the original award is not taxable, the periodic interest income is fully taxable. Is it therefore necessary to increase the size of the damage award to cover the taxes payable on the investment income? The Ninth Circuit decision, Hollinger v. United States, gave an affirmative answer to this question. [FN44] The court opined that the principal amount required to yield a specified after-tax income would have to be increased in proportion to the recipient's tax bracket. [FN45] Thus, an award of $600,000 would be increased to $1,000,000 if the plaintiff was subject to a 40% marginal tax rate. The formula suggested by the Hollinger analysis is: N = O / (1 - .01 x T); where N is the new award, O is the original award (based upon after-tax earnings discounted at a pre-tax rate), and T is the percent tax bracket.
This is one of three possible ways to adjust for taxation. A second approach would be to discount after-tax earnings at an after-tax rate (the lower rate would produce a higher present value). And a third technique would discount pre-tax earnings at a pre-tax rate (the overstatement of the award from using pre-tax earnings would, it is alleged, counterbalance the understatement from using a higher, pre-tax discount rate).
*338 To compare the three alternatives, consider lost gross income of $20,000 per year for ten years, with a pre-tax discount rate of 10% and an assumed average tax bracket of 20%. [FN46]
. Method #1: After-tax earnings are $16,000 per year. The present value of $16,000 per year for ten years at the pre-tax 10% discount rate is $98,313. Applying the above formula [N = 98,313 / (1 - .01 x 20)] generates an adjusted present value of $122,891.
. Method #2: After-tax earnings are $16,000 per year. The after-tax discount rate is 8%. The present value of $16,000 per year for ten years is $107,361.
. Method #3: Pre-tax earnings are $20,000 per year. The pre-tax discount rate is 10%. The present value of $20,000 per year for ten years is $122,891.
Method #1, suggested in Hollinger, produces the same answer as Method #3. [FN47] The choices, therefore, reduce to discounting after-tax earnings at an after-tax rate (Method #2), or discounting pre-tax earnings at a pre-tax rate (Method #3). Here is how Method #2 would fund annual after-tax earnings of $16,000: [FN48]
Beginning 10% 20% Ending
Year Balance Interest Taxes Withdrawal Balance
---- --------- -------- ----- ---------- -------
1 107,361 10,736 2,147 16,000 99,950
2 99,950 9,995 1,999 16,000 91,946
3 91,946 9,195 1,839 16,000 83,302
4 83,302 8,330 1,666 16,000 73,966
5 73,966 7,397 1,479 16,000 63,883
6 63,883 6,388 1,278 16,000 52,994
7 52,994 5,299 1,060 16,000 41,234
8 41,234 4,123 825 16,000 28,532
9 28,532 2,853 571 16,000 14,815
10 14,815 1,481 296 16,000 0
*339And here is a similar tabulation of results for Method #3: [FN49]
Beginning 10% 20% Ending
Year Balance Interest Taxes Withdrawal Balance
---- --------- -------- ----- ---------- -------
1 122,891 12,289 2,458 16,000 116,723
2 116,723 11,672 2,334 16,000 110,060
3 110,060 11,006 2,201 16,000 102,865
4 102,865 10,287 2,057 16,000 95,095
5 95,095 9,509 1,902 16,000 86,702
6 86,702 8,670 1,734 16,000 77,638
7 77,638 7,764 1,553 16,000 67,849
8 67,849 6,785 1,357 16,000 57,277
9 57,277 5,728 1,146 16,000 45,859
10 45,859 4,586 917 16,000 33,528
The remaining balance from Method #3 is a windfall for the plaintiff. Using pre-tax earnings and a pre-tax discount rate, the award ($122,891) is nearly 15% higher than the correct amount ($107,361) based upon after-tax earnings and an after-tax rate. The windfall exists because the overestimate from ignoring taxes on the annual payments is not offset by the under-estimate from ignoring taxes in the discount rate. In neither case does the fund generate sufficient earnings to pay taxes and still match the employee's after- tax income. Therefore, the $16,000 withdrawals must be financed in part by a non-taxable removal of principal. When pre-tax earnings are discounted at a pre-tax rate, the allowance for taxes is too high, and the initial funding is thus larger than needed. [FN50] In sum, Hollinger is correct in principle but incorrect as to technique. [FN51]
If growth in annual wages is assumed along with a lengthy payment period, damage awards based on pre-tax earnings and pre-tax discount rates could be too low rather than too high. [FN52] The combination of growing wages and a long payment period would produce a fund with a present value that is larger than needed to generate the after-tax wages required in the early years. Interest on the fund, less taxes, would initially exceed the employee's after-tax income. The excess interest would be reinvested, but net of the taxes that must be paid when the interest is first earned. The fund will thus incur a higher tax burden than the plaintiff would have incurred as wage-earner. *340 During the later years, the situation reverses. The fund is unable to match the growth in wages from interest alone, and the tax burden recedes as principal is withdrawn. However, tax savings in later years are less than the higher burden in early years. The resultant increase in the overall tax burden requires a larger initial fund value. Under these circumstances, it is the defendant, not the plaintiff, who reaps a windfall from pre-tax earnings and pre-tax discount rates. [FN53] In either event, the use of pre-tax earnings and pre-tax discount rates yields inappropriate results. After-tax earnings and after-tax rates should be used in all cases when determining damages for lost future earnings.
It may be worthwhile at this point to counter the view that the non-taxable nature of personal injury awards constitutes a gratuity bestowed by the I.R.S. on tort victims. [FN54] In our view, a misconception of income tax, or of personal damage awards, or of both, underlies this notion. Income tax is not a tax on one's wealth or capital, but on the income produced by wealth or capital. Just as one's arm is not taxed (but only the income produced by that arm), similarly when one's arm is tortiously destroyed, the capitalized value of the limb (inter alia, the present value of the future potential income derivable from it) is non-taxable. As far as present value of future lost income is concerned, income tax would seem totally inappropriate. [FN55]
One further complication bears mentioning. The illustrations above assume that tax rates on the fund's interest income would equal the tax rate on the victim's annual earnings. In fact, because the fund will be quite large in the early years, interest income will be substantial, possibly forcing the taxpayer into a higher marginal bracket. [FN56] The transformation of pre-tax rates into after-tax equivalents should be based upon the weighted average tax bracket of the resultant fund, where the weights are the present values of the tax payments. [FN57]
*341 V. IMPLICATIONS OF INFLATION ON AWARDS FOR LOST FUTURE EARNINGS
The traditional calculation of lost future earnings disregarded inflation, chiefly because its estimation was considered to be too speculative. [FN58] Recently the traditional approach was jettisoned in recognition of inflation's increasing importance. [FN59] In the key case of Jones & Laughlin Steel Corp. v. Pfeifer, the United States Supreme Court discussed the advisability of imposing an exclusive federal rule establishing a method for calculating awards for lost future earnings in an inflationary economy. [FN60] Three approaches were evaluated in Pfeifer. [FN61] Each one is reevaluated in Section A below. A fourth method, using a differential discount rate, is analyzed in Section B.
A. Three Modern Approaches [FN62]
The three modern approaches used to calculate awards for lost future earnings in an inflationary economy are the "inflate-discount" method, the "real interest rate" method, and the "total offset" method. The "inflate-discount" method has two steps. First, future earnings are estimated based upon inflation expectations plus any demonstrable effects of experience and education, and anticipated increases in productivity. [FN63] This amount is then discounted to present value by an appropriate risk-free interest rate. [FN64] In Pfeifer, the Supreme Court discouraged the inflate-discount method, contending that projections of inflation rates are "too unreliable to be useful in many cases." [FN65] However, while it is true that there is no consensus in the *342 financial community respecting the estimation of future inflation, there are a number of models that have attained wide acceptance. [FN66]
A second method of incorporating inflation is to discount by a "real interest rate." [FN67] The conceptual underpinning for this approach is that the risk- free rate of interest can be divided into two components: anticipated inflation and the real return that an investor would demand in an inflation-free economy. Real rates are assumed to remain relatively constant between one and three percent. [FN68] Accordingly, any shift in risk-free rates must be traceable to changes in inflationary expectations. In Feldman v. Allegheny Airlines, Inc., for example, the Second Circuit reduced the risk-free rate of 4.14% by the 2.87% annual change in the Consumer Price Index over the prior 18 years. [FN69] The difference of 1.27% was then rounded off to a real interest rate of 1.5%. [FN70]
Mathematically, the use of a geometrically netted real interest rate is *343 equivalent to accelerating by an inflation rate and then discounting by a risk-free rate. [FN71] But the Feldman method is not without problems. First, in order to avoid speculative forecasts, Feldman makes the dubious assumption that future rates of inflation will replicate historical rates over an 18-year period. [FN72] Second, the real interest rate approach implicitly accelerates the victim's earnings by an inflation factor but does not allow for any modification due to productivity increases. [FN73] Third, the 1-to-3 percent recommended range for the real rate is based upon the difference between pre-tax risk-free returns and expected inflation. The pre-tax return on long-term government bonds over the past 67 years (1926 through 1992) has been 4.9% per annum, and inflation for this period averaged 3.1%. [FN74] Historically, the 1.8 point differential fell within the 1-to-3 percent range. But, as discussed in Part IV.A., it is the after-tax (not pre-tax) return which must be utilized. At any tax bracket above roughly 16%, the difference between after-tax risk-free returns and inflation lies below the suggested range. [FN75]
The Supreme Court in Pfeifer was critical of the real interest rate approach, primarily because it felt that real rates would not be stable over time. [FN76] Nonetheless, the Court indicated that lower courts adopting that approach would not be reversed if they used a 1-to-3 percent net rate and gave reasons for their choice. [FN77] Expressing its preference for a third approach, however, the Court encouraged application of the "total offset" method. [FN78] Total offset assumes the factors that would ordinarily operate to increase the victim's future earnings (e.g., inflation and productivity) are neutralized by the discounting process. [FN79] In other words, growth rates equal discount rates. Thus, the present value of an earnings stream can be determined simply by *344 summing the annual wage estimates (appropriately adjusted for mortality, morbidity, unemployment, and taxes).
Total offset was first employed by the Supreme Court of Alaska. [FN80] After a 13-year hiatus, the Supreme Court of Pennsylvania followed suit. [FN81] But whereas the Alaska court adopted a complete offset between inflation and productivity on the one hand, and the discount rate on the other, [FN82] Pennsylvania offset only the inflation component of wage growth. [FN83] It explicitly allowed for merit increases based upon the plaintiff's skill, experience and special value to her employer. [FN84] Consequently, the Pennsylvania case stands for the proposition that the victim can separately prove wage growth -- but only from sources other than inflation. Pennsylvania's offset approach is superficially similar to the use of "real interest rates," but with significantly different end results. [FN85]
The manifest advantage of the total offset method is that it eliminates the cost of predicting inflation and interest rates (and, in Alaska, productivity). This is why the Supreme Court favors total offset. Although resisting the temptation to impose one exclusive rule, the Court concluded that the total offset method was the most promising alternative. [FN86] One overriding concern dissuaded the Court from mandating the total offset approach: there was insufficient "data to judge how closely the national patterns of wage growth are likely to reflect the patterns within any given industry." [FN87] Even if wage growth and inflation were roughly equal for the nation as a whole, they might be vastly different for certain industries.
In view of the complexity of forecasting inflation, productivity, and interest rates, the Court's emphasis on efficient use of judicial resources is not *345 surprising. Nonetheless, it is puzzling that the Court would rely upon an undocumented equality between risk-free discount rates and the expected annual percentage growth rate in wages. In fact, the Court did not even express a preference that after-tax rates should be used in establishing this equality, nor that productivity changes should be included as a factor in projecting earnings. Surely, the accuracy of total offset rests on answers to these questions. Indeed, the value of total offset hinges on an additional question the Court did not raise, the stability over time and across industry groups and occupations of the alleged offset. This issue is discussed in the next section.
B. The Differential Discount Rate Approach
One method of determining the accuracy of total offset is to determine the correct differential discount rate using real-world empirical data. The differential discount is the geometric [FN88] spread between the after-tax risk-free interest rate and the rate at which wages in various industries and occupations actually grow. Thanks to two extensive studies, there is good evidence of the magnitude and stability of the differential.
In the earlier of the studies, two professors of finance, Anderson and Roberts, found that interest rates and growth rates in earnings varied in tandem over time. [FN89] The relative difference between the two appeared stable. [FN90] Furthermore, preliminary evidence suggested that average earning growth rates for different occupations were comparable over long periods. [FN91] By implication, changing economic conditions would have little impact on correct damage awards; it would not be necessary to forecast either interest rates or earnings growth rates, even though both may vary significantly with inflation and real GNP. [FN92]
In a subsequent study, Anderson and Roberts used historical data on annual earnings for 454 occupations, risk-free yields on 1-year United States Treasury notes, and average effective tax rates for 32 classifications by income over the thirty-year period 1952-1982. [FN93] They computed after-tax *346 differential discount rates for each occupation and for various periods of lost earnings. [FN94] The authors made the following assumptions: (1) the "correct" award replicates after-tax lost earnings; (2) the victim cannot work in any capacity; and (3) the victim's lost earnings equal those of the average worker in his occupation. [FN95] They found that the after-tax differential discount rate should be between 0% and -1%, a rate that is stable over time and across occupations. [FN96] Anderson and Roberts concluded that the Supreme Court should adopt a benchmark rate of -0.5%, with deviations permitted if any of the following conditions are met: (1) there is expected future variance from historical earnings growth rates; (2) the victim will suffer a short disability period during which wage contracts or unusual government monetary or fiscal policies are thought to influence interest rates and earnings growth; or (3) the victim's pre-injury earnings were atypical or were expected to progress differently than those of the average worker in her field. [FN97]
Anderson and Roberts' studies are provocative and valuable as a template for further research. But they err in two ways. A minor error is their use of 1-year Treasury notes rather than multiple instruments with durations that match the period between date of injury and date of receipt of lost earnings. By adopting a roll-over strategy in which the plaintiff reinvests annually in 1-year notes, [FN98] the authors expose the plaintiff to substantial reinvestment risk. [FN99] Their technique does reduce the volatility of the plaintiff's portfolio, [FN100] but *347 that advantage is of little value given the fixed dates and amounts of assumed withdrawals from the fund. As long as income and principal from the fund are adequate to pay for lost earnings, interim variations in portfolio value are inconsequential. The 1-year roll-over strategy assumed by Anderson and Roberts probably understated their discount rate by about 0.6 percentage points. [FN101]
The more significant omission in Anderson and Roberts' analysis is their failure to adjust lost earnings for mortality, morbidity, and unemployment risks. Each of these issues will be examined more fully in Part VII. However, two points can be made immediately:
. Mortality and morbidity rates will increase as the period of lost earnings lengthens. To illustrate, a 20-year old male has a 25% chance of dying before he reaches age 65, whereas a 60-year old male has a 9% chance of dying within five years. [FN102] Obviously, net discount rates for 45-year loss periods must be greater than for 5-year loss periods. [FN103] Growth rates in wages (one component of the net rate) will decline in proportion to the increase over time in mortality and morbidity risk.
. Unemployment rates as well as mortality and morbidity vary by occupation and by health. Discount rates for high-risk occupations and for healthy plaintiffs must be different than for low-risk occupations and unhealthy workers. It is conceivable that Anderson and Roberts would reach the same end-result if they re-computed empirically correct awards, then applied their differential discount rate to a variable stream of earnings derived from after-tax income for the year of injury, adjusted for annual mortality, morbidity and unemployment. Until it can be shown that their studies have taken account of these effects, their recommendation of a fixed -0.5% differential discount rate is not persuasive.
*348 VI. RISK-ADJUSTMENT VIA THE CAPITAL ASSET PRICING MODEL
Judge Posner has commented that "when it comes to figuring out the lump sum that will compensate a tort victim for lost future earnings, [t]he tendency is to use a riskless interest rate in discounting [to] ... present value, and this is incorrect." [FN104] Posner observed that the stream of earnings designed to be discounted was not a guaranteed amount. [FN105] Even if mortality, morbidity, and unemployment risks are properly treated, the risk averse plaintiff will still prefer a sum certain to its probabilistic counterpart. [FN106]
The required risk-adjustment is for an element of economic risk that is not incorporated in the wage structure. Workers demand a higher salary to compensate for the risk of physical injury, but this premium is already reflected in the wages used in estimating lost future earnings. [FN107] Some other economic risks (e.g., the expected net losses from unemployment) are also built into the wage structure. But the risk averse truck driver who receives a salary of $20,000 with an anticipated layoff rate of 10% is less certain of his outcome than a civil servant guaranteed to earn $18,000--even though both parties have the same expected income. When courts convert the injured truck driver's probabilistic outcome into the civil servant's sum certain, they are over-compensating. That is the element of economic risk that the courts are missing. [FN108]
How significant is this over-compensation? One way of quantifying it would be to ask workers how much they would pay for greater certainty of income. [FN109] Another approach, explored in this section, is to measure the dispersion of possible outcomes (e.g., for the truck driver, 90 chances of $20,000 plus 10 chances of zero), then compare this against a similarly computed measure of dispersion for a capital asset that has a computable discount rate (e.g., common stocks). With the assistance of the Capital Asset Pricing Model ("CAPM"), we can then determine a risk-adjusted discount rate for the worker's earnings stream. [FN110]
*349 A. Risk Measurement and CAPM [FN111]
Risk may be defined in terms of uncertainty of outcomes. Variability is one form of uncertainty. Empirical evidence indicates that investors demand and receive greater returns when variability is high, thus suggesting that variability and risk are at least related, if not synonymous. [FN112] Perhaps the most widely used measure of variability is the standard deviation, which reflects the dispersion of the possible outcomes around their average. [FN113]
But standard deviation measures only the variability of an individual asset, in disregard of its interaction with other assets that might be held within a portfolio. To see this, consider the risk of two assets whose returns vary inversely. By owning both, the investor can stabilize his or her rate of return. Multiple assets, each of which may be risky in isolation, can be combined to form a lower risk portfolio. When multiple assets are owned, the standard deviation is overbroad as a risk measure for each asset--it includes risk that could be eliminated by diversification.
There are thus two perspectives regarding the riskiness of an asset. The broader perspective is variability of expected returns assuming the asset is the only one held. A narrower view is the extent to which the asset's returns contribute to the variability of a portfolio of diversified holdings. The broader measure can be reduced or even eliminated by further diversification. The narrower measure already assumes a diversified portfolio.
CAPM provides a framework to separate the portion of risk that is "systematic" and cannot be eliminated by diversification, from the portion that is "unique" and thus diversifiable. [FN114] The "beta" coefficient measures *350 systematic risk by expressing the covariation between an individual asset and the overall market. [FN115] According to CAPM, investors are not automatically compensated for incurring unnecessary risk. [FN116] Only non- diversifiable "beta" risk will be compensated. [FN117]
The underlying assumptions of CAPM are self-evidently unrealistic, [FN118] and some critics maintain that CAPM is not a good predictor--i.e., that rates of return are not a linear function of beta coefficients. [FN119] Richard Roll, in a widely-quoted 1977 article, contended that the proper computation of beta is hampered by the unavailability of a fully diversified market index. [FN120] Even CAPM's proponents admit to the unrealistic nature of its assumptions, but counter that the model sheds light on how the real world operates, and provides a structure within which assumptions can be altered as necessary. [FN121]
The criticisms pertaining to the validity of beta as a risk measure are not easily dismissed. However, in the context of this article, these criticisms are irrelevant. As we shall see in the next section, CAPM is adopted for its structure and rationale -- but without using betas as a measure of risk. Moreover, the ostensible shortcomings of CAPM have not diminished its *351 durability as an important tool of investment analysis and corporate finance. "'CAPM combines so many strands of theoretical innovation that it remains the keystone of investment theory, theories of market behavior and the allocation of capital in both private and public enterprises."' [FN122]
B. Employment Risk Versus Common Stocks
We wish to apply CAPM to answer the question: How much of a premium should be added to the risk-free discount rate in order to avoid over-compensating when probabilistic outcomes are converted into certainty equivalents?
Appendix A, Employment Risk Versus Common Stocks, and its accompanying notes illustrate the CAPM approach to risk-adjustment. First, various probabilities of employment are hypothesized, ranging from .995 to .050. These probabilities imply aggregate risks of death, disability and unemployment from 0.5% to 95%, respectively. Second, the standard deviation of each probability distribution is computed, [FN123] then transformed into the coefficient of variation -- a normalized measure of dispersion. [FN124] Third, the coefficient of variation for the Standard & Poor 500-Stock Index is displayed. [FN125] Fourth, the ratio of the two coefficients is calculated. This ratio represents the relative riskiness of employment compared to common stocks. Finally, relative risk is used in lieu of the beta coefficient in the CAPM formula [FN126] to determine the pre-tax risk premium. [FN127]
*352 The result, displayed at Appendix A, is a premium as small as 0.2% when the probability of employment is .995, but as large as 14.4% when the probability of employment drops to .05. Given reasonable risks of death, disability and unemployment ranging from, say, .5% to 50%, the corresponding pre-tax risk premiums would be .2% to 3.3% respectively. At a 30% tax bracket, the after-tax premiums would be .1% and 2.3%. To illustrate the impact of a 2.3% risk premium, [FN128] assume a 4% after-tax risk-free discount rate and annual earnings of $30,000. The comparable present values for loss periods ranging from 5 to 40 years would be:
Loss Period in Years 4.0% Rate 6.3% Rate % Reduction
-------------------- --------- --------- -----------
5 133,555 125,346 6.1
10 243,327 217,698 10.5
20 407,710 335,872 17.6
40 593,783 434,843 26.8
Two major objections remain to the use of CAPM for purposes of developing the employment risk premium. First, employment probabilities are not normally distributed. It has been argued that the standard deviation is an unsatisfactory measure of dispersion for non-normal distributions. [FN129] Second, the substitution in the CAPM formula of the relative coefficient of variation in lieu of the beta coefficient is justified only if employment risk is non-diversifiable. [FN130] On the one hand, wage variation induced by mortality *353 and morbidity is uncorrelated with the returns on capital assets. Theoretically, this variation can be eliminated by diversifying. On the other hand, as a practical matter, a large portion of a typical worker's wealth is attributable to his wage-earning capacity. It would be rare for a typical worker to own a portfolio sufficiently large to permit meaningful diversification against wage variation.
The latter view was adopted by Judge Posner. "'Human capital' [here meaning earning capacity] is not diversifiable -- you cannot hold a diversified portfolio of jobs." [FN131] But this overlooks the ability of workers to form associations. When multiple workers pool their risks, ex post death and disability outcomes are likely to be offsetting, thus stabilizing aggregate earnings. With insurance companies as intermediaries, the prospect of pooled risk has become an everyday reality. By purchasing term insurance, workers can "diversify" against death and disability. Of course, diversification is not free; insurance premiums will exceed expected benefits. The relationship of premiums to benefits--the loading factor--is the foundation for our new look at risk-adjustment.
VII. RISK-ADJUSTMENT VIA HYPOTHETICAL INSURANCE LOADING
The pricing of single-premium term insurance follows several steps. [FN132] First, the expected benefit payment is estimated. Let us assume that a worker wishes to insure his wages in the year 2003 against the possibility of his death between the date of the policy (December 31, 1993) and December 31, 2003. [FN133] His forecasted after-tax wages in 1993 are $50,000. To simplify calculations, assume that he is paid annually on the last day of the year, and if he dies in the interim, his estate will not be paid until December 31, 2003. He is 35 years old on the policy date. Mortality tables indicate that his cumulative chance of dying over the succeeding ten years is .02965. [FN134] The insurance company's expected payout is $1,483 (i.e., .02965 x $50,000).
This expected payout must be discounted to December 31, 1993, the date on which the premium is to be paid. The appropriate discount rate will be roughly the weighted average return on the insurance company's invested *354 assets. [FN135] At an 8.5% discount rate, the present value of $1,483 for ten years is $656. [FN136] This is the net premium--it covers the expected mortality risk to be incurred by the insurance company, but does not include an allowance for expenses or profits.
The gross premium paid by the policy holder is equal to the net premium plus a loading factor to cover expenses and profits. Some expenses (e.g., administrative) are basically fixed per policy; some vary with the principal amount of insurance ($50,000 in our example); and some vary with the net premium ($656). Since net premiums are higher for older and unhealthy policy holders, and even for policy holders with risky vocations or avocations, the loading factor could vary by age, health, job, and lifestyle, as well as by the amount of insurance. These factors will be discussed in Part VII.C. For purposes of our illustration, assume a load factor of 25% of the gross premium. [FN137] Dividing the net premium by .75 produces a gross premium of $875. This is the price on December 31, 1993 of a $50,000 ten-year policy, payable on December 31, 2003 if death should occur anytime prior to that date.
With this brief background, we consider the pros and cons of a new solution to the risk-adjustment problem. We then examine the potential impact of this solution on damage awards, as well as its practicality.
A. Basing Risk-Adjustment on the Loading Factor
A court in the above example would calculate damages for the year 2003 of $48,517 (i.e., $50,000 forecasted after-tax wages times .97035 probability that the employee would still have been working on December 31, 2003). [FN138] Analytically, the court would be proceeding in two steps. First, it is offering a probabilistic payoff on December 31, 2003 of .97035 chance of $50,000 *355 plus .02965 chance of zero--precisely what the worker faced ex ante on December 31, 1993. Second, the court is removing any uncertainty in the outcome by converting the probabilistic recovery into a fixed sum of $48,517. This can be viewed as requiring the defendant to have provided life insurance to the plaintiff. For a "premium" of $1,483 (i.e., 50,000 - 48,517), to be paid on December 31, 2003, the defendant "issued" a policy to the plaintiff with a $50,000 non-taxable death benefit. If the insured is still working on December 31, 2003, he receives an expected wage of $50,000 less an insurance premium of $1,483. If he dies, his estate collects a death benefit of $50,000 less the premium of $1,483. [FN139] Either way, the insured recovers $48,517.
It is crucial to note that this hypothetical insurance policy is bargain- priced, as the premium of $1,483 (in year 2003 dollars) is exactly equal to the expected benefit payment (.02965 x $50,000). No loading factor is added to the net premium. Yet full compensation to the victim called only for part one of the bifurcated award--the probabilistic outcome. The receipt of a sum certain, effectuated through the insurance "policy," is a bonus--at least to the extent that the policy is priced below market.
In order to prevent over-compensation, the award must therefore be reduced by the plaintiff's savings on the bargain insurance. That reduction, again in year 2003 dollars, is the difference between the net premium and the gross premium, inclusive of the loading factor, that the insured would have paid in a competitive market. Assuming a 25% loading factor, the gross premium would have been $1,483 / .75, or $1,977; the savings is thus $494. Instead of $48,517 for year 2003, the court should have awarded $48,023--the certainty equivalent that the plaintiff could rightly expect in return for a .97035 probability of $50,000.
The difference of $494 (even less when discounted to December 31, 1993, the date of the award) seems inconsequential. But several factors could increase its importance. First, the year 2003 was one year from among all the years until the victim's anticipated retirement from work. A similar analysis for each of the other years is in order. If, for example, the victim was expected to work from age 35 through age 65, 30 hypothetical insurance policies would have to be diagnosed. The aggregate dollar effect could be substantial. Over time, the cumulative dollar effect of the hypothetical insurance policies will change both absolutely and as a percentage of the damage award. [FN140] Second, only mortality risk was considered here; morbidity *356 and unemployment risks were not examined. Third, the selected year was 10 years from the accident date--since mortality and morbidity risks increase rapidly with advancing age, later years would produce larger disparities. Fourth, standard mortality rates were assumed. However, both life and disability policies are sometimes issued using sub-standard risk ratings. The mortality and morbidity factors can be much higher on sub-standard policies, [FN141] with a substantial effect on premiums and loading factors.
B. The Percentage Impact of Loading Factors and Loss Periods
The percentage reduction of the damage award in our example was 494 / 48,517, or 1.018%. [FN142] As the loading factors increase, the percentage reduction increases. The same relationship applies as the mortality, morbidity, and unemployment factors increase. Since wages are likely to be growing, awards in the later years will be higher, and larger percentage reductions will have an even greater dollar impact. However, the present value of the dollar impact might not grow, depending in part on whether the rate of acceleration in forecasted wages exceeds the after-tax risk-free discount rate.
In short, there are many permutations and combinations that will have differing effects on the size of awards. Appendix B, Illustrative Adjustment for Certainty Equivalents, is an attempt to better understand the interaction of the various factors:
. The victim is assumed to have died at age 20 when earning $20,000 annually after taxes. He was expected to work until age 65. Wage growth is estimated at 6% per annum. The after-tax risk-free discount rate is set at 5%; [FN143] and the assumed loading factor on the hypothetical insurance policy is 25% of the gross premium.
. The column labeled EMPLOY. PROBAB. is the product of three factors. First, the cumulative probability of death at each age is *357 determined from standard mortality tables for male lives. [FN144] Second, the cumulative probability of disability at each age is determined from standard morbidity tables for male lives. [FN145] Third, the prospective unemployment rate is assumed to be 6.4%. [FN146] These three factors are multiplied together to ascertain the employment probability (i.e., the chance that the worker will still be working in the identified year). [FN147]
. Year-by-year damage awards are the product of forecasted wages times the probability of employment, discounted to present value at the after-tax risk-free rate. The total of present values for the 45-year loss period in Appendix B is $893,000, which represents the court's award before adjustment for certainty equivalence.
. The initial step in making the adjustment is to calculate an equivalent employment probability. The formula is straightforward: (E - L) / (1 - L); [FN148] where E is the original employment probability and L is the loading factor in decimal form. The entire adjustment for certainty equivalence can be accomplished by reducing the original employment probability--using this formula to incorporate the loading factor. Once the revised employment probability is determined, the remaining calculations are *358 exactly the same as they would have been without an adjustment. The equivalent damage award is equal to forecasted future after-tax wages times the revised employment probability, and the discounting process is identical.
After adjustment for certainty equivalents, the total damage award in Appendix B is $814,754. This represents an 8.8% decrease from $893,000. If each year's damage award as originally computed were discounted to equal the lower $814,754 present value, the discount rate would be 5.4%. In other words, the risk premium would be 0.4 percentage points above the 5.0% after-tax risk-free rate. The size of the risk premium as well as the size of the reduction in damages is of course sensitive to both the loading factor and the length of the loss period.
Appendix C, Effect of Certainty Equivalents Adjustments, investigates the extent of this sensitivity. Wage growth is again estimated at 6% per annum; the after-tax risk-free discount rate is set at 5%; and the retirement age is 65. But the loading factor, instead of being fixed at 25%, is varied from 5% to 50% in 5 percentage point increments. And the age of death, instead of being fixed at 20, is varied from 20 to 60 in 5-year increments. The upper half of Appendix C tabulates the percentage reduction in awards. These range from a trivial 1.4% (death at age 20, loading factor of 5%) to a massive 50.7% (death at age 60, loading factor of 50%). A similar pattern emerges in the bottom half of Appendix C where after-tax risk-adjusted discount rates are recorded. They range from 5.1% to 36.9%, equivalent to risk premiums of 0.1 to 31.9 percentage points. [FN149]
Which load factor is "correct"? What is the impact on the load factor when higher mortality and morbidity rates are applied to policy holders with sub- standard risk profiles? Is it even possible to make these determinations without unduly burdening litigants and the courts? The next section addresses these questions.
C. Determining the "Correct" Loading Factor
The determination of an appropriate loading factor presents two problems, *359 one large and one small. We are interested in a series of year-by-year single-premium term insurance policies payable on termination if death should occur anytime within the coverage period. The premiums are not due until the policies expire. The small problem is that such policies do not exist. But reasonably close substitutes are available. The scheduling of the payment of both premiums and benefits involves the time value of money, which should not materially affect the loading percentage needed to cover expenses and profits. Expenses (e.g., sales fees over the life of the policy) typically vary with the size of the policy or the amount of the premium, not with the timing of receipts and payments. For an approximate answer, we should be able to reference the loading factors used to price term insurance policies that are actually marketed.
The second problem is more formidable. Loading factors, if fully disclosed, might provide information to competitors about an insurance company's mortality experience, profit margin, or expense structure. Such proprietary information could compromise the confidential process of insurance products. As a result, there are no published sources, nor are insurance executives willing to provide internal data or to be quoted. Consequently, we have relied primarily on anonymous sources, confirmed only by aggregate industry data on insurance company expenses, profits and premiums. We have concluded that an appropriate loading factor for standard-rated [FN150] single- premium term insurance should be about 25%. Estimates range as low as 20% and as high as 50%, with a convergence near 25%. This is not out of line with a claim by one commentator that the loading factor for workers' compensation insurance is 20%. [FN151] Very rough confirmation is also available from aggregate data for United States life insurance companies. In 1991, for example, operating expenses plus taxes and dividends totaled 23% of gross premiums. [FN152] This composite percentage is based upon an amalgam of companies providing ordinary and term life, group health and credit insurance, and annuities. [FN153] It varies widely among *360 companies, depending on type of coverage offered and the ratio of newly issued insurance to total insurance in force. [FN154]
Even if a 25% loading factor is correct on average, it will err in specific cases. Loading factors may vary based in part on the face amount of the policy. Some portion of the loading factor covers relatively fixed administrative costs and policy expenses. Of course, as the policy increases in size, the impact of fixed expenses becomes less significant. [FN155] More troublesome is the non- linearity that necessarily exists between loading factors and the amount of the premiums paid. [FN156] Policy applicants with a high risk profile (usually attributable to health or job or avocation) will pay significantly higher premiums to reflect their significantly higher mortality and morbidity risks. Here too, the pricing data are proprietary. Many companies maintain mortality tables for sub-standard applicants, but their tables are not available for public inspection. [FN157]
*361 Research produced the following information: (1) Preferred (i.e., low-risk) ratings can result in term insurance premiums as low as 60-70% of standard; (2) At least one major company maintains mortality tables reflecting risks 2000% of standard; (3) Many companies write term insurance using risk factors that are 500-800% of standard; and (4) A principal with a large consulting actuary volunteered that a 25% loading factor applied to a standard- rated policy might be reduced to as low as 10-15% on policies written at 500% of standard. [FN158]
In view of the confidential nature of the data, the absence of published information, and the non-linearity of the loading factors, it is unlikely that guidelines with broad legal applicability can be established. Nonetheless, there are grounds for believing that ad hoc adjudication will not impose unreasonable burdens upon litigants or courts. First, the impact of sub- standard risks on loading factors may be of major importance when it occurs, but it will occur infrequently. Only 5% of life insurance applications are rated for extra-risk, and only 3% of applicants are rejected. [FN159] Standard (or better) risk ratings apply to the remaining 92% of all applicants. [FN160] Second, expert witnesses should be able to fill in gaps between narrow boundaries dictated by known industry practices. While actuaries and insurance executives may be reluctant to talk to authors of law review articles, their reticence may diminish in proportion to consulting fees proffered--especially when asked to estimate a loading factor for a hypothetical policy that cannot pose a competitive threat.
D. Food for Thought
This final section sets forth five issues directly or peripherally related to risk-adjustment via hypothetical insurance loading. Each of the issues opens up significant opportunities for future excursions into tort theory. None of them can be adequately addressed in the limited space available.
First, insurance policies are priced to incorporate adverse selection and moral hazard. But in tort cases, the hypothetically insured party is already dead or disabled. Why should the tortfeasor get the benefit of reducing his payout by an insurance loading factor when the victim's risks are based upon *362 mortality and morbidity rates that reflect non-existent or de minimis adverse selection and moral hazard? One possible solution is to use mortality and morbidity rates based upon the entire United States population, not limited to policy holders. [FN161] This approach might, however, lead to larger rather than smaller loading factors. [FN162]
Second, since the tortfeasor is the de facto insurer of the victim, and the premium is set by the court, there are no policy expenses incurred nor profits realized as a return on investment. Why then should recovery to the victim be reduced by the tortfeasor's "loading factor"? The corollary of this question is whether the tortfeasor should be obliged to subsidize his victim's acquisition of insurance at less than a competitive price. If we decide that the loading factor ought to be zero because the "insurer" has neither expenses nor capital at risk, we effectively reject the need for risk-adjustment of the damage award. At a zero loading factor, the victim pays nothing for the privilege of converting his probabilistic outcome into a certainty equivalent. Although the tortfeasor can ex post provide insurance for a price equal to the expected benefit, should he be required to do so? Does corrective justice only mandate that ex ante he competitively eliminate the victim's risk? [FN163]
Third, why force the victim to buy insurance at all, with or without a load? Since insurance premiums include expenses and profits, the premiums exceed the benefits that policy holders can rationally expect to collect. Many persons are willing to pay the competitive premium in order to avoid risk--an ultra-risk- averse party would be willing to pay more than the competitive premium, but a risk-neutral person or a risk preferrer probably [FN164] would not buy the policy.
Fourth, what about the tort victim whose dangerous hobby increases his *363 mortality and morbidity profile, exposing him to a sub-standard rating? Ratings determine premiums, which affect loading, which underlies risk- adjustment. Thus, a daredevil tort victim may be harmed more by the risk- adjustment process than his counterpart who has no adventurous hobbies. Yet, it is the cautious person to whom the insurance is a better bargain, and the daredevil whom we are coercing into purchasing a policy. Is it appropriate to force the daredevil to purchase this policy? Is it sufficient to waive this problem because of evidence that most persons are risk-averse? [FN165] Is it reasonable to invoke the enormous evidentiary burden which would be imposed on courts that are forced to deal with idiosyncratic cases of risk preference? [FN166] May one blithely respond that the daredevil may not suffer much? [FN167] Or that few people are affected anyway? [FN168]
Fifth, should the tort victim be compensated for having lost the opportunity to decide whether she is content with the "bird in the hand" that constitutes expected damages? The disabled ballplayer has lost any chance to make the Majors. An injured hand denies a young amateur pianist the option of a musical career. This capacity to self-determine goes beyond risk preference. Even risk-averse persons want to be able to elect if and when they will be risk-averse. When their autonomy is compromised, part of life's pleasures are taken. Is this deprivation worth something in itself? [FN169]
*364 Sixth, does risk-adjustment destroy the dichotomous view of probability, embedded in private adjudication, requiring proof by a "preponderance of the evidence"? Advantages of this view of probability include economy of judicial resources, lower costs for litigants, and a lesser number of legal errors (counterbalanced by legal errors of greater average magnitude). [FN170] Should this view be extended to cover damages for lost future income? [FN171] If so, this would obviate risk-adjustment entirely.
VIII. SUMMARY AND CONCLUSIONS
Recovery for lost future earnings is an essential element of tort litigation. This paper has analyzed several critical issues associated with the determination of appropriate awards for lost future income. Part III dealt with the selection of a risk-free discount rate. Part IV addressed income taxes. Part V examined the implications of inflation. The three topics serve as background for the central focus of the paper: assessing the potential for over-compensation when the court converts probabilistic outcomes into certainty equivalents. In Part VI, we approached this latter problem from a traditional risk-adjustment perspective, using the Capital Asset Pricing Model. Part VII introduced a different and new solution which avoids the pitfalls of CAPM by viewing the damage award as the linkage of probabilistic future earnings and a non-loaded term insurance contract. Here, briefly summarized, are our recommendations for each of the issues raised in the paper.
A. Selection of a Risk-Free Discount Rate
Courts have used the yield on United States Government bonds as their discount rate for reducing damage awards to present value. The term to maturity of such bonds has matched the total loss period over which future earnings are to be discounted. Two problems arise. First, it is incorrect to use a constant rate for the full period since bonds do not earn interest at a constant rate. Second, the yield to maturity on a coupon-paying government bond cannot be guaranteed in the face of fluctuating interest rates (i.e., the bond is *365 exposed to the risk of coupon reinvestment). The solution to the first problem is to revise the discount rate from year-to-year, consonant with the yield to maturity on government bonds of varying lengths. Lost future earnings assignable to the 20th year must be discounted by the rate on 20-year instruments; earnings assignable to the first year must be discounted by the rate on 1-year instruments; etc. The second problem is resolvable by immunizing against interest rate fluctuations. The easiest remedy is to use a discount rate that reflects the yield on zero-coupon bonds. Alternatively, bonds may be selected that have the same "duration" (not maturity) as the time horizon over which each year's earnings are to be discounted.
B. Income Taxes
A threshold question is whether lost future earnings should be reduced by the income taxes that the victim would have paid. Secondly, should the present value of lost earnings be increased to allow for the taxability of income to be earned on the damage award? Third, can both adjustments be ignored on the grounds that they are offsetting? We conclude that income taxes must be subtracted from projections of lost earnings, since using pre-tax income produces a larger award for the plaintiff than if he had continued to earn his taxable salary. Because subsequent earnings on damage awards will be taxable when realized, the initial fund that generates the earnings must be large enough to cover the taxes as well. This requires that an after-tax discount rate be applied to an after-tax earnings stream. When pre-tax earnings are coupled with a pre-tax discount rate, the two errors are not offsetting.
Growth in future earnings is generally projected based upon inflation expectations plus demonstrable increases in productivity. Some have argued that if both wage growth and risk-free discount rates are dependent primarily on inflation, perhaps the estimating process can be simplified. Four approaches were examined. Only the two-step "inflate-then-discount" method is supportable--notwithstanding the facts that it may be cumbersome and that the Supreme Court considers it speculative.
Three single-step methods have been proposed: (1) discounting constant earnings by a real rate; (2) summing constant earnings without discounting (i.e., assuming that wage growth and inflation will totally offset one another); and (3) discounting constant earnings by a differential rate based upon empirical data. Each of these methods has unique drawbacks. Both the real rate approach and the total offset method assume, without substantiation, that the gap between wage growth and risk-free interest rates will be constant over *366 time and across occupations. Neither method properly considers productivity nor income tax effects. The empirically-derived differential discount rate is a more promising approach. But it remains to be tested for the impact of mortality, morbidity and unemployment, which vary by age and risk profile of the plaintiff.
D. Risk-Adjustment Via the Capital Asset Pricing Model
The stream of earnings to be discounted is not a guaranteed amount. Workers sometimes become unemployed or disabled, and may even be deceased by the time the earnings would have been earned. When the court applies a risk-free discount rate, a probabilistic outcome is converted into a certainty equivalent. The risk-averse plaintiff pays nothing for this privilege. Some higher discount rate should be used to prevent over-compensation.
CAPM provides a framework by which a risk premium for uncertainty can be established. Given a combined mortality, morbidity and unemployment risk ranging from 0.5% to 50%, CAPM suggests an after-tax risk premium of 0.1% to 2.3%, respectively. If the high end of the range were to be added to a 4% risk- free rate, damage awards over five years would be reduced by roughly 6%, while awards over 40-year loss periods would be reduced by as much as 27%. There are, however, two major objections to the use of CAPM for this purpose. First, employment probabilities are not normally distributed; and CAPM risk measures may be unsatisfactory for non-normal distributions. Second, the beta coefficient, required by the CAPM formula, would be zero since wage variation is not correlated with other capital assets. Substitution of the relative coefficient of variation in lieu of beta can only be justified if employment risk cannot be eliminated by diversification. However, workers can and do diversify against death, disability, and unemployment by pooling their risks via acquisition of insurance. Therefore, use of the CAPM formula is unjustified.
E. Hypothetical Insurance Loading
If an accident victim's mortality, morbidity and unemployment risks totaled, say, 20% for a given year, then she would be entitled to an 80% chance of earning her wages as forecasted (say $100,000), plus a 20% chance of earning zero. But the court also removes any uncertainty in the outcome by requiring the tortfeasor to insure the victim. For a premium of $20,000, the tortfeasor "issues" a hypothetical policy with a $100,000 death benefit. If the insured is working in the forecast year, she receives an expected wage of $100,000 less an insurance premium of $20,000. If she is dead, disabled *367 or unemployed, she collects $100,000 from her policy less the $20,000 premium. Either way, the insured recovers $80,000.
The hypothetical insurance policy is bargain-priced because the premium of $20,000 is exactly equal to the expected benefit payment. There is no loading factor added to the net premium to cover the insurer's expenses and profits. The receipt of a sum certain, effectuated through the insurance policy, is a bonus to the extent of the loading factor that the insured would have paid in a competitive insurance market. Her savings represents over-compensation, and reduction of the damage award by the amount of the loading factor is a method of risk-adjusting the outcome.
A determination of the "correct" loading factor to apply is inhibited by the competitive sensitivity of the data. Based on numerous conversations with insurance company executives, trade association staff and consulting actuaries, we conclude that an appropriate loading factor for standard-rated single- premium term insurance should be roughly 25% -- in which case damage awards would be reduced by about 9% in the case of a tort victim with 45 working years remaining at the time of the accident. The reduction is larger as the loss period recedes. For five-year loss periods, the reduction in the award is nearly 17%.
Sub-standard risk profiles result in significantly higher premiums. While loading factors will decline in percentage terms as premiums increase, the combined effect of the two variables will cause significantly larger reductions in damage awards for all loss periods.
In view of the confidential nature of the data and the non-linearity of the loading factors, it is unlikely that broad-based guidelines can be established. Nonetheless, there are grounds for believing that case-by-case adjudication will not impose unreasonable burdens upon litigants or courts. The impact of sub-standard risks on loading factors may be of major importance when it occurs. However, it will occur only infrequently.
FNa1. Professor of Law, George Mason University. LL.M., Yale University; LL.L., Universite de Sherbrooke; B.A., Carleton University.
FNaa1. Law clerk to the Honorable Douglas H. Ginsburg, United States Court of Appeals for the District of Columbia Circuit. J.D., George Mason University, 1994; Ph.D., The American University, 1966.
FN1. Settlements are occasionally structured to spread the payment of damages over time. If the periodic payments are fixed in amount and duration, they are the functional equivalent of a lump sum, and still require a forecast of future events. Only when payments are variable -- keyed to ongoing interest rates, inflation, tax rates and continued disability -- is the forecasting problem mitigated. But variable payments increase administrative costs and produce perverse incentives to prolong under-employment. With a lump sum payment, an accident victim is motivated to overcome his disability as quickly as possible. With a variable settlement, the victim who returns to work and loses his tax- free stipend might in effect pay more than a 100% tax on earned income, while incurring working expenses such as commuting and clothing that he would otherwise have avoided. See RICHARD A. POSNER, ECONOMIC ANALYSIS OF LAW 192 § 6.11 (4th ed. 1992) (discussing damages for loss of earning capacity).
FN2. To be precise, the probability of death should be limited to non-tortious causes plus wrongful acts committed by judgment-proof parties. Otherwise, an infinite regress ensues as we attempt to deduct that portion of lost earnings that would have been recoverable from future tortfeasors. Because the adjustment is trivial, courts typically ignore this problem.
FN3. It should be noted that this reduction is allegedly not required under a view of tort that might be styled "dichotomous" or "all-or-nothing." Under this view, plaintiffs have the burden of proving their claim by a preponderance of the evidence. See, e.g., Herskovits v. Group Health Coop., 99 Wash. 2d 609, 630, 664 P.2d 474, 484-85 (1983). Once such proof is persuasively provided, their claim is proven. Thus, according to this view, negligence, causation and damages would each have to be proven by a preponderance of the evidence. For damages, a plaintiff in our example would have to establish that he probably would have earned $100,000 in 1999. If he establishes this by a preponderance of the evidence (say, a 60% likelihood), he would recover the discounted value of $100,000 as discussed below. If he fails to establish this by a preponderance of the evidence (if, say, there is only a 40% chance that he would have been employed in 1999), then he would recover nothing for that year's lost income. Some judges lean towards abandoning this dichotomous reasoning. Id. at 618-21, 664 P.2d at 478-480 (Pearson, J., concurring).
For reasons the examination of which is beyond the purview of this paper, even "traditional" courts (i.e., which adopt dichotomous reasoning to establish negligence and causation) are not likely to use dichotomous reasoning for future damages. For example, a "traditional" court rejected plaintiff's suit for injuries resulting from a negligent misdiagnosis of a bone fracture because the increased chance of permanent injury due to this misdiagnosis was less than 50%. Hotson v. East Berkshire Area Health Auth.,  A.C. 750, 757. The court reasoned as follows: "In determining what did happen in the past a court decides on the balance of probabilities. Anything that is more probable than not it treats as certain." Id. (quoting Mallett v. McMonagle,  A.C. 166, 176) (emphasis added).
Thus, in determining what will happen in the future, courts are willing to abandon dichotomous reasoning. Had the causal link between the malpractice and the disability been "treated as certain" in Hotson, damages would nonetheless have been determined probabilistically.
FN4. Risk aversion is indicated by purchase of insurance. Since insurance companies incur expenses and must earn a competitive profit, the premiums they demand typically exceed the benefits that policy holders can expect to receive. A willingness to pay the premium reflects a desire to avoid uncertainty. Further evidence of risk aversion is available from the capital markets where investors have demanded and obtained higher returns on higher risk assets such as common stocks, rather than on lower risk assets such as government bonds. The excess return is an inducement for investors to assume added risk.
FN5. A perplexing problem -- not addressed in this paper -- is how to value services in an occupation for which there is no established financial compensation. See POSNER, supra note 1, at 193. See, e.g., Cummins v. Rachner, 257 N.W.2d 808, 814-15 (Minn. 1977) (allowing the cost of replacement services to establish damages for injuries to a housewife). More generally, the perspective of the authors of this paper is that, when tort damages are payable, what is payable is all that has been lost by the wrongfully injured plaintiff. We are sensitive to the question of whether future income is the only, or best, proxy for the loss suffered by the plaintiff. Indeed, one of us is working on a draft proposing a general expansion of non-pecuniary damages in tort. See Michael I. Krauss, Ruminations on Hedonic Damages and Tort Law (Aug. 1995) (unpublished manuscript, on file with the Gonzaga Law Review). But see David Friedman, What Is "Fair Compensation" for Death or Injury?, 2 INT'L REV. L. ECON. 81 (1982) (denying that non-pecuniary damages should be payable in tort).
FN6. If wage acceleration and discounting are presumed to offset one another, then it may be appropriate to simply multiply current earnings by the number of years that will be lost. See discussion infra part V.B. (discussing the differential discount rate approach). But once current earnings are projected into the future, taking inflation and productivity into account, it is no longer correct to merely sum them without adjusting for their present value.
FN7. See O'Shea v. Riverway Towing Co., 677 F.2d 1194, 1198-1200 (7th Cir. 1982) (setting forth a general analysis of calculating the present value of future wages).
FN8. A complex set of problems turns on whether a deduction for wages from an alternative job should be based upon likely alternatives, highest-paying alternatives, or some other formulation. Thus, for example, if we deduct the highest-paying post-injury alternative wages and the victim was not employed pre-injury in her highest-paying occupation, is it necessary to substitute the higher-pay pre-injury job for her actual pre-injury job in determining lost wages? These and related questions touch upon the broader issue of the victim's hedonic damages, which presumably account for the difference between the victim's highest paying pre-injury occupation and the job she in fact held pre- injury.
FN9. At common law, there was no recovery for wrongful death, as tort actions did not survive the death of the injured party. W. PAGE KEETON ET AL., PROSSER AND KEETON ON THE LAW OF TORTS 945 § 127 (5th ed. 1984). Lord Campbell's Act, the first wrongful death statute, was passed in England in 1846. Id.
Today, every American jurisdiction has some type of statutory remedy for wrongful death. Id. "Survival" statutes authorize any claim that the decedent himself might have maintained, including pain and suffering, medical expenses, lost future earnings, and any other costs sustained by the estate on account of his death. See id. at 946. "True" wrongful death statutes are instituted for the benefit of particular surviving relatives (e.g., spouse, children, parents) and often permit recovery only of the pecuniary losses that they suffer. Id. Any claim that the victim would have had against the tortfeasor (e.g., pain and suffering) must be sought separately by his estate, although the two actions are usually joined. Id. at 947.
FN10. POSNER, supra note 1, at 197. United States personal consumption as a percent of disposable personal income was over 95% in 1989 (i.e., the savings rate was 4.6%). UNITED STATES BUREAU OF THE CENSUS, STATISTICAL ABSTRACT OF THE UNITED STATES 438 tbl. 708 (111th ed. 1991) [hereinafter USBC 1991]. This does not suggest a 95% reduction in damages for lost earnings. First, subtraction of personal consumption expenditures is particularly troublesome in familial settings. Because many commodities are jointly consumed, the reduction will not be proportional to the number of household members. Second, many expenditures are more in the nature of investments than consumption; that is, they create utility over time (e.g., education). If all personal expenses were to be subtracted in death cases, the implicit assumption would be that the decedent obtained no utility from living. POSNER, supra note 1, at 197. Only those expenditures representing pure consumption (e.g., food, clothing) should be subtracted from future earnings.
FN11. See generally discussion infra part IV.A. (discussing the controversy over subtraction of income taxes).
FN12. See discussion supra note 2.
FN13. See discussion infra part III.A.
FN14. This article discusses problems involved in compensating for future lost earnings. A disabling accident will also diminish the productivity of those hours that would have been devoted to recreation, avocations, love or the production of household commodities. Wage rates for moonlighting jobs could be used as a minimum estimate of the opportunity cost of these additional hours. A downward adjustment from these wage rates might be required for any costs or risks of a second employment that would not have accompanied non-market use of the time. However an upward adjustment is dictated by the victim's expressed preference not to work during those hours. See POSNER, supra note 1, at 196. Courts have evidenced a willingness to recognize this type of hedonic damage for loss of the pleasures of life. See Mariner v. Marsden, 610 P.2d 6 (Wyo. 1980) (holding damages are recoverable for loss of enjoyment of life).
FN15. The pattern of yields to maturity on bonds of various lengths is known as the term structure of interest rates. Its graphic representation, with yield on the vertical axis and time on the horizontal, is called the yield curve. Usually, short-term instruments yield less than long-term. A quick look from time to time at the financial pages of any major newspaper will reveal that the spread between 1-year and 20-year bonds is typically under 2.5 percentage points, although the gap varies considerably and can even be negative. The 4- percentage-point spread posited above -- 3% and 7% yields on 1-year and 20-year issues respectively -- is unusually large, but close to the actual spread during the early months of 1993. More recently, the gap has narrowed to about 2.4 percentage points. The Wall Street Journal reports the following yields as of May 1, 1994: 5.1% on 1-year issues; 6.6% on 5-year issues; 7.0% on 10-year issues; and 7.5% on 20-year issues. WALL ST. J., May 2, 1994, at C2.
FN16. ($1,000 / 1.07) + ($100 / 1.0720) = $961.42.
FN17. If 20-year bonds yielded 7% in their first year while 1-year bonds only yielded 3%, arbitrage would force the yields to converge. Investors seeking a short-term holding would sell 1-year bonds and buy 20-year bonds, then liquidate after one year. The 4-percentage-point premium would be more than adequate to compensate short-term holders for the greater price volatility of a long-term security. Sale of 1-year bonds would depress their price and raise their yields. Purchase of 20-year bonds would increase their price and lower their yields. Accordingly, if we observe a 3% yield on 1-year instruments, we can be reasonably assured that the first-year yield on 20-year instruments is not greatly different. That is, a 7% coupon 20-year bond purchased at $1,000 par would likely decline in price by about $40 over the first year. The $70 coupon minus the $40 price depreciation would produce a net $30 return on a $1,000 investment, or 3%. It is, of course, still possible to achieve a 7% average yield over the full 20-year period, even when the first-year yield is only 3%. The "forward rate" for years 2 through 20 would average 7.215%. In other words, if the bond owner earns 3% the first year and an average of 7.215% in each of the next 19 years, then his full 20-year yield will be 7% per annum. Any price depreciation in the early years is ultimately reversed when the bond matures and the investor receives full par value.
FN18. $961.42 x 1.03 = $990.26.
FN19. $20,000 x 1.0645 = $275,292.
FN20. Commissioners' 1980 Standard Ordinary Mortality Table -- Male Lives, reprinted in EMMETT J. VAUGHAN, FUNDAMENTALS OF RISK AND INSURANCE 204 tbl. 12.1 (6th ed. 1992).
FN21. See HEALTH INSURANCE ASSOCIATION OF AMERICA, SOURCE BOOK OF HEALTH INSURANCE DATA 101 (1992).
FN22. See discussion supra note 15.
FN23. Stated differently, the yield to maturity on a bond is a time-weighted rate. It assumes equal returns on all equal-length time periods within the overall term of the bond. Returns for any given sub-period are thus proportional to the length of the period. By comparison, the discount rate required for lost earnings computation must be dollar-weighted; it must adjust for varying amounts of capital available for investment as the damage award is progressively liquidated to pay the lost earnings. The only means of accomplishing dollar weighting is to use yields that explicitly correspond to the interval over which each capital component will be invested.
FN24. The impact of reinvestment rate risk on realized returns can be estimated by the following equation: ROR = (D/H) x YTM + (1 - D/H) x RR; where ROR is the realized rate of return, D is the duration of the bond (see discussion infra note 26), H is the investor's time horizon, YTM is the bond's yield to maturity, and RR is the average reinvestment rate over the time horizon. See Guilford Babcock, A Modified Measure of Duration, Remarks at the Annual Meeting of the Western Finance Association (June 1976) (transcript on file with author). Babcock's equation is a linear approximation of a more complicated nonlinear relationship. However, the linear version is satisfactory whenever YTM and RR are reasonably close to one another.
FN25. Zero coupon bonds, as their name implies, do not pay periodic interest. Instead, they sell at a discount from their par value. The investor's return arises solely from price appreciation; the discount gradually disappears as maturity approaches.
FN26. FREDERICK R. MACAULAY, SOME THEORETICAL PROBLEMS SUGGESTED BY THE MOVEMENTS OF INTEREST RATES, BOND YIELDS AND STOCK PRICES IN THE UNITED STATES SINCE 1856, 44-46 (1938) (developing the concept of duration). See generally Martin L. Leibowitz, How Financial Theory Evolves in the Real World -- Or Not: The Case of Duration and Immunization, 18 FIN. REV. 271 (1983) (chronology of duration from 1938 through its rediscovery in the 1970s).
FN27. Every element of the income stream (i.e., coupons and principal) is discounted to its present value and multiplied by the number of years that will have elapsed on the date of payment. The sum of the products is then divided by the market price of the bond. To illustrate, consider the simplified case of a 5-year 14% coupon bond priced at $1,000 par and paying interest once a year:
Year Cash Flow Present Value of Col. (2) at 14% Col. (1) x Col. (3)
---- --------- -------------------------------- -------------------
(1) (2) (3) (4)
1 140 122.81 122.81
2 140 107.72 215.44
3 140 94.50 283.50
4 140 82.89 331.56
5 1140 592.08 2960.40
Duration = 3913.71/1000.00 = 3.91 years
If more refined calculations were made, taking into account semi-annual compounding and semi-annual coupon receipts, the actual duration of a 5-year 14% coupon bond priced at par would be 3.76 years. An identical bond maturing in 10 years would have a duration of 5.67 years. A 20-year version of the same bond would have a 7.13-year duration, and a 50-year version would have a 7.63- year duration. The longer the term to maturity and the higher the coupon, the greater the difference between term and duration. Only for a zero-coupon bond will term to maturity and duration be equal since there is but one cash flow to be discounted -- the principal amount of the bond, payable at maturity. There are no earlier receipts of cash by the investor.
FN28. 26 U.S.C. § 104(a)(2) (1994). However, there is some dispute concerning the tax status of punitive damages. See, e.g., Wesson v. United States, 843 F. Supp. 1119 (S.D. Miss. 1994) (finding punitive damage awards are taxable, even in personal injury tort suits), aff'd, 48 F.3d 894 (5th Cir. 1995).
FN29. 26 U.S.C. § 61(a) (1994).
FN30. 26 U.S.C. § 165(a) (1994) (Losses are not deductible if reimbursed, by insurance or otherwise.).
FN32. We do not imply here that tax deductions represent largess to a taxpayer by relinquishing a public claim on his assets. To the contrary, assets are owned by the taxpayer. Tax deductions are merely a reduction of government's expropriation. When we state that the federal government "absorbs" a portion of the damage award, we mean only to distinguish those cases where the payment of the award is deductible from those cases where it is not.
FN33. It is an interesting question as to how the deterrent objective of tort law is affected by the government's indirect assistance of some tortfeasors via the tax code. One might posit that under-deterrence would result. However, the business deductibility of the costs of precautions may have a countervailing effect. In any event, the focus of this paper is on appropriate compensation to the victim.
FN34. Other relevant issues are not addressed in this paper. See, e.g., Norfolk & W. Ry. Co. v. Liepelt, 444 U.S. 490, 496-97 (holding that a jury instruction on the non-taxability of damage awards would be proper to prevent the jury from inflating the award in order to cover the victim's non-existent tax liability), reh'g denied, 445 U.S. 972 (1980).
FN35. See, e.g., Stokes v. United States, 144 F.2d 82, 86 (2d Cir. 1944). See also discussion infra note 40 (providing a brief history of individual income taxes expressed as a percentage of personal income).
FN36. See Briggs v. Chicago Great W. Ry., 80 N.W.2d 625, 635-36 (Minn. 1957).
FN37. See Mitchell v. Emblade, 298 P.2d 1034, 1037-38 (Ariz. 1956).
FN38. See C. T. Foster, Annotation, Propriety of Taking Income Tax into Consideration in Fixing Damages in Personal Injury or Death Action, 63 A.L.R.2d 1393, 1401 (1959).
FN39. The implication of this argument is that the government's decision not to tax the capital value of a personal injury award is largess, or a "gift" to the victim. This is not obvious. Logic would dictate that an income tax would avoid targeting capital. Many jurisdictions have, however, modified the common-law doctrine of collateral benefits to allow setoff for purely gratuitous payments by third parties. See, e.g., CONN. GEN. STAT. §§ 52-225A-225d (1992 & Supp. 1994) (abolishing collateral source rule unless the collateral source has the right of subrogation); CAL. GOV'T CODE § 985 (West Supp. 1989) (abolishing certain collateral source recoveries when a government entity is the tortfeasor); N.Y. CIV. PRAC. L. & R. § 4545(a) (McKinney 1994) (abolishing collateral source rule, except for past and future premiums paid by tort victim to obtain collateral source). In this context, the tax savings might be seen as gratuitous in nature, as distinguished from collateral benefits arising from sources like an insurance contract, where consideration in the form of policy premiums was given by the plaintiff, and in regards to which the collateral benefits doctrine of common law has rarely been abrogated. In the case of this tax benefit, no "consideration" has been paid by the plaintiff -- previously paid taxes having been in consideration of other government services, or perhaps in consideration of non-imprisonment for tax evasion.
FN40. See Robert J. Aalberts & Melvin W. Harju, Utilizing Net Income as the Basis for Calculating Lost Earnings in Personal Injury and Wrongful Death Actions: A Case for Creating Consistency and Fairness in Louisiana, 51 LA. L. REV. 943, 955-56 (1991). Marginal tax rates have changed frequently and substantially; and the rules governing the computation of taxable income have indeed been volatile. Id. Nevertheless, when measured in terms of the total effective tax burden, the impact on taxpayers has been relatively stable. Id. Over the past 30 years, individual income taxes as a percentage of personal income have averaged 10.0%. Id. at 956. The range has been from a low of 8.8% in 1965 to a high of 11.3% in both 1969 and 1981. Id. Nearly two thirds of the years were between 9.5% and 10.5%. Id. It is the effective rate on total income, not the nominal rate at the margin, that is relevant for purposes of converting pre-tax earnings to their post-tax equivalents.
FN41. See Norfolk & Western Ry. v. Liepelt, 444 U.S. 490, reh'g denied, 445 U.S. 972 (1980).
FN42. Ruff v. Weintraub, 519 A.2d 1384, 1387 (N.J. 1987).
FN43. RESTATEMENT (SECOND) OF TORTS § 901 cmt. a (1979).
FN44. 651 F.2d 636, 642 (9th Cir. 1981). In DeLucca v. United States, 670 F.2d 843, 845 (9th Cir. 1982), the defendant attempted unsuccessfully to undermine Hollinger by noting that plaintiff DeLucca could have invested the damage award in tax-free municipal bonds. The court rejoined that such investments yield a lower interest rate than other securities of comparable risk. Id. The use of after-tax discount rates was given additional support by the Supreme Court in Jones & Laughlin Steel Corp. v. Pfeifer, 462 U.S. 523, 526 (1983).
FN45. Hollinger, 651 F.2d at 642.
FN46. See Aalberts & Harju, supra note 40, at 958-68.
FN47. Algebraically, Method #1 simply multiplies the annual earnings by .8, and then divides the resultant present value by the .8. The multiplication and division cancel one another. Thus Method #1 is equivalent to discounting pre- tax earnings at a pre-tax rate.
FN48. Aalberts & Harju, supra note 40, at 959 tbl. 2.
FN49. Aalberts & Harju, supra note 40, at 961 tbl. 3.
FN50. See Aalberts & Harju, supra note 40, at 960.
FN51. See discussion supra notes 44-50 and accompanying text (noting the court properly recognized the need for an increased damage award to allow for the taxability of investment income).
FN52. See, e.g., Aalberts & Harju, supra note 40, at 967.
FN53. Aalberts & Harju, supra note 40, at 963.
FN54. See Norfolk & Western, 444 U.S. at 500 (Blackmun, J., dissenting).
FN55. Past lost income (i.e., income lost before final judgment) is of course non-capitalized and should be considered income for purposes of taxation. To the extent that income tax does not reach past lost income, it is incoherent. This paper's focus on future lost income precludes discussion of this issue.
FN56. Aalberts & Harju, supra note 40, at 968.
FN57. This is a recursive problem. The size of the fund determines the marginal tax bracket, which determines the after-tax discount rate, which determines the size of the fund. A relatively simple computer program should be able to converge on the correct answer in a few seconds.
FN58. Johnson v. Penrod Drilling Co., 510 F.2d 234, 236 (5th Cir.), cert. denied, 423 U.S. 839 (1975), overruled, Culves v. Slater Boat Co., 688 F.2d 280 (5th Cir. 1982).
FN59. Culver v. Slater Boat Co., 688 F.2d 280 (5th Cir. 1982), rev'd on other grounds, 722 F.2d 114 (5th Cir. 1983), cert. denied, 467 U.S. 1252 (1984).
FN60. 462 U.S. 523, 538-47 (1983).
FN62. The material in this section is based upon Patrick J. Maxwell, Computing Lost Future Earnings in Light of Jones & Laughlin Steel Corp. v. Pfeifer, 12 FLA. ST. U. L. REV. 375, 387-94 (1984).
FN63. Alexander M. Waldrop, Accounting for Inflation and Other Productivity Factors When Calculating Lost Future Earnings Capacity, 72 KY. L.J. 951, 961 (1984) (suggesting that exclusive focus on inflation is unrealistic). The major cause of increases in money earnings is not inflation, but factors associated with increases in productivity (e.g., mechanization, experience, merit raises and maturity). Id. Yet, over the period 1980-1989, real percent changes in hourly earnings ranged from -5.0% in 1980 to +1.4% in 1983, with a compound average change of -0.7% per annum. USBC 1991, supra note 10, at tbl. 675.
FN64. See, e.g., Turcotte v. Ford Motor Co., 494 F.2d 173, 187 (1st Cir. 1974).
FN65. Pfeifer, 462 U.S. at 548.
FN66. See, e.g., ROGER G. IBBOTSON & REX A. SINQUEFIELD, STOCKS, BONDS, BILLS AND INFLATION: THE PAST AND THE FUTURE (1982). The following is the essence of the IBBOTSON & SINQUEFIELD model:
1. The market for risk-free securities (i.e., United States Government issues) is assumed to be an efficient market in which the yield to maturity reflects all available information regarding anticipated interest rate changes.
2. The "forward risk-free rate of interest" is determined. The forward rate is the rate that, when compounded year-by-year, will produce the yield to maturity indicated by the United States Government yield curve. These rates represent the market's consensus forecast of the year-by-year return on government bonds.
3. United States Treasury bills ("T-bills") pay no interest; they typically mature in 90 days and are sold at a discount from par value. T-bills over the past half century have yielded less on average than long-term government bonds. The difference between the yield on these two instruments is the "maturity premium," which compensates investors for greater sensitivity of longer-term debt securities to interest rate changes. 4. To forecast T-bill returns, subtract the average historical maturity premium from the year-by-year forward rates on government bonds. An exception applies in the first year; only half the maturity premium is subtracted, conforming to historical evidence that the difference between T-bills and one-year government bonds is half as large as the difference between T-bills and government bonds maturing in two or more years.
5. The projected T-bill return now has two components: the real or "pure" rate of interest, plus compensation for anticipated inflation.
6. The real component is accurately forecasted using an autoregressive equation (i.e., projecting the current year's return based solely upon knowledge of the prior year's return). The inflation rate is simply the difference between the real rate, forecasted autoregressively, and the T-bill rate forecasted from the yield curve in Step 4.
An application of the IBBOTSON & SINQUEFIELD model as of May 1, 1994 generates an inflation forecast of 6.0% compounded annually over the next 20 years, compared to a 6.2% historical rate of growth over the prior 20 years.
FN67. See, e.g., Pfeifer, 462 U.S. at 542.
FN68. O'Shea v. Riverway Towing Co., 677 F.2d 1194, 1199 (7th Cir. 1982).
FN69. 524 F.2d 384, 387 (2d Cir. 1975).
FN71. The results are exactly equivalent only if the netting process is done geometrically rather than arithmetically. That is, if the risk-free rate is 8% (i.e., RF = .08) and the inflation rate is 5% (i.e., I = .05), then the real rate is not RF - I = .03. Instead, the proper computation, allowing for compounding, would be %AD(1 + RF) / (1 + I)] - 1 = (1.08 / 1.05) - 1 = . 0286.
FN72. Feldman, 524 F.2d at 387.
FN73. See discussion supra note 63 and accompanying text.
FN74. See, e.g., IBBOTSON & SINQUEFIELD, supra note 66, at 125-26. Results from 1976 through 1992 were updated by CDA Investment Technologies, Inc., Rockville, Maryland [hereinafter CDA], using Lehman Brothers long-term government bond index and the Consumer Price Index (CPI).
FN75. At a 16% tax bracket, the after-tax bond return would have been .84 x 4.9%, or 4.1% -- roughly one percentage point above the 3.1% rate of inflation. Higher tax brackets would have produced smaller after-tax returns, thus differentials below 1%.
FN76. Pfeifer, 462 U.S. at 547-48.
FN77. Id. at 548-49.
FN78. Id. at 548.
FN80. Beaulieu v. Elliott, 434 P.2d 665 (Alaska 1967).
FN81. Kaczkowski v. Bolubasz, 421 A.2d 1027 (Pa. 1980).
FN82. Beaulieu, 434 P.2d at 671.
FN83. Kaczkowski, 421 A.2d at 1038.
FN84. Id. at 1029 n.5.
FN85. In fact, the Pennsylvania approach is the equivalent of a negative discount rate, i.e., wages are accelerated for inflation plus productivity and then discounted for inflation alone. The present value will be larger than the arithmetic sum of the wages pre-acceleration and pre-discounting. By contrast, the real interest rate method accelerates for inflation, then discounts by a risk-free rate, which includes both inflation and the real return demanded in an inflation-free environment. Thus, the present value will be smaller than the arithmetic sum of the nominal wages.
FN86. Pfeifer, 462 U.S. at 548. The Supreme Court's favorable view in Pfeifer could encourage state courts to opt for the total offset approach. See, e.g., Meier v. Bray, 475 P.2d 587 (Or. 1970) (expressly rejecting total offset).
FN87. Pfeifer, 462 U.S. at 548. Over the period 1975 through 1988, for example, the average annual percent change in output per hour ranged from a high of +11.8% for semiconductors to a low of -1.4% for laundries. USBC 1991, supra note 10, at tbl. 670. While wages do not precisely mirror the variations in physical output, they are clearly correlated.
FN88. See discussion supra note 71.
FN89. See Gary A. Anderson & David L. Roberts, Economic Theory and the Present Value of Future Lost Earnings: An Integration, Unification, and Simplification of Court Adopted Methodologies, 39 U. MIAMI L. REV. 723, 748-49 (1985).
FN92. Id. at 750.
FN93. Gary A. Anderson & David L. Roberts, Stability in the Present Value Determination of Future Lost Earnings: An Historical Perspective with Implications for Predictability, 39 U. MIAMI L. REV. 847, 851 (1985).
FN94. Id. at 850-51.
FN95. Id. at 857. The computer program works backward from the last year of lost earnings to the date of injury. Id. First, the program determines the after-tax earnings in the terminal year, dependent on occupation and effective income tax rates. Id. Next, the program calculates the investment required at the beginning of the year in order to have sufficient principal plus interest income to cover the lost earnings and the taxes on the interest. Id. This amount of investment is then added to the prior year's lost earnings to determine the total sum required to be funded that year. Id. From the correct award and the after-tax earnings for the year of the injury, the program can compute the proper differential discount rate. Id.
FN96. Id. at 857-58, 870-72. The average discount rate for all 20-year periods from 1952 through 1982 was -0.67%. Id. at 870-71. If this rate had been used, the largest understatement of the correct award for the average worker would have been 5%, and the largest overstatement would have been 3.6%. Id. For 10-year intervals, the largest under and overstatement would have been 6.4% and 4.8% respectively. Id. And if individual occupations are considered over 20-year periods, the use of -0.67% as the discount rate would have misstated the correct award by less than 13% in the worst case. Id. at 871.
FN97. Id. at 871-72.
FN98. Anderson & Roberts, supra note 93, at 856.
FN99. See discussion supra note 24 and accompanying text (discussing reinvestment risk).
FN100. The annual standardized deviation of monthly returns over the period 1973 through 1992 averaged roughly 11.4% for long-term government bonds, 6.3% for intermediate-term government bonds, and 0.4% for short-term Treasury bills. IBBOTSON ASSOCIATES, STOCKS, BONDS, BILLS AND INFLATION 1994 YEARBOOK 103 (1994). Statistics are not available for 1-year notes; but it is evident that the returns on 1-year instruments will have a lower standard deviation than equivalent instruments of longer maturity.
FN101. This is the rough difference in returns between 1-year notes and longer- term government bonds over the period 1926 through 1992. Id. at 263, 271 (estimated at one-half of the difference between the returns on Treasury bills and long-term bonds over the same period). While the spread varies significantly from year-to-year, it has shown no systematic tendency to expand or contract over time. See IBBOTSON & SINQUEFIELD, supra note 66, at 33.
FN102. VAUGHAN, supra note 20, at 204 tbl. 12.1.
FN103. If a dichotomous "all or nothing" civil burden of proof were to be adopted, any chance of dying above 50% would be treated as certain death, and any chance below 50% would be treated as certain survival. It would then be appropriate to use the same discount rate for two persons who have 9% and 25% probabilities of dying.
FN104. Richard A. Posner, Law and the Theory of Finance: Some Intersections, 54 GEO. WASH. L. REV. 159, 161 (1986).
FN106. Id. at 162.
FN107. See generally W. KIP VISCUSI, FATAL TRADEOFFS (1992).
FN108. Posner, supra note 104, at 162-63.
FN109. Difficulties include proper sampling, eliciting reliable responses, interpreting data, and developing a coherent theory that would have broad application beyond the concrete question posited in such a survey. In short -- a formidable task.
FN110. See, e.g., RICHARD A. BREALEY & STEWART C. MYERS, PRINCIPLES OF CORPORATE FINANCE 206-07 (4th ed. 1991). Once a risk-adjusted discount rate is determined, it is possible to express any component of the earnings stream in terms of its "certainty equivalent." The method is straightforward. First, discount the earnings by the risk-adjusted rate; then compound the resultant present value by the risk-free rate. Alternatively, the certainty equivalent can be calculated directly.
FN111. Portions of the material in this section appear, in modified form, in Robert A. Levy, The Prudent Investor Rule: Theories and Evidence, 1 GEO. MASON U. L. REV. 1 (1994).
FN112. See William F. Sharpe, Mutual Fund Performance, 39 J. BUS. 119 (1966). It could be argued that variability is not an adequate yardstick of risk because it does not reflect the probability of achieving returns that are below average. For example, successive monthly returns of -4%, -4%, -4% would have zero variability, while successive monthly returns of +15%, +6%, +9% would be more variable. As a practical matter, however, there would be no market for any asset with ex ante expected returns below the risk-free rate.
FN113. The standard deviation is calculated by: (1) computing the average of possible outcomes; (2) expressing each outcome in terms of its deviation from the average; (3) squaring the deviations (which both eliminates minus signs and gives more weight to the more extreme deviations); (4) determining the average of the squared deviations; and (5) computing the square root of this average.
FN114. Seminal contributions on CAPM include William F. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk, 19 J. FIN. 425 (1964), and John Lintner, Security Prices, Risk, and Maximal Gains from Diversification, 20 J. FIN. 587 (1965).
FN115. The market model for computation of the beta coefficient is: R suba = ALPHA+ BETAR subm + e; where R suba is the return for a specific asset, R subm is the market return, ALPHA and BETA are respectively the intercept and slope of a linear regression of R suba on R subm , and e is an error term. Beta is the slope (BETA) of the regression line. It can be interpreted as the change in asset return that has accompanied a one percentage point change in market index return. Assets that are about as volatile as the market will have a coefficient around 1.00; those that are half as volatile will have a beta of .50, etc.
FN116. See, e.g., Sharpe, supra notes 112, 114.
FN118. Edwin J. Elton & Martin J. Gruber, The Lessons of Modern Portfolio Theory, in BEVIS LONGSTRETH, MODERN INVESTMENT MANAGEMENT AND THE PRUDENT MAN RULE 169-70 (1986). The key underlying assumptions of CAPM are that: (1) there are no transactions costs, (2) there are no taxes, (3) investors make decisions solely in terms of expected return and standard deviation, (4) unlimited lending and borrowing is available at the risk-free rate, and (5) all investors have identical expectations and the same time horizon. Id.
FN119. BURTON G. MALKIEL, A RANDOM WALK DOWN WALL STREET 242-48 (5th ed. 1990). See also STUDIES IN THE THEORY OF CAPITAL MARKETS (Michael Jensen ed., 1972) (returns are higher for low beta stocks and lower for high beta stocks than expected under CAPM); Eugene F. Fama & Kenneth R. French, The Cross-Section of Expected Stock Returns, 47 J. FIN. 427 (1992) (returns depend on company size and the ratio of market price to book value).
FN120. See generally Richard Roll, Critique of the Asset Pricing Theory's Tests; Part I: On Past and Potential Testability of the Theory, 4 J. FIN. ECON. 129 (1977) (citing the lack of market information as an impediment to accurate asset pricing). See supra note 115 (discussion of the market model used to compute beta coefficients).
FN121. Elton & Gruber, supra note 118, at 170.
FN122. Michael Peltz, USA: The Revolt Against Free-Market Finance -- Is This the Night of the Living Beta?, INST. INVESTOR, June 1992, at 42 (quoting Peter Bernstein).
FN123. Employment probability is a binomial variable -- either an employee is working or he is not. The shortcut formula for the standard deviation of a binomial variable is the square root of P x (1 - P); where P is the probability of working. The product of multiplying this standard deviation by the forecasted wage in a given year -- say $30,000 -- would yield the standard deviation of a distribution in which there was P chance of earning $30,000 and 1-P chance of earning zero.
FN124. This step is necessary to be able to compare two standard deviations -- employment risk and common stocks -- which are expressed in differing magnitudes. The normalization process consists simply of dividing the standard deviation by the mean.
FN125. This index is a broad-based, frequently quoted barometer of overall stock market movement. It comprises 500 widely-held common stocks; each has a weight in the overall index proportionate to the aggregate market value of its outstanding shares.
FN126. If betas for employment risk were calculated directly, they would almost certainly approach zero. See discussion supra note 115 (providing formula). This would indicate that employment risk was not compensable by the market -- a counter-intuitive conclusion. The coefficient of variation for employment relative to common stocks is a beta-like measure that avoids the zero-beta problem.
FN127. The CAPM formula for an asset's risk premium is BETA suba x (R subm - R subf ); where BETA suba is the asset's beta coefficient, R subm is the market's expected return, and R subf is the expected risk-free return. For our purposes, the asset in question is the present value of an employee's wage- earning potential; the beta coefficient is replaced by the coefficient of variation for employment relative to common stocks; the market is the Standard & Poor 500-Stock Index; and the risk-free return is based upon U.S. Treasury Bills. The quantity (R subm - R subf ) represents the risk premium for the overall market.
Over the 67-year period 1926 through 1992, the market's risk premium was 6.6 percentage points per annum. IBBOTSON ASSOCIATES, supra note 100, at 251, 271. While there is substantial variation in the premium from year-to-year, it has not shown any systematic tendency to expand or contract. See IBBOTSON & SINQUEFIELD, supra note 66, at 33. Accordingly, it is permissible to assume a continuation of the same market risk premium in the foreseeable future. Employment risk premium is thus 6.6 times relative risk.
FN128. It is important to note that a risk premium as large as 2.3% would apply only when mortality, morbidity and unemployment factors were as high as .50. This might occur in the outlying years of a long loss period for a young plaintiff -- but otherwise, such a figure is unlikely.
FN129. See, e.g., RICHARD A. BREALEY, AN INTRODUCTION TO RISK AND RETURN FROM COMMON STOCKS 133-39 (2d ed. 1969) (asserting that the use of standard deviation is appropriate only if the investor is risk averse and either: (1) the investor's utility function can be described by a quadratic equation, or (2) outcomes are normally distributed).
FN130. If the risk of a particular asset is totally non-diversifiable, the correlation coefficient between the asset's returns and the market's returns is perfect. Under these conditions, the relative risk of the asset, as measured by the ratio of its coefficient of variation to the market's coefficient of variation, will exactly equal the asset's beta coefficient.
FN131. Posner, supra note 104, at 162.
FN132. See FLOYD S. HARPER & LEWIS C. WORKMAN, FUNDAMENTAL MATHEMATICS OF LIFE INSURANCE 192-95, 231-35 (1970).
FN133. Though this illustration is couched in terms of life insurance, the same principles would apply to the pricing of disability insurance. Id. at 331-32.
FN134. VAUGHAN, supra note 20, at 204 tbl. 12.1.
FN135. At the end of 1990, life insurance portfolios were allocated approximately 15% to government bonds, 41% to corporate bonds, 9% to common stocks, 19% to mortgages and 15% to miscellaneous assets. AMERICAN COUNCIL OF LIFE INSURANCE, LIFE INSURANCE FACT BOOK UPDATE 44 (1991). The reported pre-tax rate of investment income on these assets was 9.3% in 1990. Id. at 39. However, the reported rate excludes capital appreciation and depreciation, and applies historically rather than prospectively. Using forecasted returns provided by CDA as of December 31, 1990 (government bonds 7.6%, corporate bonds 8.1%, common stocks 13.5% and mortgages 7.9%), the projected weighted average return would be 8.5%.
FN136. Properly, the insurance company's after-tax expected benefit payment should be discounted by their after-tax investment return. The use of pre-tax inputs provides a close approximation and avoids immersion in the intricacies of insurance company taxation.
FN137. See discussion infra part VII.C.
FN138. The probability that the employee would still have been working is . 02965 (1-the mortality rate). Risks of disability and unemployment have been ignored for simplification.
FN139. By providing for payment of the insurance premium concurrent with receipt of either the insured's wages or his death benefit, we avoid the need to discount for time value. All cash flows are on December 31, 2003, and whatever discount rate would apply to inflows would also apply to outflows.
FN140. See discussion infra part VII.C.
FN141. See discussion infra part VII.C.
FN142. The formula for the percentage reduction in the damage award for a given year is: 100 x L x M / [(1 - L) x (1 - M)]; where L is the loading factor, expressed as a percent of the gross premium, and M is a combination of mortality, morbidity and unemployment risks. In our example, which disregards morbidity and unemployment, the percentage reduction is calculated as: 100 x . 25 x .02965 / (.75 x .97035) = .74125 / .72776 = 1.018.
FN143. The size of the estimate for wage growth is not critical for purposes of the illustration at Appendix B, nor is the choice of a risk-free discount rate. Under current conditions, 6% seems reasonable as an estimate of wage growth (inflation plus changes in productivity); 5% was roughly the after-tax yield on risk-free securities as of May 1, 1994.
FN144. VAUGHAN, supra note 20, at 204 tbl. 12.1.
FN145. HEALTH INSURANCE ASSOCIATION OF AMERICA, supra note 21, at 101.
FN146. From 1980 through 1989, unemployment for males averaged 7.3%. USBC 1991, supra note 10, at tbl. 659. Government unemployment insurance, paid by employers, covered 34.2% of unemployed workers in an amount averaging 36.2% of their wages. USBC 1991, supra note 10, at tbl. 602. Multiplying 34.2% by 36.2% yields 12.4% -- the portion of unemployed hours that are already compensated by state "insurance." Accordingly, uncompensated unemployment is the remaining 87.6% of 7.3%, or 6.4%. That represents the risk of unemployment, without income, that the worker in Appendix B assumes. We acknowledge that there are endless possibilities for refinement of this figure. For example, unemployment rates are readily available by sex, age, race, experience, family status, education, industry and occupation. See, e.g., USBC 1991, supra note 10, at tbls. 659, 661-63.
FN147. Mortality, morbidity and unemployment are joint risks. Morbidity risk only applies if the worker is alive. Unemployment risk only applies if the worker is both alive and able. Joint probabilities are calculated by multiplication. To illustrate, for year 55 of Appendix B: The risk of death is .117; the risk of disability is .120; and the risk of unemployment is .064. See app. infra part X. To be employed, the worker must be alive, able and employed. The EMPLOY PROBAB column is thus .883 x .880 x .936 = .727. See app. infra part X. The complement of .727 (i.e., .273) is the combined risk of death, disability and unemployment -- which is not the same as the arithmetic sum of the three risks.
FN148. This relationship is derived algebraically from the equation for the percentage reduction in the damage award. See discussion supra part VII.A. (Note that E in the current formula is equal to 1 - M in the earlier formula.).
FN149. It is difficult to compare the after-tax risk-adjusted discount rates at Appendix C with the pre-tax risk premiums derived from the CAPM process at Appendix A. See apps. infra parts IX., XI. But an examination of Appendix A, risk premiums for realistic employment probabilities (ranging from .995 to . 500), shows that they average about 1.7 percentage points -- equivalent to roughly 1.3 percentage points after taxes. See app. infra part IX. Approximately the same average risk premium appears at Appendix C when a 25% loading factor is applied to loss periods ranging from 10 to 45 years (i.e., for ages of death between 20 and 55). See app. infra part XI.
FN150. The term "standard-rated" usually refers to applicants who, after examination for insurability, would be issued policies based upon "standard" mortality factors. These persons, because they have passed a preliminary screen, may have a significantly better risk profile than the average American.
FN151. W. Kip Viscusi, Toward a Diminished Role for Tort Liability: Social Insurance, Government Regulation, and Contemporary Risks to Health and Safety, 6 YALE J. ON REG. 65, 68 n.12 (1989) (citing workers' compensation as a program that suffers the least from loading factors). Viscusi adds that the loading factor is even higher for private insurance, given adverse selection and marketing costs. Id.
FN152. AMERICAN COUNCIL OF LIFE INSURANCE, LIFE INSURANCE FACT BOOK 76 (1992).
FN154. Expenses are relatively higher for new policies due to the initial cost of issuing and selling.
FN155. Price quotes for term insurance of varying amounts from $100,000 to $5,000,000 were provided to the authors by Chubb Sovereign Life Insurance Company. Facsimile from Steven D. Lockshin, Meltzer & Associates, to Robert A. Levy, CDA (Apr. 2, 1993) (on file with the Gonzaga Law Review). The quotes covered a 30-year-old male non-smoker. Id. Premiums bore a near-perfect linear relationship with face amounts for policies above $500,000. Id. Below $500,000, premiums were more expensive per dollar of insurance. Id. Part of the higher cost of smaller policies is undoubtedly due to higher loading factors. It is also possible that mortality risk varies by size of policy -- perhaps due to moral hazard, which may increase geometrically as the face amount of insurance exceeds a certain limit. No reliable information is publicly available.
FN156. The necessity of a non-linear relationship between loading factors and premiums can be illustrated as follows: Let us assume that mortality risk is 76% for a 5-year policy covering a 60-year-old man in a high-risk occupation who sky dives for a hobby and is in bad health. If the loading factor were 25%, the gross premium would have to be 101% of the face amount of the policy (i.e., the expected benefit payment would be $760,000 on a $1,000,000 policy, and the gross premium would be $760,000 / .75, or $1,013,333). No insurance company would write such a policy since no rational person would buy it. In order to induce customers to insure, the issuer of the policy would have to decrease its loading factor. While many policies simply would not be written, others would be -- either by companies with lower expense ratios, or companies willing to vary their loading factors to reflect fixed expenses, or companies that would accept reduced percentage profit rates on large premium policies.
FN157. The only authoritative, published information on sub-standard risks examined mortality statistics related to various diseases, addictions and intoxications, occupational hazards, environmental risks and family history. See generally MEDICAL RISKS: PATTERNS OF MORTALITY AND SURVIVAL (Richard B. Singer, M.D. & Louis Levinson, F.S.A. eds., 1976) (compiled for The Association of Life Insurance Medical Directors of America and The Society of Actuaries). Data was drawn chiefly from papers published in medical journals, along with government publications and studies of life insurance experience. Mortality rates were as high as 4,300% of standard for high-risk persons under 30 years of age, insured within pension funds but declinable for insurance in a non- pension application. Id. at 28 tbl. 3-2. Even persons who would qualify for automatic-issue of insurance pursuant to pension agreements (i.e., actively employed persons not otherwise examined for insurability) experienced 220% of standard mortality. Id.
FN158. For example, one quote obtained from Chubb Sovereign Life Insurance Company indicated that their sub-standard risk rating required a premium nearly five times the premium on their standard-rated policy. See Lockshin, supra note 155.
FN159. AMERICAN COUNCIL OF LIFE INSURANCE, supra note 152, at 117.
FN161. Id. at 126-27.
FN162. A comparison of mortality rates for the United States population as a whole with mortality rates for life insurance policy holders might reveal whether risk profiles of insurance applicants differ from profiles of non- applicants. Traditional notions of adverse selection suggest that applicants would be a poorer risk group than persons who do not seek insurance. On the other hand, perhaps many non-applicants are persons who know they would be rejected; and perhaps socio-economic classes with higher risk profiles are less likely to apply for insurance, due to ignorance, inadequacy of financial resources or disinterest (e.g., single non-parents are less likely than married parents to have a need for life insurance).
FN163. See, e.g., Michael I. Krauss, Tort Law and Private Ordering, 35 ST. LOUIS U. L.J. 623 (1991) (addressing perspectives on corrective justice as the foundation for tort law). See also Kenneth W. Simons, Corrective Justice and Liability for Risk Creation: A Comment, 38 UCLA L. REV. 113 (1990); Christopher H. Schroeder, Corrective Justice, Liability for Risks and Tort Law, 38 UCLA L. REV. 143 (1990).
FN164. Because of the reductions in risk brought about by the "law of large numbers," even risk-neutral persons might well buy insurance. The modest point is that for any given premium some people will prefer to self-insure.
FN165. See discussion supra note 4.
FN166. If a court did want to grapple with individualized risk preferences, it could do so in the following manner: Suppose that the lost earnings forecasted for a given year are $100,000, with an employment probability of 85% (i.e., the expected compensation is $85,000). Suppose further that the certainty equivalent determined by a risk-adjustment process is $80,000. The court could offer the victim a choice. If he takes the certainty equivalent, he gets $80,000 (discounted to present value); but if he takes the probabilistic outcome, he gets a roulette wheel (or its computerized counterpart) with 100 numbered slots. If the wheel stops on numbers 1 through 85, the victim gets his full $100,000 (discounted to present value, of course) -- if the wheel stops on numbers 86 through 100, he gets nothing. Even aside from the public policy implications, this Monte Carlo process does not resolve all of the problems. For example, if the victim is deceased, whose risk preference (the decedent's or his survivors') should govern the choice? What if he is severely disabled and his risk preference has changed since before the injury: should his current or original preference prevail? What of the moral hazard that tempts the victim to "go for broke" knowing that his worst-case outcome is welfare rather than pennilessness?
FN167. The relationship between premiums and loading factors is non-linear; thus, it is unclear that persons paying higher premiums due to sub-standard ratings will be harmed more by the risk-adjustment process. See supra note 155 and accompanying text.
FN168. Sub-standard ratings are infrequently applied. See supra note 157 and accompanying text.
FN169. The answer is almost certainly, "yes." However, this issue, while perhaps tangential to risk-adjustment, is more appropriately addressed under the rubric of a separate recovery for hedonic damages. See Krauss, supra note 5. There is little justification for abandoning risk-adjustment, with its diminishing impact on damage awards, merely because we may have identified a phenomenon which suggests that tort awards generally should be augmented. Any intimation that the effects are exactly offsetting is surmise. The same rationale might just as well be advanced for not discounting to present value, or not subtracting income taxes, or not undertaking a variety of other well- established adjustments.
FN170. Continuous probabilities will be virtually always wrong. Whenever the distribution of possible outcomes is binary (e.g., working or not working), any estimated probability other than 0.00 or 1.00 will be incorrect. On the other hand, estimates between 0.00 and 1.00 will never be incorrect by as much as +- 1.00.
FN171. See supra note 3 and accompanying text.
*368 IX. APPENDIX A: EMPLOYMENT RISK VERSUS COMMON STOCKS
EMPLOYMENT S&P 500 EMPLOYMENT
COEF. COEF. PRE-TAX
STD. OF OF REL. RISK
PROBABILITY DEV. VAR. VAR. RISK PREMIUM
0.995 0.0705 0.0709 1.9961 0.0355 0.2
0.990 0.0995 0.1005 1.9961 0.0503 0.3
0.975 0.1561 0.1601 1.9961 0.0802 0.5
0.950 0.2179 0.2294 1.9961 0.1149 0.8
0.900 0.3000 0.3333 1.9961 0.1670 1.1
0.850 0.3571 0.4201 1.9961 0.2104 1.4
0.800 0.4000 0.5000 1.9961 0.2505 1.7
0.750 0.4330 0.5774 1.9961 0.2892 1.9
0.700 0.4583 0.6547 1.9961 0.3280 2.2
0.650 0.4770 0.7338 1.9961 0.3676 2.4
0.600 0.4899 0.8165 1.9961 0.4090 2.7
0.550 0.4975 0.9045 1.9961 0.4531 3.0
0.500 0.5000 1.0000 1.9961 0.5010 3.3
0.450 0.4975 1.1055 1.9961 0.5538 3.7
0.400 0.4899 1.2247 1.9961 0.6136 4.0
0.350 0.4770 1.3628 1.9961 0.6827 4.5
0.300 0.4583 1.5275 1.9961 0.7652 5.1
0.250 0.4330 1.7321 1.9961 0.8677 5.7
0.200 0.4000 2.0000 1.9961 1.0019 6.6
0.150 0.3571 2.3805 1.9961 1.1925 7.9
0.100 0.3000 3.0000 1.9961 1.5029 9.9
0.050 0.2179 4.3589 1.9961 2.1837 14.4
EMPLOYMENT PROBABILITY: Probability of working based upon various risks, including mortality, morbidity and unemployment.
EMPLOYMENT STD. DEV.: The standard deviation of the binomial distribution of EMPLOYMENT PROBABILITY (P); i.e., the square root of P x (1-P).
*369 EMPLOYMENT COEF. OF VAR.: The ratio of EMPLOYMENT STD. DEV. to EMPLOYMENT PROBABILITY, known statistically as the coefficient of variation.
S&P 500 COEF. OF VAR.: The ratio of the S&P 500 standard deviation to its mean, known statistically as the coefficient of variation. The mean (.0981) and standard deviation (.1959) for the Standard & Poor 500-Stock Index were computed from continuously compounded annual returns, including dividends, from 1926 through 1992. IBBOTSON ASSOCIATES, supra note 100, at 251, 271.
EMPLOYMENT REL. RISK: The ratio of the coefficient of variation for EMPLOYMENT to the coefficient of variation for the S&P 500; a measure of the relative riskiness of employment compared to common stocks.
EMPLOYMENT PRE-TAX RISK PREMIUM: The product of EMPLOYMENT REL. RISK times 6.6%; represents the excess return, above the risk-free rate, to compensate for mortality, morbidity and unemployment risk. Pre-tax excess return for the S&P 500 from 1926 through 1992 was 6.6 percentage points per annum. IBBOTSON ASSOCIATES, supra note 100, at 251, 271.
*370 X. APPENDIX B: ILLUSTRATIVE ADJUSTMENT FOR CERTAINTY EQUIVALENTS
AFTER-TAX INSURANCE LOAD FACTOR 25.0%
WAGES: PRESENT EQUIV EQUIV PRESENT
GROWTH EMPLOY DAMAGE VALUE EMPLOY DAMAGE VALUE
YEAR AT 6.0% PROBAB AWARD AT 5.0% PROBAB AWARD AT 5.0%
21 21200 0.93334 19787 18845 0.91112 19316 18396
22 22472 0.93058 20912 18968 0.90745 20392 18496
23 23820 0.92793 22104 19094 0.90391 21531 18600
24 25250 0.92528 23363 19221 0.90037 22734 18703
25 26764 0.92263 24694 19348 0.89684 24004 18807
26 28370 0.92008 26103 19479 0.89344 25347 18915
27 30073 0.91754 27593 19610 0.89005 26766 19022
28 31877 0.91417 29141 19724 0.88556 28229 19106
29 33790 0.91071 30772 19836 0.88095 29767 19188
30 35817 0.90735 32499 19951 0.87647 31392 19272
31 37966 0.90391 34318 20065 0.87187 33102 19354
32 40244 0.90047 36238 20179 0.86729 34903 19435
33 42658 0.89704 38266 20293 0.86271 36802 19517
34 45218 0.89351 40403 20406 0.85802 38798 19596
35 47931 0.88991 42654 20517 0.85321 40895 19671
36 50807 0.88622 45026 20627 0.84829 43099 19744
37 53855 0.88234 47519 20732 0.84312 45407 19811
38 57087 0.87848 50149 20838 0.83797 47837 19877
39 60512 0.87344 52854 20916 0.83126 50301 19906
40 64143 0.86833 55697 20992 0.82444 52882 19931
41 67991 0.86304 58679 21063 0.81739 55575 19948
42 72071 0.85750 61801 21127 0.81000 58377 19956
43 76395 0.85179 65072 21186 0.80239 61298 19957
44 80979 0.84494 68422 21215 0.79325 64236 19918
45 85837 0.83784 71918 21238 0.78379 67278 19867
46 90987 0.82962 75485 21229 0.77283 70318 19776
47 96447 0.82117 79199 21213 0.76156 73450 19673
48 102233 0.81250 83064 21189 0.74999 76675 19559
49 108367 0.80351 87074 21154 0.73802 79977 19430
50 114870 0.79336 91133 21086 0.72448 83221 19255
51 121762 0.78113 95111 20959 0.70817 86228 19001
52 129067 0.76864 99206 20820 0.69152 89253 18731
53 136811 0.75582 103405 20668 0.67443 92269 18442
54 145020 0.74176 107570 20477 0.65568 95087 18100
55 153721 0.72724 111793 20267 0.63632 97817 17733
56 162944 0.70811 115383 19922 0.61082 99529 17184
57 172721 0.68873 118959 19561 0.58498 101038 16614
58 183084 0.66897 122478 19181 0.55863 102276 16017
59 194069 0.64878 125909 18779 0.53171 103189 15390
60 205714 0.62758 129101 18338 0.50344 103564 14711
61 218056 0.60222 131318 17765 0.46963 102405 13854
62 231140 0.57670 133298 17174 0.43560 100684 12972
63 245008 0.55092 134979 16563 0.40122 98303 12062
64 259709 0.52487 136314 15930 0.36650 95183 11123
65 275291 0.49800 137095 15258 0.33067 91030 10131
TOTALS 893000 814754
PERCENT REDUCTION IN AWARD 8.8
AFTER-TAX RISK-ADJUSTED DISCOUNT RATE 5.4
NOTE: See discussion in main article,
supra part VII.B.
*372XI. APPENDIX C: EFFECT OF CERTAINTY EQUIVALENTS ADJUSTMENTS
ASSUMPTIONS: (1) AFTER-TAX RISK-FREE RATE 5.0%;
(2) ANNUAL WAGE GROWTH 6.0%;
(3) RETIREMENT AT AGE 65.
A. Percent Reduction in Awards
AGE AT INSURANCE LOADING FACTOR
DEATH 5 10 15 20 25 30 35 40 45 50
------ ----- ------ ------ ------ ------ ------ ------ ---- ---- ----
20 1.4 2.9 4.6 6.6 8.8 11.3 14.2 17.5 21.5 26.3
25 1.4 3.0 4.8 6.8 9.1 11.7 14.7 18.2 22.3 27.3
30 1.5 3.2 5.1 7.2 9.6 12.4 15.5 19.2 23.6 28.9
35 1.6 3.4 5.5 7.7 10.3 13.3 16.7 20.6 25.3 30.9
40 1.8 3.7 5.9 8.4 11.2 14.4 18.0 22.3 27.4 33.5
45 1.9 4.1 6.5 9.2 12.2 15.7 19.7 24.4 30.0 36.7
50 2.1 4.5 7.1 10.1 13.5 17.4 21.8 27.0 33.1 40.5
55 2.4 5.0 8.0 11.3 15.1 19.4 24.4 30.2 37.1 45.3
60 2.7 5.6 8.9 12.7 16.9 21.7 27.3 33.8 41.5 50.7
B. After-Tax Risk-Adjusted Discount Rates
AGE AT INSURANCE LOADING FACTOR
DEATH 5 10 15 20 25 30 35 40 45 50
------ ----- ------ ------ ------ ------ ------ ------ ---- ---- ----
20 5.1 5.1 5.2 5.3 5.4 5.6 5.7 5.9 6.2 6.5
25 5.1 5.2 5.3 5.4 5.5 5.7 5.9 6.1 6.4 6.8
30 5.1 5.2 5.3 5.5 5.6 5.8 6.1 6.3 6.7 7.2
35 5.1 5.2 5.4 5.6 5.8 6.0 6.3 6.7 7.2 7.8
40 5.2 5.3 5.5 5.8 6.0 6.4 6.8 7.3 7.9 8.8
45 5.2 5.4 5.7 6.0 6.4 6.9 7.4 8.1 9.1 10.3
50 5.3 5.6 6.0 6.5 7.1 7.8 8.6 9.7 11.1 13.2
55 5.5 6.0 6.7 7.5 8.4 9.5 11.0 12.9 15.4 19.2
60 6.0 7.1 8.5 10.1 12.0 14.5 17.6 21.8 27.7 36.9
NOTE: See discussion in main article, supra part VII.B.
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