Gonzaga Law Review

1995-96

*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

*326 I. SYNOPSIS

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.

II. OVERVIEW

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:

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

*339 And 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.

C. Inflation

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.

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

                 --------------------------------  -------------------

                                          1000.00              3913.71

   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.

*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

Notes:

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.

*372 XI. 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.

END OF DOCUMENT