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Concluding Remarks

With academics debating the value of the CAPM, what are companies that now use it in their capital budgeting process to do? Maybe nothing different. Obviously, capital budgeting decisions were made before there was a CAPM, and they can be made again without it. But the data seem to suggest that those who choose to use the CAPM now despite the academic debate will actually not be getting worthless advice. Recall our Chart 5, where we plotted the return/beta relationship for four types of assets over a period as long as 66 years. The result was more-or-less a positively sloped, straight line, just as the CAPM predicts. As we saw, that straight-line relationship breaks down over shorter time periods, and academics continue to debate why that is so. But for now, for those interested in the longer view, the CAPM still seems to have something to offer.

a The authors thank Jaeuk Khil for research assistance and Gordon Alexander, V. V. Chari, David Marshall, David Runkle, and especially John Boyd for helpful comments.

For a discussion of how corporate managers use models like the CAPM, see the box displayed later in the article. According to the description given by the source for these data, Ibbotson Associates 1992; the common stock returns are based on Standard & Poor's composite index. This index-includes 500 stocks now, but it included only 90 stocks before March 1957: For the period 1926-81, the small-firm stock index consisted of stocks in the smallest quintile of firms in terms of their market value of equity (their share price times shares outstanding) listed in the New York Stock Exchange; the portfolio composition is rebalanced once-every five years. Starting in 1982, the small-firm stock index corresponds to the Dimensional Fund Advisors' Small Company Fund. For the period 1926-76, the total returns on long-term U.S. government bonds are from the Center for Research in Security Prices (CRSP) at the University of Chicago Graduate School of Business. Each year one bond portfolio is constructed with a maturity of about 20 years. For the period 1977-91, data from the Wall Street Journal are used to compute the total returns on bond funds. For U.S. Treasury bill returns, data from the CRSP U.S. government bond file are used through 1976. Data reported in the Wall Street Journal are used for the period thereafter Table 1 also reports the implied annual returns that would produce those dollar values. To calculate these returns, we flint calculate the value of the asset if $1 were invested in the first year of the period. We then raise that value to the power of 1 over the number of years for the period and subtract 1. Note that we could have started our derivations of equation (10) by using the fact that investors trade off expected returns (that is, means) and risk (that is, variances) when making portfolio decisions. Suppose that investors are indifferent between assets that yield the same return/risk ratios: that is, suppose that (dR/dxi)/(dS/dxii)|z = 0, x[sub p] = 1is constant for all i, where R = xiRi + xpRp - x1,R0. Then (ERi-R0) betaiimust be constant; hence, equation (10) holds. For a discussion on computing the sampling errors associated with fire estimates of the coefficients in the cross-sectional regression, see Shahken 1992 and Jagannathan and Wang, forthcoming. For a description of better alternatives for econometric evaluation of the CAPM that rely on either the method of maximum likelihood or the generalized method of moments, see Gibbons 1982, Stambaugh 1982, Shahken 1985, Mackinlay and Richardson 1991, and Jagannathan and Wang 1993. Support the relation being estimated is yt = gammaxt + ur. If we observe Xt = xt + vt rather than just xt where vt is measurement error uncorrelated with xt then the least squares estimate for gamma will be biased toward zero. The larger is the variance of vt, the greater is the bias. These figures are from Fama and French's (1992) regressions of individual NYSE stocks on beta for 1941-90. Chari, Jagannathan, and Ofer (1988) also point out this bias in the Compustat Compustat claims that it rarely adds more than two years of back data when it adds a firm to its list. In view of this, in their follow-up article, Fama and French (1993) omit the flint two years of data, but they still find that average returns are strongly related to the book-to-market equity ratio in the cross section. Hence, the reason for this effect is still unknown.

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Table 1 Financial Asset Returns and Inflation During 1926-91 Legend for Chart:A - Type of Calculation and Time PeriodB - Stocks, S& 500 C - Stocks, Small FirmsD - U.S. Treasury, BondsE - U.S. Treasury, Bills F - Consumer Price Index A B C D E F Annual Rate of Return[a]Average 1926-91 11.94% 16.05% 4.94% 3.64% 3.11% 1926-75 10.89 14.71 3.14 2.30 2.29 1976-80 14.17 35.55 2.27 7.51 8.85 1981-91 15.71 13.27 14.14 7.98 4.25Variability 1926-91 20.22% 31.02% 7.62% .94% 2.01% 1926-75 21.46 33.59 5.38 .61 2.15 1976-80 14.48 25.87 11.16 .82 1.14 1981-91 16.31 18.25 12.41 .75 .97 Result of $1 invested Start of PeriodValue at End of Period 1926-91 $675.59 $1,847.63 $20.95 $11.01 $7.67 1926-75 73.86 109.34 4.29 3.14 3.08 1976-80 1.92 4.89 1.09 1.45 1.55 1981-91 4.81 3.53 4.33 2.40 1.59 Implied Annual Growth Rate[c] 1926-91 10.38% 12.07% 4.72% 3.70% 3.14% 1926-75 8.99 9.84 2.95 2.32 2.22 1976-80 13.95 37.35 1.68 7.77 9.21 1981-91 15.34 12.14 14.24 8.28 4.33

a The annual rate of return is the assets monthly return multiplied by 12.

b The variability of the return is its standard deviation multiplied by the square root of 12.

c 'The implied annual growth rate is calculated by this formula: (Value of $1 at end of period)1/ n-1, where n is the number of years in the period.

Source: Ibbotson Associates 1992

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Table 2 Selected Stock Returns, Volatilities, and Betas During 1972-91 Relation to Total Portfolio[a] Effect on Portfolio Monthly Rate S.D. of $1 of Return Stock Increase Firm (i) Mean S.D. Beta (delta S/ (Ssj.) (Beta) deltax i American Telephone and Telegraph 1.19 5.36 .552 2.63Bristol-Myers Squibb 1.56 7.08 .986 4.70 Coca-Cola 1.40 6.75 .917 4.37Consolidated Edison 1.61 7.38 .566 2.70 Dayton Hudson 1.53 9.69 1.191 5.68 Digital Equipment 1.13 10.25 1.278 6.09 Exxon 1.47 5.26 .729 3.47 Ford Motor 1.15 8.32 .968 4.61International Business Machines .61 6.03 .769 3.66 McDonald's 1.37 8.15 1.129 5.38 McGraw-Hill 1.41 8.15 1.075 5.12

a The total portfolio is $1,000 invested in all stocks traded on the NYSE and AMEX.

Source: Center for Research on Security Prices, University of Chicago

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Table 3 Estimated Betas for Four Types of Assets During 1926-91 Stocks U.S. Treasury Period S&500 SmalIFirms Bonds Bills 1926-91 1.03 1.39 .07 .00 1926-75 1.03 1.44 .03 .00 1976-80 .94 1.46 .22 .00 1981-91 1.01 .99 .31 -.01

Source of basic data: Ibbotson Associates 1992

GRAPH: Chart 1: How the Value of $1 Invested in Four Assets Would Have Changed Since 1926

Source of basic data: Ibbotson Associates 1992

GRAPH: Chart 2: Beta of the Stock

GRAPH: Chart 3: Standard Deviation of the Stock Return

Source of basic data: Center for Research on Security Prices, University of Chicago

GRAPH: Chart 4: A Classic Test of the CAPM

Source: Black, Jensen, and Scholes 1972

GRAPH: Chart 5: Repeating a Classic Test of the CAPM

Source: Ibbotson Associates 1992

GRAPH: Chart 6: During 1926-75

GRAPH: Chart 7: During 1976-80

GRAPH: Chart 8: During 1981-91

Source of basic data: Ibbotson Associates 1992

GRAPH: Chart 9: A Standard One-Beta Model

GRAPH: Chart 10: A Model With Human Capital and Time-Varying Betas..

GRAPH: Chart 11: . . . And Firm Size

Source: Jagannathan and Wang, forthcoming (Figures 1, 3, and 4)

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References Amihud, Yakov; Christensen, Bent Jesper; and Mendelson, Haim. 1992. Further evidence on the risk-return relationship. Working Paper S-93-11. Salomon Brothers Center for the Study of Financial Institutions, Graduate School of Business Administration, New York University. Banz, Rolf W. 1981. The relationship between return and market value of common stocks. Journal of Financial Economics 9 (March): 3-18. Black, Fischer. 1972. Capital market equilibrium with restricted borrowing. Journal of Business 45 (July): 444-55. -----. 1993. Beta and return. Journal of Portfolio Management 20 (Fall): 8-18. Black, Fischer, Jensen, Michael C.; and Schules, Myron. 1972. The capital asset pricing model: Some empirical tests. In Studies in the theory of capital markets, ed. Michael Jensen, pp. 79-121. New York:: Praeger. Breen, William L and Korajczyk, Robert A. 1993. On selection biases in book-to-mar-ket based tests of asset pricing models. Working Paper 167. Northwestern University. Chari, V. V.; Jagannathan, Ravi; and Ofer, Aharon R. 1988. Seasonalities in security returns: The case of earnings announcements. Journal of Financial Economics 21 (May): 101-21. Fama, Eugene E, and French, Kenneth R. 1992. The cross-section of expected stock returns. Journal of Finance 47 (June): 427-65. -----. 1993. Common risk factors in the returns on bonds and stocks. Journal of Financial Economics 33 (Fcbrury): 3-56. Fama, Eugene E, and MacBeth, James D. 1973. Risk, return and equilibrium: Empirical tests. Journal of Political Economy 81 (May-June): 607-36. Ferson, Wayne E., and Harvey, Campbell R. 1991. The variation of economic risk premiums. Journal of Political Economy 99 (April): 385-415. -----. 1993. The risk and predictability of international equity returns. Review of Financial Studies 6 (3): 527--66. Ferson, Wayne E., and Korajczyk, Robert A. 1995. Do arbitrage pricing models explain the predictability of stock returns? Journal of Business 68 (July): 309-49. Gibbons, Michael R. 1982. Multivariate tests of financial models: A new approach. Journal of Financial Economics 10 (March): 3-27. Harvey, Campbell R. 1989. Time-varying conditional covariances in tests of asset pricing models. Journal of Financial Economics 24 (October): 289-317.Ibbotson Associates. 1992. Stocks, bonds, bills, and infiation--1992 yearbook. Chicag Ibbotson Associates. Jagannathan, Ravi, and Wang, Zhenyu. 1993. The CAPM is alive and well. Research Department Staff Report 165. Federal Reserve Bank of Minneapolis. -----. Forthcoming. The conditional CAPM and the cross-section of expected returns. Journal of Finance. Kothari, S. R; Shanken, Jay; and Sloan Richard G. 1995. Another look at the cross-section of expected stock returns. Journal of Finance 50 (March): 185-224. Lintner, John. 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47 (February): 13-37. Mackinlay, A. Craig, and Richardson, Matthew P. 1991. Using generalized method of moments to test mean-variance efficiency. Journal of Finance 46 (June): 511-27. Mayers, David. 1972. Nonmarketable assets and capital market equilibrium under uncertainty. In Studies in the theory of capital markets, ed. Michael Jensen, pp. 223-48. New York: Praeger. Shanken, Jay. 1985. Multivariate tests of the zero-beta CAPM. Journal of Financial Economics 14 (September): 327-48. -----. 1992. On the estimation of beta-pricing models. Review of Financial Studies 5 (1): 1-33. Shaspe, William F. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19 (September): 425-42. Stambaugh, Robert E 1982. On the exclusion of assets from tests of the two-parameter model: A sensitivity analysis. Journal of Financial Economics 10 (November): 237-68.

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By Ravi Jagannathan, Visitor, Research Department, Federal Reserve Bank of Minneapolis and Piper Jaffray Professor of Finance Carlson School of Management University of Minnesota and Ellen R. McGrattan, Senior Economist, Research Department, Federal Reserve Bank of Minneapolis

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HOW THE CAPM HELPS CORPORATE MANAGERS

Models like the capital asset pricing model (the CAPM) help corporate managers by providing them with a practical way to learn about how investors judge the riskiness of potential investment opportunities. This helps managers use the sources of their firms more efficiently.

The Manager's Problem

In modern industrial economics, managers don't easily know what the firm's owners want them to do. Ownership and management are typically, quite separate. Managers are hired to act in the interests of owners, who bold stock in the corporation but are otherwise not involved in the business.

Owners send some general messages to managers through the stock market. If stockholders do not like what managers are doing, they sell their stocks, and the market value of the firm's stock drops. The representatives of stockholders on the firm's board of directors notice this and turn to the managers for corrective action. In this way, therefore, stock prices act like an oversight mechanism. They monitor the activities of managers by aggregating the opinions of the stockholders.

However, stock prices don't act fast enough. They don't give managers specific directions ahead of time about which projects to pursue and which to avoid. Managers must make these capital expenditure decisions on their own and then later find out, by the stock market's reaction, whether or not the firm's owners approve.

Disapproval can be costly. In the United States in 1992, for example, capital expenditures by the corporate business sector (excluding farming and finance) totaled $397 billion (or 6.6 percent of the annual gross domestic product). These expenditures usually cannot be recovered if stockholders disapprove of them.

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The Classic Solution

In view of this, capital budgeting has a central role in both the theory and the practice of managerial finance.

Theory suggests one simple nile for corporate managers to follow when making capital expenditure decisions: Maximize the value of the firm. Then, if some stockholders disagree with management decisions, they can sell their stock and be at least as well off as if management had made different decisions. This idea is the basis for the classic theoretical recommendation that managers only invest in those projects which have a positive net present value.

In practice, however, following that simple role is not simple. It requires, among other things, estimating the net present value of every project under consideration. Corporations thus spend a substantial amount of resources evaluating potential projects.

A key input to that process is the cost to the firm of financing capital expenditures, known more simply as the cost of capital. This is the expected rate of return that investors will require for investing in a specific project or financial asset. The cost of capital typically depends on the particular project and the risk associated with it. To be able to evaluate projects effectively, managers must understand how investors assess that risk and how they determine what risk premium to demand.

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The CAPM's Role

Providing such an understanding is the focus of most research in the area of asset pricing. An asset pricing model provides a method of assessing the riskiness of cash flows from a project. The model also provides an estimate of the relationship between that riskiness and the cost of capital (or the risk premium for investing in the project).

According to the CAPM, the only relevant measure of a project's risk is a variable unique to this model, known as the project's beta. In the CAPM, the cost of capital is an exact linear function of the rate on a risk-free project and the beta of the project being evaluated. A manager who has an estimate of the beta of a potential project can use the CAPM to estimate the cost of capital for the project.

If the CAPM captures investors' behavior adequately, then the historical data should reveal a positive linear relation between the average rerum on financial assets and their betas. Also, no other measure of risk should be able to explain the differences in average returns across financial assets that are not explained by CAPM betas. Empirical studies of the CAPM have supported tiffs model on both of those points -- recently, as the accompanying article describes.

toeinriver

Coolll!!![em02][em02]

sleepless

The article is great!!

but can you post the chart and figure ?