New Estimator of Expected Returns (Multi-Factor CAPM) vs. Fundamental Asset Risk (Single-Factor CAPM)

Transcription

1 New Estimator of Expected Returns (Multi-Factor CAPM) vs. Fundamental Asset Risk (Single-Factor CAPM) Seung-Mo (Jeff) Hong, PhD Assistant Professor of Economics Fordham University Dept. of Economics 441 E. Fordham Rd. DE E-530 Bronx, NY Tel: Fax: or JEL Classification: G0 Originally written in Fall

2 Table of Contents I. Introduction...3 II. NEER...4 II. A. The Model...4 II. B. Empirical Evidence...5 II. B. 1. Test Method...5 II. B. 2. Interpreting the Test Results...5 III. FAR...6 III. A. Time Horizon and Optimal Hurdle Rate III. B. Financing Considerations and Optimal Hurdle Rate...8 III. B. 1. NPV of Invesment...8 III. B. 2. Market Timing Gains or Losses...8 III. B. 3. Costs of Deviating from Optimal Capital Structure...9 III. B. 4. Optimal Investment and Financing Decisions...9 III. C. Case-specific Analysis...9 III. C. 1. When Capital Structure Is Not a Binding Constraint...10 III. C. 2. When Capital Structure Constraint is Binding without Price-Pressure Effects...10 III. C. 3. When Capital Structure Constraint is Binding with Price-Pressure Effects...10 III. D. Summary on Effects of Financing Considerations...11 IV. Conclusion...12 Bibliography

3 I. Introduction Over the years Sharpe-Lintner s original CAPM has given rise to several variations and improvements. Among some of them are approaches to interpret the model from intertemporal, conditional, multifactor, or consumption perspectives. Most of these attempts have been motivated by efforts to better explain and minimize the discrepancy between the hurdle rate that the CAPM beta requires to clear and the realistic rate of return the market requires to clear. A large volume of recent empirical research has found that i) cross sectional stock returns bear little or no discernible relationship to beta and ii) a number of other variables besides beta have substantial predictive power for stock returns. For example an important and reliable predictor is the book-to market ratio: the higher a firm s BE/ME, the greater its conditional expected return, ceteris paribus. 1 If the stock market is efficient and the predictable excess returns documented in recent studies are just compensation for risk, the hurdle rate should correspond exactly to the prevailing expected return. Then, which regression specification gives the best estimates of expected return? According to Fama & French, one must give up CAPM for the new and improved statistical method to set hurdle rates, which I will borrow the term from J. Stein and collectively label NEER (New Estimator of Expected Return). The NEER approach is advocated by Fama and French(1993). They couch the predictive content of the BE/ME ratio and other variables in a linear multifactor setting that can be interpreted as a variant of the APT or intertemporal CAPM. In response to NEER, Jeremy Stein(1996) favors FAR(Fundamental Asset Risk), a more elaborate version of CAPM in which he uses multi-facetted explanation in implementing CAPM, which will be discussed later. 2 In this paper, I will particularly attempt to compare, inter alia, the FF multifactor explanation of asset pricing anomalies, a version of NEER, with J. Stein s FAR and analyze contributions each of them makes to perfecting the methodology of CAPM application. 1 Fama and French (1992), Lakonishok, Schleifer, and Vishny (1994) 2 Actually, Stein isn t exactly discrediting or against NEER. He rather develops ground rules for selecting appropriate criteria to set hurdle rates according to different market conditions. I am only arbitrarily bending the terminology to contrast Stein vis-à-vis FF. 3

4 II. NEER II. A. The Model According to FF, average stock return is related to its size(me, stock price times n o. of shares), book to market equity(be/me, the ratio of the book value of common equity to its market value), earnings/price(e/p), cash flow/price(c/p), and past sales growth. 3 Fama and French maintain that many of the CAPM average-return anomalies are related, and they are captured by the three-factor model (1993), which says that the expected return on a portfolio in excess of the risk-free rate [E(Ri) Rf] is explained by the sensitivity of its return to three factors: i) the excess return on a broad market portfolio(rm Rf); ii) the difference between the return on a portfolio of small stocks(smb, small minus big); and iii) the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of low-book-to-market stocks (HML, high minus low) 4. E(Ri) Rf = b i [E(Rm) Rf] +s i E(SMB)+h i E(HML)...(1). E(Rm) Rf, E(SMB), and E(HML) are expected premiums, and the factor sensitivities or loadings, b i, s i, and h i are the slopes in the time-series regression. E(Ri) Rf = α i +b i [(Rm) Rf]+s i (SMB)+h i (HML)+ε i...(2). FF(1995) show that BE/ME and slopes on HML proxy for relative distress. Weak firms with persistently low earnings tend to have high BE/ME ratio and positive slopes on HML; strong firms with persistently high earnings tend to have low BE/ME and negative slope on HML. 5 The three-factor model captures the returns to portfolios formed on E/P, C/P, and sales growth. Low E/P, low C/P, and high sales growth are typical of strong firms that have negative slopes on HML. These negative loadings imply lower expected returns in (1) 6 Stocks with high E/P, C/P, or low sales growth 7 tend to load positively on HML. They 3 Banz(1981), Basu(1983), Rosenberg, Reid, Lanstein(1985), and Lakonishok, Shleifer and Vishny(1994) 4 The average HML return can be thought of as the premium for distress due to survivor bias; the data source for BE(COMPUSTAT) contains a disproportionate number of high BE/ME firms that survive distress, so the average return for high-be/me firms is overstated. Another view is that the distress premium is just data snooping ; researchers tend to search for and fixate on variables that are related to average return, but only in the sample used to identify them (Black(1993), McKinlay(1995)). A third view is that the distress premium is real but irrational, the result of investor over-reaction that leads to underpricing of distressed stocks and overpricing of growth stocks. (Fama and French, Multifactor Explanations of Asset Pricing Anomalies, The Journal of Finance, vol. 51, no. 1, March 1996) 5 High BE/ME < low BE/ME HML < 0 makes sense as assets rated high in the market would have low BE/ME. 6 Negative HML results in low E(R i ). 7 Because it s relatively difficult to trade. This may seemingly be counter-intuitive. However, weak firms will generally have higher variance and thus, higher return, i.e. higher E/P, but low sales growth as riskaverse investors shy away from these assets. 4

5 have higher average returns. 8 Stocks with low long-term past returns (losers) tend to have positive SMB and HML slopes on HML and low future returns. 9 The following instance of empirical success of (1) suggest that it is an equilibrium pricing model, a three factor version of Merton s (1973) intertemporal CAPM (ICAPM) or Ross s (1976) APT. II. B. Empirical Evidence II. B. 1. Test Method Summary of Three-Factor Regressions for Simple Monthly Percent Excess Returns on 25 Portfolios Formed on Size and BE/ME: 7/63-12/93, 366 Months. Rf is the one-month Treasury bill rate observed at the beginning of the month (from CRSP). The explanatory returns, Rm, SMB, and HML are forms as follows. At the end of June of each year t ( ), NYSE, AMEX, NASDAQ stocks are allocated to two groups (S or B) based on whether their June ME (stock price times shares outstanding) is below or above median ME for NYSE stocks. NYSE, AMEX, and NASDAQ stocks are allocated in an independent sort to breakpoints for the bottom 30%, middle 40%, and top 30% of the values of BE/ME for NYSE stocks. SMB is the difference between the average of the return on the three small-stock portfolios (S/L, S/M, and S/H) and the average of the returns on the three big-stock portfolios (B/L, B/M and B/H). HML is the difference between the average of returns on the two high-be/me portfolios (S/H and B/H), and the average of the return on the two low-be/me portfolios (S/Land B/L). BE is the COMPUSTAT book value of stockholders equity, plus balance sheet deferred taxes and investment tax credit, minus the book value of preferred stock. The BE/ME ratio used to form portfolios in June of year t is then book common equity for the fiscal year ending in calendar year t-1, divided by market equity at the end of December of t-1. Only firms with ordinary common equity (as classified by CRSP) are included in the tests. The market return Rm is the value-weighted return on all stocks in the size-be/me portfolios, plus the negative BE stocks excluded from the portfolio. II. B. 2. Interpreting the Test Results Average excess returns on the 25 Fama-French (1993) size -BE/ME portfolios of valueweighted NYSE, AMEX and NASD stocks show that small stocks tend to have higher returns than big stocks and high BE/ME stocks have higher returns than low BE/ME stocks. It also reports estimates of the three-factor time-series regression (2). If the threefactor model (1) describes expected returns, the regression intercepts should be close to Model (1), α 1 =0. The estimated intercepts say that the model leaves a large negative unexplained return for the portfolio of stocks in the smallest size and lowest 8 Positive HML results in higher E(R i ). 9 However, HML is not the causation for future returns. 5

6 BE/ME quintiles, and a large positive unexplained return for the portfolio of stocks in the largest size and lowest BE/ME quintiles.- Model (2), α 2 0. The F-test of Gibbons, Ross, and Shanken (GRS 1989) rejects the hypothesis that (1) explains the average returns on the 25 size-be/me portfolios at the level. - GRS rejects H 0 : Model(1), α i = 0. The rejection of the three factor model is testimony to the explanatory power of the regressions. The average of the 25 regression R 2 is 0.93, so small intercepts are distinguishable from zero. The model does capture most of the variations in the average returns on the portfolios. In the time series regression (2), the regression intercepts are net of (conditional on) variations in the expected premiums. Forming portfolios periodically on size, BE/ME, E/O, C/P, sales growth and past returns results in loadings on the three factors that are roughly constant. III. FAR III. A. Time Horizons and Optimal Hurdle Rates At t 0 the firm is initially all equity financed. At t 1 it will produce a single net cash flow of F. From the perspective of t 0, F is a normally distributed random variable. The firm also has the opportunity to invest $1 more at t 0 in identical asset if it chooses to and its physical assets will yield a total of 2F at t 1 in that case. If it does invest, the investment will be financed with riskless debt. The manager of the firm is assumed to have rational expectations and F r = EF denotes the manager s rational t 0 forecast of F. The shareholders biased expectations and their biased forecast of F is denoted by F b = EF(1+d). Thus d is a measure of outside investor s over-optimism. M denotes the NCF payoff on the Market Portfolio (Rm) at t 1. Pm denotes the price of the market portfolio at t 0. Rm=M/Pm-1 denotes the realized percentage return on the market. First, calculate the initial market price, P, of the firm s shares, before the investment decision has been made at t 0. Investors will all hold the market portfolio, and the market portfolio will be - in their eyes - mean-variance efficient. Second, the equilibrium return required by investors, k = Rf+β r [E(Rm) Rf]...(3) where β r is the usual rate of return β defined as β r = cov(f/p, m)/var(rm)...(4). The initial price of the firm s shares, P = F b /(1+k)...(5). Rearranging terms, P = Fβ β d [E(Rm) Rf]}/(1+Rf)...(6), where β d is dollar β defined as 6

7 β d = cov(f,rm)/var(rm)...(7). Analogous expressions with rational expectations would be k* = Rf+β*[E(Rm) Rf]...(8) β* = cov(f/p*, Rm)/var(Rm)...(9) P* = F r (1+k*)...(10) P* = {F r β[e(rm)-rf]}/(1+rf)...(11) where asterisk denotes unobserved rational expectation values. The best estimate of conditional expected return, CER = F r /P 1 = (1+k)/(1+δ)-1...(12). From a perspective of a rational observer, the stock may have a CER that is either greater or less than the CAPM rate k. In this sense, the model crudely captures that empirical irregularity that there are predictable returns on stock that are not related to their β s. These predictable returns simply reflect the biases of the outside investors. When δ = 0, investors have no bias, CER = k = k*. When δ > 0, the stock is overpriced, CER < k < k*. When δ < 0, the stock is underpriced, CER > k > k*. Two Possibilities about the Objective Function First, in NEER approach managers try to maximize outside investors perception of value. If they are acting on behalf of the shareholders who have to sell their stock in the near future, they will be more inclined to maximize current stock price. As long as the market s current valuation of the assets exceeds the acquisition cost, the current stock price will be increased if the assets are purchased. From manager s perspective, the expected cash flow on the investment is F r. Thus, the short-horizon hurdle rate, h s, that has the property that F r /(1+h s ) = P. Therefore, the manager should discount his F r at h s = CER. The implication is that if the manager is interested in maximizing the current stock price, he must cater to any misperception that investors might have. 10 Second, in FAR approach managers seek to maximize the PV of the firm s future CF. If they are acting on behalf of shareholders who will be holding for the longer term, they will be more inclined to maximize the PV of future CF. In this long-horizon case, the manager seeks to maximize his perception of the present value of future CF. The manager should only invest if the rational expectations value of the assets exceed their acquisition cost. Thus, the long-horizon hurdle rate, h l, has the property that F r /(1+h l ) = P*. The manager should discount Fr at h l = k*. According to equations (8) and (9), 10 In the sense that BE/ME is based upon investor s biased expectation, abnormally high ME means large bias or bubble. As the bubble is soon to fizz off, BE/ME can be considered short-term variable. Therefore, FF model may be treated as NEER in the same vein as h s. 7

8 the β* that is needed for this CAPM-like calculation is the unobserved rational expectations β. III. B. Financing considerations and Optimal Hurdle Rate In choosing an investment-financing combination in an inefficient market, Stein suggests to consider three factors: i) the NPV of the investment, ii) the market timing gains and losses, and iii) the extent of deviation from optimal capital structure of the firm. 11 III. B. 1. The NPV of Investment To the extent that financing considerations have consequence for hurdle rates, it will effectively shorten manager s time horizon. This will make him behave in more of a NEER fashion. In the absence of financing concerns, managers take a FAR approach, and seek to maximize the PV of future CF. The FAR-based NPV is thus f(k)p*/f r K, or f(k)/(1+k*) K, where k* is given by (8) and (9). The amount invested at t 0 will be a continuous variable, K. The gross expected proceeds at t 1 from this investment are given by f(k), an increasing, concave function. III. B. 2. Market Timing Gains or Losses We adopt Eq > 0 means equity issue by the firm and Eq < 0 means repurchase, where Eq denotes the dollar amount of equity raised by selling new shares at t 0. If the firm is able to repurchase its own equity w/o any price-pressure effects, the market timing gains from the perspective of the manager are given by the difference between market s initial t 0 valuation of the shares and the manager s t 0 valuation. For a transaction of size Eq, this market timing gain is simply E(1 P*/P). 12 We assume that the announcement effects completely eliminate the potential for market timing gains. However, the net-ofpressure market timing gains are given by E(1 P*/P) i(eq), where i(eq) is the priceimpact-related losses associated w/ an equity transaction of size Eq, with i(0) = 0. Other restrictions are: i) when Eq > 0, di/deq 0, when Eq < 0, di/deq 0; ii) d 2 i/deq 2 0 everywhere which means that equity issues tend to knock prices down, while repurchases push prices up w/ larger effects for larger transactions in either direction. III. B. 3. Costs of Deviating from Optimal Capital Structure If a firm decides to invest and to engage in repurchases to take advantage of low stock price, leverage may increase to the point where expected costs of financial distress 11 One possibility that Stein ignores is that managers might wish to take advantage of market inefficiencies by transacting in the stock of other firms. He treats this in the later part of his paper, and maintains that it need not materially affect the conclusions of his analysis. 12 We continue to assume that when the firm issues debt, this debt is fairly priced, so that there are no market timing gains or losses. This assumption can be relaxed w/o affecting the qualitative results to follow. 8

9 become significant. Assume that the optimal debt ratio is D and that prior to the investment and financing choices at t 0, the firm is exactly at this optimum. Thus, after it has invested an amount K and raised an amount of new equity Eq, it will be overleveraged by an amount L = K(1 D) Eq. Assume this imposes a cost of Z(L). To the extent that there are costs of deviating, these costs are a convex function of the distance from the optimum. So, dz/dl 0 when L > 0, and dz/dl 0 when L < 0. Also, d 2 Z/dL 2 0 everywhere. III. B. 4. Optimal Investment and Financing Decisions Taking all three considerations together, the manager s objective function is max f(k)p*/f r -K+E(1 P*/P) i(eq) Z(L)...(13) subject to L = K(1 D -Eq. The first order conditions are df/dk-[1+(1 D)dZ/dL]F r /P* = 0... (14), (1 P*/P) di/deq+dz/dl = 0...(15). Optimal investment satisfies df/dk = DF r /P*+(1 D)(F r /P+di/dEq) = D(1+k*)+(1 D)(1+CER+di/dEq)...(16). III. C. Case-Specific Analysis III. C. 1. When Capital Structure is Not a Binding Constraint First, if dz/dl= 0, i.e., there are no marginal costs or benefits to changing leverage, the Z function must be flat in the neighborhood of the optimal solution. If the Z function happens to be flat in the region near L = 0, the firm will be left in a position where incremental increases in leverage would have only a trivial impact on costs of financial distress. When dz/dl = 0, investment and financing decisions are fully separable, because capital structure can adjust costlessly to take up the slack between the two at the margin. The optimal behavior in this case is as follows: When capital structure is not a binding constraint, and the manager has long horizon, the optimal policies are always to set the hurdle rate at the FAR value of k* and to issue stock if the CER < k*(meaning δ > 0 that the stock is overpriced), but repurchase stock if CER > k*(meaning δ < 0 that the stock is under-priced). In other words, when the stock price is low and the CER is high, the firm repurchases shares. However, the repurchase does not affect its hurdle rate, because capital structure is fully flexible (dz/dl = 0). Rather, the firm adjusts to the repurchase purely by taking on more debt. Therefore, investment should be evaluated vis-à-vis fairly priced debt 9

10 finance. Conversely, when the stock price is high and the CER is low, the firm issues shares. III. C. 2. When Capital Structure Constraint is Binding without Price-Pressure Effects Suppose dz/dl 0 and di/deq = 0, then df/dk = D(1+k*)+(1 D)(1+CER)...(17), which means When the capital structure constraint is binding and there are no pricepressure considerations, the optimal hurdle rate is between the NEER and FAR values of CER and k* respectively. As D approaches 0, the hurdle rate converges to CER, and as D approaches 1, the hurdle rate converges to k*. When capital structure imposes a binding constraint, one cannot separate investment and financing decisions. For each dollar devoted to investment, there is less cash available to engage in such repurchases, holding the capital structure fixed. In the extreme case where D = 0, each dollar of investment leaves one full dollar less available for repurchase(the opportunity cost of investment is simply the expected return on the stock), and financial constraints force managers into behaving exactly as if they were interested in maximizing short-term stock prices simply because, in order to leave capital structure undisturbed, any investment must be fully funded buy an immediate stock issue. In the intermediate cases, where 0 < D < 1, investment need only be partially funded by stock issue. This implies that the hurdle rate moves less than one-for-one with the CER. When D = 1, and investment can be entirely debt financed, the hurdle rate remains at the FAR value of k*, irrespective of CER on the stock. III. C. 3. When Capital Structure Constraint is Binding with Price-Pressure Effects When Stock is undervalued(δ < 0), L >0, the firm will choose to be over-leveraged relative to the static optimal capital structure of L = 0. However, the firm may either issue or repurchase shares meaning the sign of Eq is ambiguous, because on the one hand, the fact that δ < 0 makes a repurchase attractive from a market timing standpoint; on the other, given that the firm is investing, it needs to raise some new equity if it does not wish to see its capital structure deviate too far out of line. Depending on which effect dominates, there can either be a net share repurchase or share issue. When the capital structure constraint is binding, there are price-pressure considerations, δ < 0 and Eq < 0, the optimal hurdle rate is always between the NEER and the FAR values. The stronger the price-pressure effects - i.e. the larger di/deq in absolute magnitude - the lower the hurdle rate, ceteris paribus, and therefore, the closer the hurdle rate to the FAR value of k*. When price-pressure effects are strong, the hurdle rate is more according to a FAR approach, because price-pressure leads the firm to limit the scale of its repurchase activity. Consequently, capital structure is not much distorted, and there is less influence 10

11 of financial constraints on investment. When price-pressure effects are very weak, again, the optimal hurdle rate is between the NEER and FAR values of CER and k* respectively. As D approaches 0, the hurdle rate converges to CER, and as D approaches 1, the hurdle rate converges to k*. When the capital structure is binding and there are price-pressure considerations, δ < 0, and Eq > 0, then the optimal hurdle rate no longer necessarily lies between the NEER and FAR values. It may exceed them both, though it will never be below the lower of the two, the FAR of k*. The stronger are price-pressure effects -i.e., the larger di/deq is in absolute magnitude - the higher the hurdle rate, ceteris paribus. Equation (16) stipulates that optimal investment will satisfy df/dk = (1+k*)+(1-D)di/dEq. In other words, the hurdle rate is a mark-up over the NEER/FAR value of k*, with the degree of mark-up determined by the magnitude of price-pressure effect. If δ > 0, stock is overvalued. When δ > 0, there is no ambiguity about the sign of Eq, because both market timing considerations and the need to finance investment now point in the same direction, implying a desire to sell the stock. So, Eq > 0. When the capital structure constraint is binding, there are price pressure considerations, δ > 0 and Eq > 0, then the optimal hurdle rate no longer necessarily lies between the NEER and FAR values. It may exceed them both though it will never be below the lower of the two, the NEER value of CER. The stronger the pricepressure effects - i.e., the larger di/deq in absolute magnitude, the higher the hurdle rate, ceteris paribus. III. D. Summary on the Effects of Financing Considerations Financing considerations shape the optimal hurdle rate in three distinct ways. First, the shape of Z function measures the degree to which deviations in capital structure are costly. When such deviations are insignificant, this tends to favor a FAR-based approach. When such deviations are costly, the optimal hurdle rate is pushed in the NEER direction. Second, the debt capacity, D, of the new investment: The lower is D, the more pronounced an effect capital structure constraints have in terms of driving the hurdle rate toward the NEER value. Third, the extent to which share issues or repurchases have price-pressure consequences. Although the impact of which is ambiguous, in case where the firm engages in repurchase, price-pressure considerations unambiguously move the hurdle rate closer to the FAR value of k*; when the firm issues equity, price pressure exerts an upward influence on the hurdle rate. 11

12 Overall, in order for a FAR-based approach to make sense, i) not only must managers have long horizons, ii) but they also must be relatively unconstrained by their current capital structure. IV. Conclusion Empirical results seem to support NEER approach quite well. In CAPM, all sources of return variance are equivalent to investors. Investors hold mean-variance-efficient portfolios and the market portfolio is MVE. This means that the expected excess returns on all market portfolio are fully explained by their market βs. Thus, one way to test whether a multifactor return process collapses to CAPM is to test whether the expected excess returns on MMV (multifactor-minimum-variance) portfolios are explained by their market βs. If the test is run by CAPM, FF size-be/me portfolios report that the GRS tests always rejects the CAPM at the 0.99 level (p-values less than 0.01). The CAPM fails because univariate market β s show little relation to variables like BE/ME, E/P, C/P and sales rank, that are strongly related to average returns. According to FF size-be/me test mentioned in II. B. 1., the average absolute pricing errors (intercepts) of the CAPM are large (25 to 30 basis points per month), and they are three to five times those of the threefactor model. It is critical, however, to the Fama-French logic that the return differentials associated with the BE/ME ratio and other predictive variables be thought of as compensation for fundamental risk. While variables such as BE/ME do indeed have predictive content, it is much less clear whether this reflects anything to do with risk. As discussed in III. C., it seems obvious that NEER makes the most sense when either i) managers are interested in maximizing short-term stock prices or ii) the firm faces financial constraints. FAR, on the other hand, is preferable when managers are interested in maximizing long-run value and the firm is not financially constrained. In contrast to detailed empirical test results of FF, Stein doesn t provide as much empirical results. However, he cites an existing evidence from the empirical studies undertaken in earlier periods by Ball and Brown(1969), Beaver, Kettler and Scholes (1970). In this literature, the basic hypothesis being tested is whether accounting β s for either individual stocks or portfolios are correlated w/ β s estimated from stock returns. In the work by Beaver and Manegold (1975), accounting β s are defined in a very similar way to the following equation which develops an empirical analog of β*: β* = cov( F i /F i, M/M)/var( M/M)...(18) 12

13 where F i and M are the CF accruing to stock i and the market. 13 According to this, Beaver and Manegiold s (1975) results would seem to indicate that there is indeed a fairly close correspondence between stock market β s and fundamental risk. Then, Stein s bottom line is that at least it may not be totally unreasonable to assume simultaneously that stocks are subject to large pricing errors and that a β estimated from stock returns can provide a good measure of the fundamental asset risk β*. In the right circumstances, therefore, the textbook CAPM approach may ultimately be justifiable, which rests on three key premises. First, one must be willing to assume that the cross-sectional patterns in stock returns reflect pricing errors, rather than compensation for fundamental sources of risk. Second, the firm must have long horizons and be relatively unconstrained by its current capital structure. Finally, it must be the case that a β estimated from stock returns is a satisfactory proxy for the fundamental riskyness of the firm s CF. 13 We need also to assume that the rational expectations value of a stock is the PV of the expected CF to equity discounted at a constant rate, and further that CF follows random walk, so today s level is a sufficient statistic for future expectations. 13

14 Bibliography Ball, R., and Brown, P Portfolio theory and accounting, Journal of Accounting Research 7 (Spring): Banz, Rolf W The relationship between return and market value of common stocks. Journal of Financial Economics 9 (March): 3-18 Beaver, William; Kettler, Paul; and Scholes, Myron The association between market-determined and accounting-determined risk measures. Accounting Review (October): Beaver, William and Manegold, James The association between market-determined and accounting determined measures of systematic risk: Some further evidence. Journal of Financial and Quantitative Analysis 43 (June): Chan, K. C. and Nai-fu Chen, 1991, Structural return characteristics of small and large firms, Journal of Financial Economics 40: DeBondt, Werner F.M., and Thaler, Richard H Does the stock market overreact? Journal of Finance 40 (July): Fama, Eugene F., and French, Kenneth R The cross-section of expected stock returns. Journal of Finance 47 (June): Fama, Eugene F., and French, Kenneth R Common risk factor in the returns on stocks and bonds. Journal of Financial Economics 33 (February): 3-56 Fama, Eugene F., and French, Kenneth R. 1995, Size and book-to-market factors in earnings and returns, Journal of Finance 50: Fama and French, Multifactor Explanations of Asset Pricing Anomalies, The Journal of Finance, vol. 51, no. 1, March 1996 Huberman Gur, and Shumel Kandal, 1987, Mean-variance spanning, Journal of Finance 42: Lakonishok, Josef; Schleifer, Andrei; and Vishny, Robert W Constrarian investment, exploration, and risk, Journal of Finance 49 (December): McKinlay, A. Craig Multifactor models do not explain deviations from the CAPM, Journal of Financial Economics 38 (May): 3-28 Roll, Richard, 1977, A critique of the asset pricing theory s tests Part I: On past and potential testability of the theory, Journal of Financial Economics 4: Schleifer, Andrei, and Vishny, Robert Liquidation values and debt capacity: A market equilibrium approach, Journal of Finance 47 (September): Stein, Jeremy C., Rational Capital Budgeting in Irrational World, Journal of Business, 1996, vol 69, no. 4: