Empirical Evidence. r Mt r ft e i. now do second-pass regression (cross-sectional with N 100): r i r f γ 0 γ 1 b i u i

Transcription

1 Empirical Evidence (Text reference: Chapter 10) Tests of single factor CAPM/APT Roll s critique Tests of multifactor CAPM/APT The debate over anomalies Time varying volatility The equity premium puzzle 1 Tests of single factor CAPM/APT recall CAPM: E r i r f β i E r M r f early tests: take 5 years of monthly data for a sample of stocks (e.g. 100), M proxy, monthly r f for each stock i estimate β i using a first-pass regression on the 60 months of data: r it r ft a i b i r Mt r ft e i now do second-pass regression (cross-sectional with N 100): r i r f γ 0 γ 1 b i u i where r i r f is the sample average (over the 60 monthly observations) of excess returns on the stocks 2

2 note that CAPM implies γ 0 0, γ 1 r M r f can also incorporate non-systematic risk: r i r f γ 0 γ 1 b i γ 2 σ 2 e i u i note the additional implication of CAPM that γ 2 0 results (Lintner 1965): γ 0 γ 1 γ 2 Coefficient Standard error r M r f = problems: b i s are measured with error since they are estimates b and σ 2 e are correlated Black, Jensen and Scholes (1972) advocate using portfolios, not individual stocks (reduces measurement errors in βs, also reduces σ 2 e) increases data requirements to maximize statistical power, we should group stocks by β when forming portfolios 4

3 recall zero β CAPM: E r i E r Z M E r M E r Z M β i BJS estimated the zero β return over time for each stock and averaged, finding r Z M r f implication: E r i r f E r Z M r f r i r f γ 0 γ 1 b i u i E r M E r Z M β i Fama and MacBeth (1973) augment BJS methods by also testing for nonlinear effect of β and effect of σ e : r i γ 0 γ 1 b i γ 2 b 2 i γ 3 σ ei u i 5 Roll s critique Roll (1977) uses properties of the efficient set to argue that CAPM is not directly testable the only testable hypothesis is that M is mean-variance efficient: all other implications (e.g. linear relationship with β) follow directly from efficiency of M in any sample of observations, there is an infinite number of historically efficient portfolios: returns of individual assets computed using β s with respect to such portfolios will automatically satisfy the SML relationship, regardless of whether M is efficient or not 6

4 for BJS/FM tests, we need to use M and not a proxy since β estimates can be quite different even if the proxy is highly correlated with M. Moreover, the proxy might be efficient even if M isn t, and if the proxy is inefficient, M might still be. Roll and Ross (1994) show analytically that using proxies which are very close to the efficient set can easily lead to rejections of CAPM (text Figure 10.1) 7 however, indirect evidence about CAPM can be found by comparing the performance of mutual fund managers vs. a good proxy for M if mutual fund managers outperform the proxy, then either the proxy is inadequate or the CAPM is wrong; if they cannot beat the proxy, it can be viewed as efficient (implying CAPM might be consistent with the data) the evidence here is strong: very few funds outperform the market index on a risk-adjusted basis, especially if MER s are accounted for. some funds do outperform the market over a given period: is it luck? Does superior performance persist over time? 8

5 Tests of multifactor CAPM/APT Chen, Roll, and Ross (1986) hypothesize that factors are: industrial production short term interest rate inflation risk premium on corporate debt term premium on government debt again test using 20 portfolios (grouped by size) first-pass regression: where X s are the factors r a b M r M b 1 X 1 b 5 X 5 e 9 second pass regression: r γ 0 γ M b M γ 1 b 1 γ 5 b 5 u γ s are estimated factor risk premia found that most important factors are industrial production, risk premium on corporate debt, and inflation M doesn t seem to matter if other factors are included conclusions don t seem to apply to Canada: market index still matters if other factors are included 10

6 The debate over anomalies note that we can interpret evidence of market inefficiency as counter to CAPM (or APT). Examples might include technical trading rules and anomalies (size, January, Mondays, holidays, etc.) recall the Fama and French (1992) paper, which found that size and book-to-market were better able to explain average returns than β (see text Table 10.4) some researchers have used more sophisticated econometric procedures and found evidence that is more supportive of CAPM an important recent study is Jagannathan and Wang (1996) argue that only a small percentage of the value of assets is actually traded try to account for value of human capital also argue that need to use conditional CAPM (because βs are conditional on the state of the economy) 11 factors include stock market index, size, risk premium on corporate debt, and growth rate of labour income if all variables are included, most important variables are the risk premium and labour income growth, size no longer matters also find that book-to-market is not important if risk premium and labour income growth are included moreover, report that the remaining Chen, Roll and Ross factors (term premiums, inflation, industrial production) do not matter if the human capital and risk premium factors are considered for importance of conditional version of CAPM, see text Figures 10.2 and

7 Time-varying volatility stock prices change primarily in reaction to new information the rate of arrival of new information varies over time volatility (i.e. variance or standard deviation) will not be constant over time, rather it should tend to be persistent (clustered) a large body of empirical evidence supports this improved modeling techniques should ultimately provide better tests of the risk/return relationship the most popular volatility models are GARCH models (generalized autoregressive conditional heteroskedasticity) there are numerous variations, a simple version is σ 2 t a 0 a 1 e 2 t 1 a 2 σ 2 t 1 problem: haven t yet established a reliable link to the conditional mean 13 The equity premium puzzle Mehra and Prescott (1985) examined data from and argued that, on average, stock returns in the U.S. have been too high relative to the risk free rate, i.e. that historical risk premia have been so high that it is inconsistent with reasonable levels of risk-aversion by investors many authors have subsequently tried to explain this finding (different utility functions, habit formation, statistical methods, etc.) Fama and French (2000) examine data from and report that the equity premium is almost twice as big post 1949 (8.41% vs. 4.62%) note that using realized returns (not expected returns) suggests that unexpected capital gains may be part of the puzzle suggests that future stock returns will not be as high 14

8 another possible explanation is survivorship bias most statistical tests in finance use data on firms which have survived for a long period (i.e. firms which disappear are typically excluded) this causes measured ex post returns to be higher than expected ex ante returns note that this also causes problems for testing persistence of mutual fund managers, if some of them get fired for poor performance 15