THE ASSET-PRICING MODEL OF Sharpe,Lintner,and Black
has long shaped the way academics and practitioners think about average
returns and risk. The central prediction of the model is that the market
portfolio of invested wealth is mean-variance efficient in the sense of
Markowitz.The efficiency of the market portfolio implies that (a)
expected returns on securities are a positive linear function of their market
βs (the slope in the regression of a security's return on the market's return),
and (b) market βs suffice to describe the cross-section of expected returns.
There are several empirical contradictions of the Sharpe-Lintner-Black
(SLB) model. The most prominent is the size effect of Banz.
このモデルの予想の核となるものは、投資された資産の市場ポートフォリオが、マーコウィッツの言う「平均および分散能力が長けている」状態になる、ということである。
市場ポートフォリオの効率の良さは、証券の期待されるリターンが市場βの正値加法的汎関数（市場リターンにおける証券リターンの回帰の傾き）に一致することを意味し、かつ市場βは、期待されるリターンの交差部分を描写するのに十分な量に達する（b）。
Sharpe-Lintner-Blackモデル（SLBモデル）のいくつかの実証的な矛盾がある。
最も際立つのはBanzのサイズ効果である。
He finds
that market equity, ME (a stock's price times shares outstanding), adds to
the explanation of the cross-section of average returns provided by market
βs. Average returns on small (low ME) stocks are too high given their β estimates, and average returns on large stocks are too low.
Another contradiction of the SLB model is the positive relation between
leverage and average return documented by Bhandari. It is plausible
that leverage is associated with risk and expected return, but in the SLB
model, leverage risk should be captured by market β. Bhandari finds, howev
er, that leverage helps explain the cross-section of average stock returns in
tests that include size (ME) as well as β.
Stattman and Rosenberg find that average
returns on U.S. stocks are positively related to the ratio of a firm's book
value of common equity, BE, to its market value, ME. Chan, Hamao, and find that book-to-market equity, BE/ME, also has a strong
role in explaining the cross-section of average returns on Japanese stocks.
Finally, Basu shows that earnings-price ratios (E/P) help explain
the cross-section of average returns on U.S. stocks in tests that also include
size and market β. Ball argues that E/P is a catch-all proxy for
unnamed factors in expected returns; E/P is likely to be higher (prices are
lower relative to earnings) for stocks with higher risks and expected returns,
whatever the unnamed sources of risk.
Ball's proxy argument for E/P might also apply to size (ME), leverage, and
book-to-market equity. All these variables can be regarded as different ways
to scale stock prices, to extract the information in prices about risk and
expected returns. Moreover, since E/P, ME, leverage, and BE/ME are all scaled versions of price, it is reasonable to expect that some of them are redundant for describing average returns. Our goal is to evaluate the joint roles of market β, size, E/P, leverage, and book-to-market equity in the cross-section of average returns on NYSE, AMEX, and NASDAQ stocks.
Black finds that as predicted, there is a positive simple relation between average stock returns and β during the pre-1969 period.
Like Reinganum and and Shapiro,we find that the relation between
β and average return disappears during the more recent 1963-1990 period,
even when β is used alone to explain average returns. The appendix shows
that the simple relation between β and average return is also weak in the
50-year. In short, our tests do not support the most basic
prediction of the SLB model, that average stock returns are positively related
to market βs.
Unlike the simple relation between β and average return, the univariate
relations between average return and size, leverage, E/P, and book-to-market
equity are strong. In multivariate tests, the negative relation between size and average return is robust to the inclusion of other variables.
The positive relation between book-to-market equity and average return also persists in
competition with other variables. Moreover, although the size effect has
attracted more attention, book-to-market equity has a consistently stronger
role in average returns. Our bottom-line results are: (a) β does not seem to
help explain the cross-section of average stock returns, and (b) the combination
of size and book-to-market equity seems to absorb the roles of leverage
and E/P in average stock returns, at least during our 1963-1990 sample
period.
If assets are priced rationally, our results suggest that stock risks are
multidimensional. One dimension of risk is proxied by size, ME.
Another dimension of risk is proxied by BE/ME, the ratio of the book value of common equity to its market value.
It is possible that the risk captured by BE/ME is the relative distress
factor of Chan and Chen. They postulate that the earning prospects of
firms are associated with a risk factor in returns. Firms that the market
judges to have poor prospects, signaled here by low stock prices and high
ratios of book-to-market equity, have higher expected stock returns (they are
penalized with higher costs of capital) than firms with strong prospects.It is also possible, however, that BE/ME just captures the unraveling (regression
toward the mean) of irrational market whims about the prospects of firms.
Whatever the underlying economic causes, our main result is straightforward.
Two easily measured variables, size (ME) and book-to-market equity
(BE/ME), provide a simple and powerful characterization of the cross-section
of average stock returns for the 1963-1990 period.
In the next section we discuss the data and our approach to estimating β.
Section II examines the relations between average return and β and between
average return and size. Section III examines the roles of E/P, leverage, and
book-to-market equity in average returns. In sections IV and V, we summarize,
interpret, and discuss applications of the results.
