Jay Shanken

A test of the efficiency of a given portfolio

A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate test, equivalent to our multivariate-based method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics. Copyright 1989 by The Econometric Society.

Book-to-Market, Dividend Yield, and Expected Market Returns: A Time-Series Analysis

We find reliable evidence that both dividend yield and book-to-market (B/M) track time-series variation in expected real one-year stock returns over the period 1926-91 and the subperiod 1941-91. The B/M relation is stronger over the full period, while the dividend yield relation is stronger in the subperiod. For the equal-weighted index, the full- period slope coefficient on B/M is so large as to imply that expected real returns are sometimes negative, raising doubts about market efficiency. In this case, the hypothesis that expected real returns are never negative is rejected, using bootstrap methods, at the 0.02 level. A Bayesian bootstrap procedure implies that an investor with prior belief 0.5 that expected real returns are never negative comes away from the B/M evidence dramatically revising that belief, with posterior probability only about 0.05 for the hypothesis. The post-40 evidence is consistent with expected returns always being positive, however.

Intertemporal asset pricing : an empirical investigation

Abstract The conditional efficiency of an unspecified portfolio of a value-weighted stock index and a long-term government bond index is rejected in a framework that permits the factor risk-premia, asset betas, and residual variances to vary with the levels of observable state variables. Both the level and volatility of one-month T-bill rates are found to be associated with economically important shifts in the investment characteristics of size and industry portfolios and stock and bond indexes. January seasonals in equity variance and small-firm interest rate risk are also observed.

Problems in measuring portfolio performance An application to contrarian investment strategies

We document problems in measuring raw and abnormal five-year contrarian portfolio returns. ‘Loser’ stocks are low-priced and exhibit skewed return distributions. Their 163% mean return is due largely to their lowest-price quartile position. A %ith price increase reduces the mean by 25%, highlighting their sensitivity to microstructure/liquidity effects. Long positions in low-priced loser stocks occur disproportionately after bear markets and thus induce expected-return effects. A contrarian portfolio formed at June-end earns negative abnormal returns, in contrast with the December-end portfolio. This conclusion is not limited to a particular version of the CAPM.

Lack of timeliness and noise as explanations for the low contemporaneuos return-earnings association

We assess earnings lack of timeliness and value- irrelevant noise in earnings as explanations for the weak contemporaneous return-earnings association. Earnings lack timeliness because objectivity, verifiability, and conservatism conventions underlie the accounting measurement process. Noise in earnings is uncorrelated with returns in all periods. It likely gets introduced when estimates of future cash flows that differ from the markets estimates are included in earnings determined by accounting rules. Consistent with earnings lacking timeliness, we find current and future return earnings adjusted for expectational errors explain roughly 3-6 times as much of the annual return variation than current earnings alone.

Multivariate tests of the zero-beta CAPM

Abstract A ‘cross-sectional regression test’ (CSRT) of the CAPM is developed and its connection to the Hotelling T2 test of multivariate statistical analysis is explored. Algebraic relations between the CSRT, the likehood ratio test and the Langrange multiplier test are derived and a useful small-sample bound on the distribution function of the CSRT is obtained. An application of the CSRT suggests that the CRSP equally-weighted index is inefficient, but that the inefficiency is not explained by a firm size-effect from February to December.

Learning, Asset-Pricing Tests, and Market Efficiency

This paper studies the asset-pricing implications of parameter uncertainty. We show that, when investors must learn about expected cash flows, empirical tests can find patterns in the data that differ from those perceived by rational investors. Returns might appear predictable to an econometrician, or appear to deviate from the Capital Asset Pricing Model, but investors can neither perceive nor exploit this predictability. Returns may also appear excessively volatile even though prices react efficiently to cash-flow news. We conclude that parameter uncertainty can be important for characterizing and testing market efficiency.

Multivariate proxies and asset pricing relations: Living with the Roll critique

Abstract A framework is developed in which inferences can be made about the validity of an equilibrium asset pricing relation, even though the central aggregate in this relation is unobservable. A multivariate proxy for the true market portfolio, consisting of an equal-weighted stock index and a long-term government bond index, is employed in an investigation of the Sharpe-Lintner CAPM. The empirical evidence suggests that we can reject the joint hypothesis that (a) CAPM is valid, and (b) multiple correlation between the true market portfolio and proxy assets exceeds 0.7. Connections to the equilibrium factor pricing literature are also explored.

Stock return variation and expected dividends: A time-series and cross-sectional analysis

Abstract This paper examines the extent to which aggregate stock return variation is explained by variables chosen to reflect revisions in expectations of future dividends. In effect, we decompose realized dividend growth into expected and unexpected components using information in aggregate investment, dividend yield, and future returns. A parsimonious specification accounts for over 70% of annual return variation. We also conduct a cross-sectional experiment using portfolios formed on the basis of annual return performance. This analysis shows that nearly 90% of the portfolio return variation is explained by dividend and expected return variables.

A BAYESIAN APPROACH TO TESTING PORTFOLIO EFFICIENCY

Abstract This paper develops a Bayesian test of portfolio efficiency and derives a computationally convenient posterior-odds ratio. The analysis indicates that significance levels higher than the traditional 0.05 level are recommended for many test situations. In an example from the literature, the classical test fails to reject with p-value 0.082, yet the odds are nearly two to one against efficiency under apparently reasonable assumptions. Procedures for testing approximate efficiency and for aggregating subperiod results are also considered.