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Predicting Returns with Financial Ratios Authors: Jonathan Lewellen Source: Working Paper 4374-02, MIT Sloan School of Management Date: August 2002 |
Abstract
Predicting returns has been a subject of interest for a long time. Initial tests used past returns to predict future asset prices, such as those conducted by Kendall (1953). Later on, additional variables were considered, including dividend yield (DY), book-to-market (B/M) and the earnings-price ratio (E/P). These variables appear to be of particular interest in predicting asset returns, as they should be positively related to expected returns. However, empirical studies have concluded that their power to predict returns was weak. In this article, Lewellen argues that this can result from the correction of biases.
Predictive regressions are subject to biases in small samples and it is necessary to correct these biases. However, Lewellen notes that corrections used in previous studies, such as for example in Stambaugh’s (1999), may have understated the forecasting ability of these financial ratios. Therefore, in this article, he reconsiders the problem, and proposes new tests for investigating the predictive ability of these variables. The first variable considered in this article is DY, which is studied in detail. This variable is indeed the one of most concern in literature on asset predictability. B/M and E/P are also considered in this article.
The article firstly describes the predictive regression model that is used to conduct the tests, recalling the properties of these regressions. Asset returns are modelled using a predictive regression equation, where the predictive variable is one of the financial ratios. This predictive variable is modelled by an AR1 process. The residual terms of the two equations are correlated. In the case of a small sample, autocorrelations are biased downward, and this results in an upward bias in the beta coefficient of the regression. To test the predictive power of the financial ratios, Stambaugh (1999) considered an unconditional distribution of beta. According to Lewellen, it is possible to improve the small-sample adjustment by using information about the financial ratio’s sample autocorrelation. This is justified by the fact that sample autocorrelation is strongly correlated with the slope estimate in predictive regression. Therefore, the information added by the autocorrelation can help to produce a more powerful test of predictability. In particular, using information in the AR process, it is possible to derive an upper bound on the bias in beta. In this article, tests are thus based on the conditional distribution of betas. In fact, a conditional approach is superior to an unconditional approach, if the value of the autocorrelation is close to one.
Lewellen uses the described methodology to test whether DY, B/M and E/P forecast stock returns. The tests were made using the NYSE equal- and value-weighted indices. The period covered is January 1946 to December 2000 for DY and 1963-2000 for B/M and E/P. In order to test the robustness of the results, the 1946-2000 period was split into two sub-periods: 1946-1972 and 1973-2000. Recent years (1995-2000) were also considered separately. The results provide strong evidence of predictability in both the full sample and various sub-samples. This predictability is much stronger than the one determined by other studies. This is a result of the conditional standard error being much lower than the standard error estimated by Stambaugh.
The predictive power of B/M and E/P appears to be lower than that of DY, but stronger than the one found in previous studies. B/M has some power to forecast returns, but the evidence is less reliable than for DY. From 1963-1994, B/M and E/P forecast both equal- and value-weighted NYSE indices. When more recent data is included however, the ratios seem to predict only the equal-weighted index. As with DY, results show that conditional tests provide much stronger evidence of predictability than unconditional tests.
The last few years of the sample have a large impact on the results. For the value-weighted index, adding 1995-2000 to the regressions reduces the OLS slope on DY by 59%, the slope on B/M by 61%, and the slope on E/P by 28%.
References:
Kendall M., “The Analysis of Economic Time Series, part 1: Prices”, Journal of the Royal Statistical Society, vol. 96, 1953, p. 11-25.
Stambaugh R., “Predictive Regressions”, Journal of Financial Economics, vol. 54, 1999, p. 375-421.
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