Stock selection, style rotation, and risk

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Abstract

Using US data from June 1984 to July 1999, we show that the impact of firm-specific characteristics like size and book-to-price on future excess stock returns varies considerably over time. The impact can be either positive or negative at different times. This time variation is partially predictable. We investigate whether the partial predictability signals security mispricing or risk compensation by formulating alternative modeling strategies. The strategies are compared empirically. In particular, we allow for a state-dependent choice of investment styles rather than a once-and-for-all choice for a particular style, for example based on high book-to-price ratios or small market cap values. Using alternative ways to correct for risk, we find significant and robust excess returns to style rotating investment strategies. Business cycle oriented approaches exhibit the best overall performance. Purely statistical models for style rotation or fixed investment styles reveal less robust behavior.

Introduction

In examining the forecasting power of firm characteristics for excess returns, the academic literature conventionally focuses on long-term averages of monthly and annual returns. The systematic patterns found provide evidence that some equity classes generate above-average returns in the long run. In particular, value stocks outperformed growth stocks historically, and small capitalization stocks had higher annual returns than large capitalization stocks. See for example the papers of Fama and French (1992), La Porta (1996), Daniel and Titman (1997), Barber and Lyon (1997) and Lewellen (1999). In the investment management industry nowadays, value and size strategies are used for discriminating relative future performance. This implementation is known as style investing.

At least, three alternative theories have been put forward to explain the long-term outperformance of value and small capitalization stocks. First, the firm variables might proxy for a risk factor. Fama and French (1993), Jensen et al. (1997) and Lewellen (1999) argue that the higher returns are a compensation for higher risk. Firms with similar firm characteristics are sensitive to the same macroeconomic factors like economic growth surprises and interest rate risk. A second and alternative view is that the firm variables provide information about security mispricing. Lakonishok et al. (1994) suggest that the higher returns on value strategies are due to an incorrect extrapolation of past stock performance. La Porta (1996) finds evidence that value strategies work because expectations about future growth in earnings are too optimistic. As a third possible reason for reported outperformance, it can be argued that unexpected technological innovations are historically more related to particular equity classes. As a result, the uncovered return patterns can be due to data snooping, see, e.g., Lo and MacKinlay (1990), Black (1993) and MacKinlay (1995).

The performance of value or size related investment styles is not stable over time. Some periods depart from the long-term patterns documented in the literature. Chan et al. (2000), for example, show that the regular size and value effects are inverse over the period 1990 through 1998. This can be a major worry for professional investment managers with value or size-based investment styles. Returns over a multi-year period are frequently not a sufficient factor to consider a particular fixed investment style a success. Professional money managers are often assessed on their intra-year returns relative to a prespecified benchmark. Both annual outperformance and intra-year variability of the outperformance are important (Roll, 1992). Managers are therefore looking for systematic patterns in the time-varying impact of value and size on returns in order to enhance their performance. As argued above, such patterns may be caused by macroeconomic conditions.

Some authors use the time-variation in the relation between firm characteristics and returns to investigate whether the mispricing or risk compensation view provides a more plausible explanation for realized excess returns. Fama and French (1993), Daniel and Titman (1997) and Lewellen (1999), for example, examine the returns on value and size based investment styles using a factor model with three factors: (i) the returns on a value-weighted market portfolio, (ii) the excess returns on a small-capitalization over a large-capitalization portfolio, and (iii) the excess return on a high book-to-market portfolio over a low book-to-market portfolio. By relating returns on value or size-based investment styles to current realizations of the risk factors, the authors argue that excess returns are more in line with the risk compensation rather than with the mispricing view.

Our paper adds to the current literature on asset pricing by further examining whether Size and book-to-price generate excess returns. Previous papers focused on models that imply fixed investment styles, mainly small Size and/or high book-to-price. By contrast, our model allows the investment style to vary over time. We investigate whether style effectiveness shows any persistence over time. In particular, we test whether the impact of Size and book-to-price varies with macroeconomic conditions. For this, we formulate both statistical time-series models for style rotation and macroeconomic regression models. We correct any excess returns of such style rotation schemes for risk using either a standard market (one-factor) model or the Fama–French three-factor model, mentioned above. If the excess returns are explained by these factor models, risk corrected excess returns will be insignificant. As a result, the risk compensation rather than the mispricing view will then appear to be more plausible.

As a first result, we find that for no rotation and for pure statistical rotation schemes the risk compensation view provides an adequate explanation of realized excess returns. More striking results are obtained, however, if we consider a variant of our model in which we relate style effectiveness explicitly to macroeconomic conditions. This model produces a bilinear forecasting framework. Bilinear models to examine the value and size styles can also be found in He et al.(1996). Our approach and goals, however, differ markedly. They use 25 portfolios sorted by book to market and size and they assume that expectations of investors are unbiased. Their aim is to find a disrete time equilibrium multifactor model that is consistent with the returns of the 25 portfolios. He et al. (1996) conclude that their models are inconsistent with the portfolio return data. By contrast, we aim at predicting future individual stock returns. No assumptions about rational expectations are made.

We use two macroeconomic variables in our style rotation model. The first variable is the term-spread of interest rates, which is defined as the long-term interest rate minus the short-term rate. At least two reasons can be given for the potential influence of this variable on expected stock returns. First, the term spread can be considered as an indicator of economic activity. In an expanding economy, it decreases because short rates generally rise more than long rates. Similarly, during a contraction, it generally increases. Hence, the term spread may affect expected stock market returns because of the effect on expected company earnings (see, also, Schwert, 1990, Chen, 1991, Jensen et al., 1996). This suggests that in periods of a small term spread some equity classes, likely to be small and rapidly growing firms, show higher returns as a result from higher and better quality earnings expectations. Second, the term spread affects the sensitivity of stock prices to changes in interest rates. An increase in the term spread causes short-term earnings to play a relatively more important role in a dividend or free-cash flow discount model, while the long-run earnings are relatively less significant. How shifts of the term structure of interest rates influence a stock price depends on the term spread and distribution of earnings. Consequently, equity premia, which are among other factors determined by interest rate risks, may differ over equity classes. The second macroeconomic variable is a composite of leading indicators of the business cycle. Different equity classes may profit in different ways from changes in the business cycle. We hypothesize that especially small and growing firms are likely to be flexible to react on and profit from improving economic conditions. Large and mature firms are in general more diversified, which makes them less sensitive to deteriorating economic circumstances.

The results reveal that style rotation based on macroeconomic predictive variables generates historical excess returns. In order to prevent data snooping biases, we check the robustness of our results to a range of alternative specifications. In particular, we show that the excess returns remain significant after various ways of risk-correction. In addition to the earlier literature, we also investigate the robustness of the results with respect to the portfolio rebalancing period. We use monthly, quarterly, semi-annual, and annual horizons. It turns out that risk-corrected returns reveal a remarkable stability for the business cycle based model, especially for the stocks with the strongest ex-ante predicted outperformance. By contrast, excess returns on traditional, fixed investment styles (size or book-to-price) or on purely statistical style rotation schemes are not robust with respect to the rebalancing horizon. Moreover, the business cycle model returns are also robust to the way portfolios are constructed and the way potential outliers are dealt with. In short, the results point out that the rotating investment styles based on firm characteristics and macroeconomic predictors provide consistent and robust (risk-corrected) excess returns. Risk correction is performed using a one-factor market model or the three-factor Fama–French model. Therefore, the excess returns on style rotation schemes appear incompatible with the standard risk compensation view using the three Fama–French risk factors. This provides a further dimension to the current debate by allowing more flexibility in the choice of investment strategies.

The paper is organized as follows. In Section 2, we give a description of the data. In Section 3, we describe the time-varying impact of firm characteristics on excess returns. We focus on value and size-based investment styles and test whether there is any evidence of systematic patterns in the time-variation. In Section 4, we provide alternative modeling approaches to transform predictability into style rotation schemes. In Section 5, we implement the models and discuss the results. Section 6 concludes the paper.

Section snippets

The data

The firm-specific data come from two sources. Monthly stock price and dividend data in the period from June 1984 to July 1999 come from Interactive Data Corporation (IDC). IDC is a leading provider of securities pricing data. Our prices and dividends are adjusted for stock splits. Monthly total returns are calculated using these price and dividend data. The monthly returns are used to compute quarterly, semi-annual and annual returns. For the annual frequency, we consider the July–July end of

Time variation

In this section, we illustrate how the effect of Size and B/P varies over time. As a reference point, we use the standard factor model representation of returns,Rit=βitftit,where Rit is the (excess) return on asset i over period t, βit is a k-dimensional vector of factor loadings, ft is a vector of common risk factors, and εit is an idiosyncratic risk component independent of ft. Of course, Eq. (1) is too general to be useful. One way to go about is to drop the time index from βit and use

Modeling frameworks

Given the evidence from the previous section on potential serial correlations in the impact of Size and B/P on returns, we now discuss alternative modeling frameworks for capturing the time-variation in γt in Eq. (3). We distinguish between two approaches. First, we consider simple statistical approaches like pooling, averaging cross-sectional coefficients, and building time-series models for the coefficients. Second, we consider a framework where time variation in the coefficients is related

Results

In this section, we present the results of our empirical analysis. We first discuss the results of a monthly rebalancing period in depth. Next, we go over the results for longer holding periods. Finally, we discuss the robustness of the results.

Concluding remarks

This paper develops a framework for capturing the time-varying impact of firm characteristics like size and book-to-price on excess returns. We showed that both the magnitude and direction of this impact displayed considerable time-variation. Using standard statistical techniques, however, did not help in predicting the future direction of impact. By contrast, by linking the impact to macroeconomic conditions through the term structure and a business cycle leading indicator, we found

Acknowledgements

We thank Christopher Gilbert, Stacey Nutt, Herbert Rijken, an associate editor and anonymous referee, and seminar participants at the I/B/E/S conference Amsterdam, Free University Amsterdam, and the University of Ghent for useful comments and suggestions. The return and firm data were generously provided by VESTEK Systems. André Lucas also thanks the Dutch Organization for Scientific Research (N.W.O.) for financial support.

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