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Article Excerpt
1. Introduction
Equity returns tend to continue over short horizons (momentum) and revert over longer horizons (mean reversion). (1) If stock returns are predictable, an investor modifies her optimal strategy in two important ways. First, the investment strategy reflects the current conditioning information. Second, investors with different horizons hold different optimal portfolios as a result of hedging demands.
Recent studies show that mean reversion in equity returns induces positive hedging demands and economically significant market timing opportunities. (See, for instance, Brandt 1999, Campbell and Viceira 1999, Wachter 2002.) However, these studies ignore that returns tend to continue over short horizons. Return continuation adds to the market timing opportunities, and it may also affect hedging demands by increasing the risk of a position in equities. This paper is the first to study a dynamic, long-term investment problem in a financial market that features both momentum and mean reversion. We show that momentum at the index level does impact hedging demands and market timing opportunities, and that this result is strong at horizons up to five years. In addition, changes in the allocation to stocks induced by momentum yield remarkable gains in investor's welfare. Momentum is most important at short horizons, whereas mean reversion in equity returns is the dominant force for longer investment horizons. These gains are preserved in the cases of discrete-time trading and standard borrowing and short-sales constraints.
As a starting point, we develop a novel continuous-time financial market model that features both momentum and mean reversion in equity returns. The state variable that captures momentum in stocks' performance is a weighted average of recent stock returns. Expected returns relate positively to the performance variable, the key feature of momentum. The state variable that captures mean reversion in equity returns is the dividend yield. (2) Our model is sufficiently tractable to allow the derivation of the investor's optimal strategy in closed form.
Expected returns relate positively to both the performance variable and the mean-reversion variable. However, innovations to expected returns relate positively to innovations in the performance variable, but negatively to innovations in the dividend yield. The difference in the correlation structure of the innovations determines the sign of the hedging demands induced by momentum and mean reversion. The investor hedges the performance variable by optimally reducing the allocation to stocks, whereas the mean-reversion variable is hedged by optimally increasing the allocation to stocks. Because we find that the performance variable is less persistent than the mean-reversion variable, hedging demands induced by momentum are dominant at short horizons. At longer horizons, mean reversion is most prevalent. Our model therefore implies that the total allocation to stocks does not increase monotonically with the investor's horizon. (3) Consequently, there is a strictly positive investment horizon at which the investor behaves as if she were myopic.
The economic importance of hedging demands is an empirical question. To quantify the economic significance of including momentum as an input for strategic allocation, (4) we calibrate the model on the basis of the Center for Research in Security Prices (CRSP) value-weighted and equally weighted return series of stocks present in the AMEX/NASDAQ/NYSE. The sample period we consider is January 1946-December 2005. The value-weighted and equally weighted indices exhibit monthly first-order autocorrelations of about 6% and 20%, respectively. By means of these two indices we explore the predictions of our model in two well-differentiated environments: one represented by the value-weighted index, in which continuation is rather weak, and the other represented by the equally weighted index, in which continuation is more prominently present. It is worth noticing that these numbers are in the ballpark of autocorrelation in other indices of developed economies. For example, the MSCI (Morgan Stanley Capital International) Europe index has a monthly autocorrelation of 10.32% for the period 1970-2005.
We find that the hedging demands are negative for the first year for the value-weighted index, and for the first five years for the equally weighted index. For longer investment horizons, the hedging demands are positive as mean reversion kicks in. In addition to the change in the optimal strategic allocation, momentum also strongly affects the short-term myopic allocation to stocks via tactical market timing: we find that timing the performance variable is more important than timing the slow-moving mean-reversion variable. This finding is consistent with the abundant evidence on return-chasing behavior of professional fund managers. We further analyze the practical value of our results and solve a discrete-time portfolio choice problem with standard borrowing and short-sales constraints. The benefits of momentum trading decrease with the trading frequency but are still substantial at a monthly frequency. At lower trading frequencies, there is little value of timing past stock market performance. (5) The resulting utility gains are large and unlikely to be wiped out by any realistic amount of transactions costs.
Our finding that hedging demands are negligible and even negative for investment horizons up to five years is consistent with the findings in Brandt (1999) and Ait-Sahalia and Brandt (2001). These studies bypass modeling the return-generating process and estimate the portfolio weights from the Euler conditions directly. They find small or negative hedging demands at short to intermediate investment horizons. Also, Balvers and Mitchell (1997) show that the optimal allocation to stocks is decreasing in the investment horizon when stock returns are positively correlated. All of these papers are crafted in discrete time, and Balvers and Mitchell (1997) accommodate either positive or negative correlation, but not both. We provide a tractable continuous-time model that allows studying the simultaneous impact of momentum and mean reversion on optimal dynamic asset allocation within a unified framework.
A well-known prediction of standard strategic asset allocation studies is that the fraction of wealth that an investor allocates to stocks is directly related to her investment horizon. This result typically refers to a problem that usually takes a 15-to 20-year perspective and focuses on mean reversion. We show that even the modest amount of momentum present in the indices we study can substantially weaken, and even reverse, this result at shorter horizons. We would argue that the intermediate investment horizons in which our theory delivers different predictions is relevant for the biggest actors in the financial scene, such as portfolio managers of mutual funds. There is substantial evidence that the investment horizons of many institutional investors have shortened in recent years (see Baker 1998), a phenomenon that may be due to agency problems that arise in delegated portfolio management. As John Bogle, a veteran of the mutual fund industry puts it, (6)
[A] dramatic decline in investment horizons has ... changed the
industry. ... Portfolio managers turn over at a rapid rate. The
average manager lasts just six years, and then a new broom sweeps the
portfolio. ... Fund shares--once held by long-term investors for an
average of 12.5 years--are today held for an average of just over
two years.
The emphasis on return continuation also relates our paper to the momentum literature pioneered by Jegadeesh and Titman (1993). In these strategies, momentum profits can be generated along three lines: differences in (unconditional) expected returns (see Conrad and Kaul 1998), positive autocorrelation in winning and losing portfolio returns (see Moskowitz and Grinblatt 1999), or cross-serial correlations (see Lewellen 2002). Given the fact that in our economy there is only a single stock index, we can only accommodate the second source of momentum profits. An interesting direction for future research is our model's extension to the optimal-allocation use of positive autocorrelation in momentum portfolios, while at the same time taking mean reversion into account. (7)
In summary, our paper provides two main contributions to the dynamic asset allocation literature. First, we introduce an intuitive and parsimonious continuous-time model that accommodates both momentum and mean reversion. In this model, expected index returns are governed by two state variables: a weighted average of past returns and the dividend yield. The model manages to incorporate the history of stock returns as a state variable while keeping the tractability of a Markovian framework. The model nests the well-known models of Campbell and Viceira (1999) and Wachter (2002), which therefore constitute a natural benchmark for our work. We consider these restricted versions to rigorously study the incremental effect of momentum on strategic asset allocation. Second, we explicitly focus on the case of an investor with an intermediate investment horizon, contributing in this way to bridge the gap between the long-term asset allocation literature that emphasizes the economic value of return reversal, and the tactical return continuation or momentum literature.
This paper proceeds as follows. In [section]2, we introduce a new model of stock returns in which the equity risk premium is driven by both a weighted average of past returns and a mean-reversion variable. In [section]3, the...
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