07 Sep 2006Working Paper Summaries

Optimal Value and Growth Tilts in Long-Horizon Portfolios

by Jakub W. Jurek and Luis M. Viceira

Long-term investors look for portfolio strategies that optimally trade off risk and reward, not in the immediate future, but over the long term. It is unrealistic to expect long-term investors to adopt an "invest and forget" strategy, but creating a portfolio strategy that adjusts asset allocations in response to changing risk premia, interest rates, and expected inflation remains a challenge in finance. Jurek and Viceira have devised a solution method that aims at a practical implementation of dynamic portfolio choice models with realistically complex investment opportunity sets. They have applied their method to study the role of value stocks and growth stocks in the portfolios of long-term investors, and have found that long-term investors might want to tilt their portfolios away from value stocks despite the fact that the average return on value stocks is larger than the average return on growth stocks (the so-called "value premium"). Their findings provide support for the idea that the superior performance of value stocks might reflect simply that they are riskier than growth stocks at long horizons. Key concepts include:

The solution can be readily implemented for investment opportunity sets with any number of assets and state variables.
On average, equity-only investors with short horizons optimally choose portfolios that are heavily tilted toward value and away from growth, regardless of the investor's risk aversion. Aggressive short-term investors find it best to tilt their portfolios toward value because of their higher average return. Conservative equity-oriented investors optimally tilt their portfolios toward value stocks because of their small return volatility and high correlation with growth.
However, for investors with longer horizons, the optimal allocation to value decreases dramatically as the optimal allocation to growth increases. Value stocks appear to be riskier than growth stocks at long horizons because they tend to be more highly correlated with permanent shocks to the value of the aggregate stock market, while growth stocks appear to be more highly correlated with transitory shocks.
In the presence of time varying risk premia, interest rates, and expected inflation, it is optimal for most investors to dynamically rebalance their portfolios in response to changes in investment opportunities. The paper finds that for long-horizon investors who can invest in equities, bond, and cash, welfare losses from adopting investment policies with infrequent reevaluation of portfolio weights are large, regardless of the investor's risk aversion.

Author Abstract

We develop an analytical solution to the dynamic portfolio choice problem of an investor with power utility defined over wealth at a finite horizon who faces an investment opportunity set with time-varying risk premia, real interest rates and inflation. The variation in investment opportunities is captured by a flexible vector autoregressive parameterization, which readily accommodates a large number of assets and state variables. We find that the optimal dynamic portfolio strategy is an affine function of the vector of state variables describing investment opportunities, with coefficients that are a function of the investment horizon. We apply our method to the optimal portfolio choice problem of an investor who can choose between value and growth stock portfolios, and among these equity portfolios plus bills and bonds. For equity-only investors, the optimal mean allocation of short-horizon investors is heavily tilted away from growth stocks regardless of their risk aversion. However, the mean allocation to growth stocks increases dramatically with the investment horizon, implying that growth is less risky than value at long horizons for equity-only investors. Long-horizon aggressive investors who have access to bills and bonds increase their allocation to both value stocks and growth stocks at long horizons, but they do not actively tilt their portfolios toward growth stocks. These investors increase their allocation to growth stocks as a result of their desire to optimally increase their overall allocation to equities. We also explore the welfare implications of adopting the optimal dynamic rebalancing strategy vis a vis other policies that revise portfolio weights infrequently, and find significant welfare gains from continuous rebalancing for all long-horizon investors.