Volatility Managed Portfolios
Yale University
Yale University
February 1, 2016
Abstract:
Managed portfolios that take less risk when volatility is high produce large, positive alphas and increase factor Sharpe ratios by substantial amounts. We document this fact for the market, value, momentum, profitability, return on equity, and investment factors in equities, as well as the currency carry trade. Our portfolio timing strategies are simple to implement in real time and are contrary to conventional wisdom because volatility tends to be high after the onset of recessions and crises when selling is typically viewed as a mistake. Instead, our strategy earns high average returns while taking less risk in recessions. We study the portfolio choice implications of these results. We find volatility timing provides large utility gains to a mean variance investor, with increases in lifetime utility around 75%. We then study the problem of a long-horizon investor and show that, perhaps surprisingly, long-horizon investors can benefit from volatility timing even when time variation in volatility is completely driven by discount rate volatility. The facts pose a challenge to equilibrium asset pricing models because they imply that effective risk aversion and the price of risk would have to be low in bad times when volatility is high, and vice versa.
Volatility Managed Portfolios – Introduction
We construct portfolios that scale monthly returns by the inverse of their expected variance, decreasing risk exposure when the returns variance is expected to be high, and vice versa. We call these volatility-managed portfolios. We document that this simple trading strategy earns large alphas across a wide range of asset-pricing factors, suggesting that investors can benefit from volatility timing. Motivated by these results, we study the portfolio choice implications of time-varying volatility. We find that short- and long-term investors alike can benefit from volatility timing, and that utility gains are substantial. Further, we show that the optimal portfolio can be approximated by a combination of a buy-and-hold portfolio and the volatility-managed portfolio that we introduce in this paper.
We motivate our analysis from the vantage point of a simple mean-variance investor, who adjusts his or her allocation in the risky asset according to the attractiveness of the mean variance trade-off, 
. Because variance is highly forecastable at horizons of up to one year, and variance forecasts are only weakly related to future returns at these horizons, our volatility-managed portfolios produce significant risk-adjusted returns for the market, value, momentum, profitability, return on equity, and investment factors in equities as well as for the currency carry trade. In addition, we show that the strategy survives transaction costs and works for most international indices as well. Annualized alphas with respect to the original factors are substantial, and Sharpe ratios increase by 50% to 100% of the original factor Sharpe ratios. Utility benefits of volatility timing for a mean-variance investor are on the order of 50% to 90% of lifetime utility – substantially larger than those coming from expected return timing. Moreover, parameter instability for an agent that estimates volatility in real time is negligible, in contrast to strategies that try to time expected returns (Goyal and Welch (2008)).
Our volatility-managed portfolios reduce risk taking after market crashes and volatility spikes, while the common advice is to increase or hold risk taking constant after market downturns. Thus, on average, our volatility-managed portfolios reduce risk exposure in recessions. For example, in the aftermath of the sharp price declines and large increases in volatility in the fall of 2008, it was a widely held view that market movements created a once-in-a-generation buying opportunity, and that those that reduced positions in equities were making a mistake. Yet the volatility-managed portfolio cashed out almost completely and returned to the market only as the spike in volatility receded. We show that, in fact, our simple strategy turned out to work well historically and throughout several crisis episodes, including the Great Depression, Great Recession, and 1987 stock market crash.
These facts may be surprising because there is a lot of evidence showing that expected returns are high in recessions; therefore, recessions are viewed as attractive periods for taking risks (French et al. (1987)). In order to better understand the business-cycle behavior of the risk-return trade-off, we combine information about time variation in both expected returns and variance, using predictive variables such as the price-to-earnings ratio and the yield spread between Baa and Aaa rated bonds. We run a Vector autoregression (VAR), which includes both the conditional variance and conditional expected return, and show that in response to a variance shock, the conditional variance initially increases by far more than the expected return, making the risk-return trade-off initially unattractive. A mean-variance investor would decrease his or her risk exposure by 60% after a one standard deviation shock to the market variance. However, since volatility movements are less persistent than movements in expected returns, our optimal portfolio strategy prescribes a gradual increase in the exposure as the initial volatility shock fades. On average, it takes 18 months for portfolio exposure to return to normal, and at horizons beyond this it is optimal to increase exposure further to capture the persistent increase in expected returns. The difference in persistence allows investors to keep much of the expected return benefit, while at the same time reducing their overall risk exposure.
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