Investing when Volatility Fluctuates∗

We examine how the evidence of the time-varying volatility in stock returns affects optimal dynamic portfolio choice of investors with long horizons. As return volatility shows a relatively small correlation with realized return, its time-variation is expected to cause little, if any, hedging demand (in the sense of Merton (1973)). However, we find that, once transaction costs are taken into account in portfolio rebalancing, the time-varying monthly return volatility produces significant horizon effect with stock allocations despite the negligible hedging demand. The driving force of this surprising result is newly identified in our study, and differs from the hedging demand documented in earlier studies (e.g., Brennan, Schwartz, and Lagnado (1997) and Barberis (2000)). Moreover, the horizon effect is found to be state-dependent, and could be either positive or strikingly negative, depending on the current value of return volatility. This leads to a reduced sensitivity of the initial optimal stock allocation to current return volatility as a function of the expected portfolio holding period. It also suggests that how much an investor values the knowledge of the true current return volatility depends on the investment horizons and transaction costs. ∗I am grateful to my dissertation advisor Robert Stambaugh and committee members, Craig MacKinlay, Andrew Metrick, Jessica Wachter, and Yihong Xia, for insightful comments and suggestions. The comments of Michael Brandt, Francis Diebold, Harikumar Sankaran, and seminar participants at the Wharton School and the 2003 meeting of the Eastern Finance Association are also appreciated. Any remaining errors are mine. †Correspondence address: Lee Kong Chian School of Business, Singapore Management University, 469 Bukit Timah Road, Singapore 259756. Phone: (65) 6822-0763. Email: [email protected]