Young, timid, and risk takers

Abstract

Time-varying asset returns lead highly risk-averse investors to choose market-timing exposures that increase in their horizon, in agreement with the common advice to reduce risk with age, but in contrast to theoretical work that prescribes constant portfolio weights. In a market where an investor with constant absolute risk aversion and finite horizon trades an asset with temporary fluctuations, we find asymptotically optimal investment strategies that are independent of the asset's average return and decline over time with a power of the remaining horizon, with the exponent determined by the curvature of mean reversion. For long-term safe assets, which have a zero average return, the investor's certainty equivalent declines over time at a lower rate, implying that a nonzero average return is negligible for asymptotically optimal strategies but critical to their performance.