The distribution of long-run compound returns to portfolio strategies is greatly affected by periodic rebalancing. Over time, buy-and-hold portfolios gradually lose diversification as extreme long-run skewness in individual stock returns leads to increasingly concentrated holdings. For long investment horizons, small rebalanced portfolios holding only a fraction of all stocks therefore achieve better diversification than much larger marketwide buy-and-hold portfolios. Consequently, over long horizons, rebalanced portfolios tend to outperform buy-and-hold portfolios, and risk-averse investors prefer the former. Empirical results strongly support the theoretical predictions and add further evidence to the strong empirical performance of (small) equal-weighted portfolios.

At long horizons, multiplicative compounding induces strong-to-extreme positive skewness into stock returns; the magnitude of the effect is primarily determined by single-period volatility. Consequently, at horizons greater than 5 years, returns—individual or portfolio—will be positively skewed under reasonable parameterizations. From an investor perspective, the strong positive skewness implies that the mean compound return will serve as a poor guide for typical long-horizon outcomes. Moreover, the large effects of compounding on higher-order moments are shown to affect the validity of Taylor expansions used to approximate preferences for skewness, when applied to returns of annual or longer horizons.

We study the theoretical implications of cointegrated stock prices on the profitability of pairs-trading strategies. If stock returns are fairly weakly correlated across time, cointegration implies very high Sharpe ratios. To the extent that the theoretical Sharpe ratios are “too large,” our results suggest that either i) cointegration does not exist pairwise among stocks, and pairs-trading profits are a result of a weaker or less stable dependency structure among stock pairs, or ii) the serial correlation in stock returns stretches over considerably longer horizons than is usually assumed. Empirically, there is little evidence of cointegration, favoring the first explanation.

In an intertemporal equilibrium asset pricing model featuring disappointment aversion and changing macroeconomic uncertainty, we show that besides the market return and market volatility, three disappointment-related factors are also priced: a downstate factor, a market downside factor, and a volatility downside factor. We find that expected returns on various asset classes reflect premiums for bearing undesirable exposures to these factors. The signs of estimated risk premiums are consistent with the theoretical predictions. Our most general, five-factor model is very successful in jointly pricing stock, option, and currency portfolios, and provides considerable improvement over nested specifications previously discussed in the literature.

We examine the portfolio choice of an investor with generalized disappointment-aversion preferences who faces log returns described by a normal-exponential model. We derive a three-fund separation strategy: the investor allocates wealth to a risk-free asset, a standard mean-variance efficient fund, and an additional fund reflecting return asymmetries. The optimal portfolio is characterized by the investor’s endogenous effective risk aversion and implicit asymmetry aversion. In empirical applications, we find that disappointment aversion is associated with much larger asymmetry aversion than are standard preferences. Our model explains patterns in popular portfolio advice across both risk appetites and investment horizons. Received November 12, 2015; editorial decision July 20, 2016 by Editor Stefan Nagel.