We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of linear rebalancing rules and describe an efficient computational procedure to optimize with this class. We illustrate this method in the context of portfolio execution and show that it achieves near optimal performance. We consider another numerical example involving dynamic trading with mean-variance preferences and demonstrate that our method can result in economically large benefits.

Using a database of daily institutional trades, we document that a majority of short-term institutional trades lose money. In aggregate, over 23% of round-trip trades are held for less than 3 months, and the returns on these trades average -3.91% (nonannualized). These losses are pervasive across all types of stocks, with the lowest returns occurring in small stocks, value stocks, and low-momentum stocks. Short-term trades lose more in more volatile markets. Across funds, the worst short-term returns accrue to funds that do the most trading, and there is no evidence of persistent skill or disposition effect in short-term institutional trades.

Deleveraging risk is the risk attributable to investing in a security held by levered investors. When there is an aggregate negative shock to the availability of funding capital, securities with a greater presence of levered investors experience extreme return realizations as these investors unwind their positions. Using data on equity loans as a proxy for the degree of levered positions in a given stock, we find robust evidence of deleveraging risk. Stocks with a high degree of short selling experience large positive returns and a decrease in short selling around periods of funding capital scarcity.

Exchange rate models with uncertain and incomplete information predict that investors focus on a small set of fundamentals that changes frequently over time. We design a model selection rule that captures the current set of fundamentals that best predicts the exchange rate. Out-of-sample tests show that the forecasts made by this rule significantly beat a random walk for 5 out of 10 currencies. Furthermore, the currency forecasts generate meaningful investment profits. We demonstrate that the strong performance of the model selection rule is driven by time-varying weights attached to a small set of fundamentals, in line with theory.