Equity Valuation and Portfolio Management

PERFORMANCE

We compare the performance of standard and shortfall constrained optimization in an empirical study, using three different alpha signals: relative strength, predicted earnings-to-price ratio (E/P), and cash plowback. For each signal, we create an optimal portfolio that has a forecast active risk of 4%. We use the MSCI US Prime Market 750 Index as both the universe and benchmark, and the Barra Short-Term US Equity Model (USE3S) as the risk model. We rebalance the portfolios monthly over the test period from January 1994 to May 2009. When constraining shortfall beta, we set the upper bound to 0.9 to produce portfolios with less sensitivity to extreme market losses. We also relax the long-only constraint, allowing up to 5% shorting of individual stocks.

In portfolio optimization, imposing constraints tends to alter the ex-ante active risk that the optimal portfolio achieves for a fixed level of risk aversion. To ensure that any differences between shortfall and standard optimization are not simply due to differing levels of aggressiveness, we require each portfolio to have the same forecast active risk of 4%.

Exhibit 19.1 shows the cumulative difference in returns obtained using shortfall constrained optimization and standard optimization. We see that constraining shortfall beta improves performance for most signals during two main turbulent periods—the middle of 2000 through the middle of 2002 and late 2007 through 2008. On the other hand, standard optimization performs ...