Equity Valuation and Portfolio Management

KEY POINTS

• Extreme risk can be incorporated into portfolio construction by constraining the shortfall beta of the optimal portfolio. Shortfall beta measures the relationship of a portfolio to a benchmark during periods of extreme stress. It is analogous to standard “beta” but differs in its focus on the left tail. We refer to this as the “shortfall constrained” optimization problem.
• Empirically, using three common alpha signals, shortfall constrained optimization outperformed mean-variance optimization. Constraining shortfall beta offered some downside protection in turbulent periods without sacrificing performance over longer periods.
• Decomposing an active portfolio into a portfolio due to the alpha and portfolios corresponding to each of the constraints allows one to attribute the active return to the alpha and the constraints.
• We find that the portfolio representing the net shortfall beta performed well over the historical period, especially during the Internet meltdown and again during the recent financial crisis. Moreover, during these stressful periods, the shortfall beta constraint shifts the active portfolio toward the shortfall beta portfolio. The two effects combine to drive the incremental gains we see in implementing the constraint.