### Linear Factor Stock Return Models Misleading?

**March 8, 2013** - Big Ideas, Volatility Effects

Does use of alphas from linear factor models to identify anomalies in U.S. stock returns mislead investors? In the February 2013 draft of their paper entitled “Using Maximum Drawdowns to Capture Tail Risk”, Wesley Gray and Jack Vogel investigate maximum drawdown (largest peak-to-trough loss over a time series of compounded returns) as a simple measure of tail risk missed by linear factor models. Specifically, they quantify maximum drawdowns for 11 widely cited U.S. stock return anomalies identified via one-factor (market), three-factor (plus size and book-to-market ratio) and four-factor (plus momentum) linear models. These anomalies are: financial distress; O-score (probability of bankruptcy); net stock issuance; composite stock issuance; total accruals; net operating assets; momentum; gross profitability; asset growth; return on assets; and, investment-to-assets ratio. They calculate alphas for each anomaly by using the specified linear model risk factors to adjust gross monthly returns from a portfolio that is long (short) the value-weighted or equal-weighted tenth of stocks that are “good” (“bad”) according to that anomaly, reforming the portfolio annually or monthly depending on anomaly input frequency. Using monthly returns and firm fundamentals for a broad sample of U.S. stocks, and contemporaneous stock return model factor returns, during July 1963 through December 2012, *they find that:* Keep Reading