Volatility targeting has historically enhanced the statistical alpha of standard equity strategies. That is because volatility is more predictable in the short-term than returns. Thus, Sharpe ratios tend to decline, when volatility rises. Expected returns increase after turmoil but only overtime, when volatility might already be subsiding. On its own volatility is not a pure measure of risk premia and does not indicate if actual risk is overstated or underappreciated. A flipside of mechanical volatility targeting is that it contributes to herding and escalatory price dynamics.

Moreira, Alan and Tyler Muir (2016), “Volatility Managed Portfolios”

*The post ties in with this site’s lecture on managing systemic risk, particularly the section on preparing crisis strategies.*

*The below are excerpts from the paper. Emphasis and cursive text have been added.*

### Key findings

“There is a strong relationship between lagged volatility and current volatility…[*but*] there is little relation between lagged volatility and average returns …The empirical pattern [*as shown in the figure below*] implies that investor’s willingness to take stock market risk must be higher in periods of high stock market volatility, which is counter to most theories.”

“__Because variance is highly forecastable at short horizons, and variance forecasts are only weakly related to future returns at these horizons, our volatility managed portfolios produce significant risk-adjusted returns__ for the market, value, momentum, profitability, return on equity, and investment factors in equities as well as for the currency carry trade. Annualized alphas and Sharpe ratios with respect to the original factors are substantial. For the market portfolio our strategy produces an alpha of 4.9%, an Appraisal ratio of 0.33, and an overall 25% increase in the buy-and-hold Sharpe ratio…a positive alpha implies that our volatility managed strategy expands the mean-variance frontier.”

“We show that in response to a variance shock, the conditional variance initially increases by far more than the expected return…__since volatility movements are less persistent than movements in expected returns, our optimal portfolio strategy prescribes a gradual increase in the exposure as the initial volatility shock fades__. This difference in persistence helps to reconcile the evidence on countercyclical expected returns with the profitability of our strategy.”

“We establish that the __profitability of our volatility managed portfolios is a robust feature of the data__…We show that the typical investors can benefit from volatility timing even if subject to realistic transaction costs and hard leverage constraints… Our strategy works across 20 OECD stock market indices, that it can be further improved through the use of more sophisticated models of variance forecasting, that it does not generate fatter left tails than the original factors or create option-like payoffs, that it is less exposed to volatility shocks than the original factors (ruling out explanations based on the variance risk premium), cannot be explained by downside market risk.”

### Some key details on the empirical study

“We use both daily and monthly factors from Kenneth French’s website on “Small Minus Big” (three small stock portfolios versus three big stock portfolios), “High Minus Low” (two value portfolios versus two growth portfolios), “Momentum” (a factor which goes long past winners and short past losers), “Robust Minus Weak” (two robust operating profitability portfolios versus two weak operating profitability portfolios), “Conservative Minus Aggressive” (two conservative investment portfolios versus two aggressive investment portfolios). __The first three factors are the original Fama-French 3 factors while the last two are a profitability and an investment factor that they use in their 5 factor model__.”

“We construct portfolios that scale monthly returns by the inverse of their previous month’s realized variance, decreasing risk exposure when variance was recently high, and vice versa. We call these volatility managed portfolios…An appealing feature of this approach is that it can be easily implemented by an investor in real time and does not rely on any parameter estimation.”

“Our strategy takes relatively more risk when volatility is low (e.g., the 1960’s) hence its losses are not surprisingly concentrated in these times. In contrast, large market losses tend to happen when volatility is high (e.g., the Great Depression or recent financial crisis) and our strategy avoids these episodes. Because of this, __the worst time periods for our strategy do not overlap much with the worst market crashes__…Our strategies take less risk during recessions and thus have lower betas during recessions.”

“We have implemented our strategy by rebalancing it once a month and running time series regressions at the monthly frequency… Alphas decrease with horizon.”

“While expected variance spikes on impact, this shock dies out fairly quickly, consistent with variance being strongly mean reverting. Expected returns, however, rise much less on impact but stay elevated for a longer period of time. Given the increase in variance but only small and persistent increase in expected return, the lower panel shows that it is optimal for the investor to reduce his portfolio exposure by 50% on impact because of an unfavorable risk return tradeoff.”