Volatility-Managed Portfolios

Moreira, Alan and Tyler Muir. “Volatility-Managed Portfolios” The Journal of Finance Vol. 72 No. 4 (2017) 1611-16430.

“There is little relation between lagged volatility and average returns but there is a strong relationship between lagged volatility and current volatility.” The authors exploit this relationship to show that significant gains can be made through volatility timing. Using last month’s realized variance as a proxy for a portfolio’s conditional variance, they show that, whatever the desired exposure to a variety of different portfolios, Sharpe ratios can be improved by levering down the exposure when last month’s volatility is high and levering up the exposure when last month’s volatility is low. They determine volatility-managed portfolio exposure (LHS of the equation) through weighting by the inverse of the previous month’s realized variance (RHS of the equation).

 

There is a constant, c, which is chosen by the authors to set the unconditional standard deviations of the managed and buy-and-hold portfolios equal, but it does not influence the Sharpe ratio of the managed portfolio.

Managed vs. Original Portfolio:

Here they regress the returns of the managed portfolio on those of the original portfolio. Positive alpha indicates an improvement in the Sharpe ratio. Of the chosen portfolios, only SMB and CMA from Fama and French show no significant improvement at least at the 10% level. When regressing managed portfolio returns on the Fama-French three factor model, the currency carry trade joins SMB and CMA as insignificant but the rest still show positive and significant alpha.

Expanding the Mean-Variance Frontier:

The authors use different factor models which have been shown to be effective in explaining the cross-section of stock return to construct in-sample mean-variance efficient portfolios. That is, for each model considered they find the combination of factors which produces the largest Sharpe ratio. They then run similar analysis as with the individual factors. Here, however, a positive and significant alpha also indicates an overall expansion of the mean-variance frontier. For each model considered, volatility-managed mean-variance efficient portfolios show significant improvement. They also show similar results for sub-sample analysis.

Utility Gains in the Presence of Leverage Constraints:

Relative to a risk-averse investor’s desired exposure to the market return, the authors also show here that for each desired exposure considered (x-axis) there is a positive improvement to the utility of the investor using volatility-managed portfolios even when there are leverage constraints. They consider leverage constraints at 1.5 times (consistent with a 50% margin requirement) and 1 times the portfolio. That is, the volatility managed exposure cannot exceed 1.5 or 1 times the market, respectively. This indicates that there are implementable utility gains for mean-variance investors.