Determinants of Levered Portfolio Performance

The cumulative return to a levered strategy is determined by five elements that fit together in a simple and useful formula. A previously undocumented element is the covariance between leverage and excess return to the fully invested source portfolio underlying the strategy. In an empirical study of volatility-targeting strategies over the 84-year period 1929–2013, this covariance accounted for a reduction in return that substantially diminished the Sharpe ratio in all cases.We show that the cumulative return to a levered strategy is determined by five elements that fit together in a simple and useful formula. Looking backward, the formula can be used to attribute the realized return of a levered strategy. Looking forward, the formula can be used to generate a forecast for the return of a levered strategy. Our formula is expressed in terms of the return to the source portfolio, which is the fully invested portfolio underlying the levered strategy.The most novel element of our multi-period attribution formula is the covariance between leverage and return to the source portfolio in excess of the borrowing rate. This element contributes to the return of any dynamically levered strategy. We illustrate the impact of dynamic leverage on cumulative return using a simple two-period model, in which the covariance term plays a crucial role. Over time, however, one might be tempted to think that the covariance term would wash out. The empirical examples in this article demonstrate that the covariance term does not wash out and has a substantial impact on the long-run return of widely used strategies. In empirical studies of risk parity strategies and bond strategies levered to volatility targets, we found that the covariance term makes a substantial contribution to cumulative return over a very long horizon. In all our examples, the covariance term turned out to be negative, diminishing annualized arithmetic return by amounts ranging from 0.64% to 4.23% over an 84-year period. Consequently, the Sharpe ratios of volatility-targeting strategies were lower than those of their source portfolios and fixed-leverage benchmarks.Also important over multiple periods is the cost of trading, which imposes a drag on any strategy. Leverage exacerbates turnover, so levered strategies tend to have higher trading costs than do unlevered strategies. On the basis of a linear model, we found that leverage-induced turnover diminished the annualized arithmetic return of the strategies we considered by amounts ranging from 0.27% to 2.59% over an 84-year period.Compounding imposes a variance drag on cumulative return that affects strategies differentially. For any given source portfolio, the variance drag is quadratic in leverage. If a levered strategy has high volatility, the variance drag can be substantial. We found that the variance drag diminished the annualized geometric return of the strategies we considered by amounts ranging from 0.41% to 2.84% over an 84-year period.That financing costs and the variance drag materially reduce the Sharpe ratio of a levered strategy is well known. Nevertheless, these effects are often neglected in empirical studies because much of our intuition about levered strategies comes from single-period models. In one period, there is no trading and hence there are no trading costs, there is no compounding and hence no variance drag, and leverage is necessarily fixed and hence there is no covariance term. What is new in this article is that, via the covariance term, dynamic leverage affects the Sharpe ratio even in the absence of trading costs.