Low-risk investing refers to a diverse collection of investment strategies that emphasize low-beta, low-volatility, low idiosyncratic risk, downside protection, or risk parity. Since the 2008 financial crisis, there has been heightened interest in low-risk investing and especially in investment strategies that apply leverage to low-risk portfolios in order to enhance expected returns.

In chapter 1, we examine the well-documented low-beta anomaly. We show that despite the fact that low-beta portfolios had lower volatility than the market portfolio, some low-beta portfolios had higher realized Sharpe ratios (over a 22-year horizon) than the market portfolio. This is can not happen in an efficient market, where long-run return is expected to be earned as a reward for bearing risk, if risk is equated with volatility. We expand the notion of risk to include higher moments of the return distribution and show that excess kurtosis can make low-beta stocks and portfolios riskier than higher beta stocks and portfolios.

In chapter 2, we show that the cumulative return to a levered strategy is determined by five elements that fit together in a simple, 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 1929-2012, this covariance accounted for a reduction in return that substantially diminished the Sharpe ratio in all cases.

In chapter 3, we gauge the return-generating potential of four investment strategies: value weighted, 60/40 fixed mix, unlevered and levered risk parity. We have three main findings. First, even over periods lasting decades, the start and end dates of a backtest can have a material effect on results; second, transaction costs can reverse ranking, especially when leverage is employed; third, a statistically significant return premium does not guarantee outperformance over reasonable investment horizons.