Predicting the success of volatility targeting strategies

11 Mar 2015

Volatility targeting is a strategy that rebalances between a risky asset and cash in order to target a constant level of risk over time. When applied to equities and compared to a buy-and-hold strategy it is known to improve the Sharpe ratio and reduce drawdowns. We used Monte Carlo simulations based on a number of time-series parametric models from the GARCH family to analyze the relative importance of a number of effects in explaining those benefits. We found that volatility clustering and fat tails in return distributions are the two effects with the largest explanatory power. The results are even stronger when there is a negative relationship between return and volatility, which is known to be the case not only in equities but also to some extent in corporate bonds, government bonds and commodities. We used historical returns to simulate what the performance of a volatility targeting strategy would have been when applied to equities, corporate bonds, government bonds and commodities. The benefits of the strategy are more significant for equities and high-yield corporate bonds, which show the strongest volatility clustering, fat tails and negative relationship between returns and volatility. For government bonds and investment-grade bonds, which show less volatility clustering and a weaker negative relationship between returns and volatility, the benefits of the strategy were less marked.

Volatility targeting is a systematic strategy that invests in a risky asset and in the risk-free asset rebalancing the portfolio in such a way as to keep the ex-ante risk at a constant target level. This strategy is also known as constant risk, target risk or inverse risk weighting. The strategy made no sense if risky asset returns followed an independent and identically (i.i.d.) normal distribution. The volatility  of the risky asset returns would then be constant over time and could be estimated more accurately by increasing the history of returns used in its estimation. In such a case, allocating weight w to assets in a portfolio or allocating risk budgets w x amounts to being two sides of the same coin. However, the returns of financial assets do not follow i.i.d. normal distributions and their volatility, which varies over time, is not even observable.

As noted by Mandelbrot [1963], financial asset returns show volatility clustering, which refers to the observation that large asset price fluctuations tend to be followed by large price fluctuations, either negative or positive, and small asset price fluctuations tend to be followed by small price fluctuations. Engle [1982] and Bollerslev [1986] introduced the ARCH (Auto-Regressive Conditional Heteroskedasticity) and GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) parametric models, respectively, which can be used to model asset returns taking into account volatility clustering. The survey of Poon and Granger [2003] lists 93 published and working papers that look at volatility forecasting and volatility modeling at different frequencies and for several asset classes. The survey of Andersen, Bollerslev, Christoffersen and Diebold [2005] also discusses volatility forecasting.

 There is empirical evidence that the application of a volatility targeting strategy to equities targeting constant volatility over time does add value. Hocquard, Ng and Papageorgiou [2013] observe that not only do constant volatility portfolios deliver higher Sharpe ratios than buying and holding the underlying risky asset, but also that drawdowns are reduced. They show that targeting constant volatility helps to reduce tail risk. There is also theoretical support for the success of volatility-targeting strategies. Assuming constant mean return and varying volatility, Hallerbach [2012] proves that the volatility-targeting strategy improves the Sharpe ratio. The success of the strategy increases with better volatility forecasts. He shows that the higher the degree of volatility smoothing achieved by volatility weighting, the higher the risk-adjusted performance.

 Hallerbach [2013] reviews different approaches to controlling risk in portfolios that make a clear distinction between managing risk in the cross-section and managing risk over time. He is of the view that volatility weighting over time does improve the risk-return trade off and suggests that, at least for equities, the success of volatility weighting also arises from a second effect known as the asymmetric volatility phenomenon: the fact that returns tend to be negatively correlated with volatility.

 

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