The industry of investment funds has dramatically changed over the past ten years, and we observe today a convergence between hedge funds and traditional asset management. For example, institutional as well as retail investors may now have access more easily to absolute return strategies in a mutual fund format. This convergence has been recently accelerated with the emergence of newcits and the increasing number of regulated hedge funds. Therefore, the decision-making process of investment is today more complex with the strong development of these dynamic investment strategies and the large number of underlyings and assets. Managing the exposure to risky assets is the main difference between these investment styles and the traditional long-only strategies. This difference is however conceptually huge and is not always understood by investors and fund managers themselves.

The traditional way to analyze and evaluate a strategy is to use risk-adjusted performance measurement tools like the Sharpe ratio (or the information ratio) and the Jensen’s alpha. These financial models have been developed to compare long-only strategies, but they are not well adapted to dynamic trading strategies. Indeed, dynamic strategies exhibit non-normal returns and nonlinear exposures to risk factors. In the nineties, practitioners and academics developed alternative models to take into account these properties. And some extensions of the Sharpe ratio like Sortino, Kappa and Omega ratios have become today very popular to analyze the performance of hedge funds returns. Another way to understand the risk-return profile of dynamic strategies has been proposed by Fung and Hsieh (1997) by incorporating non-linear risk factors in a Sharpe style analysis. These different measures define the empirical approach in the sense that they are computed on an ex-post basis but are not very adapted for an ex-ante analysis.

All these models are relevant, however they provide a partial answer to understand the true nature of a dynamic strategy. Let us consider for example a long exposure on a call option. Since the seminal work of Black and Scholes (1973), we know that this investment profile is equivalent to a delta-hedging strategy. Therefore, a long position on a call option is a trend-following strategy with a dynamic exposure to the underlying risky asset. Computing a risk-adjusted performance or performing a style regression are certainly not natural tools to analyse this dynamic investment strategy. A better way to understand the risk and return of such strategy is to use the theory of options. In this case, the performance of the strategy is analyzed by investigating both the payoff function and the premium of the option. And this last one is split into an intrinsic value component and a time value component. Moreover, one generally computes the sensitivity of the premium to different parameters like volatility, time decay or the price of the underlying asset. This analytical approach permits to apprehend the option strategy in a more satisfactory way than the empirical approach, which consists in analyzing the ex-post risk-return profile of the option strategy, by computing some statistics on a real-life, investment or on some backtests.

For example, with the analytical approach, we may show that the trend of the underlying asset only concerns the payoff function and has no effect on the option premium. Such property could not be derived from the empirical approach. Another interesting example of dynamic trading strategies is the constant proportion portfolio insurance (CPPI) developed by Hayne Leland and Mark Rubinstein in 1976. The large literature on this subject is mainly related to the analytical approach and the analysis of CPPI strategies is closer to the theory of options than the models developed to compute the performance of traditional mutual funds. However, the technique of CPPI is certainly one of the most famous dynamic strategy in asset management.

Given the previous remarks, we may think that the analytical method may be extended to a large class of dynamic trading strategies, and not only reserved to options and CPPI. This seventh white paper explores this approach. In this white paper, we develop a financial model to better understand the risk-return profile of several dynamic investment strategies, like stop-loss, start-gain, doubling, mean-reversion or trend-following strategies. We show that dynamic trading strategies may be decomposed into an option profile and a trading impact. In some sense, the option profile may be viewed as the payoff function of the strategy whereas the trading impact may represent the premium to buy such strategy. In this framework, implementing a trading strategy generally implies a positive cost, which has to be paid as explained by Jacobs (2000):

“Momentum traders buy stock (often on margin) as prices rise and sell as prices fall. In essence, they are trying to obtain the benefits of a call option – upside participation with limited risk on the downside – without any payment of an option premium. The strategy appears to offer a chance of huge gains with little risk and minimal cost, but its real risks and costs become known only when it’s too late.” Using this framework, we are also able to answer some interesting questions, which are not addresses in the empirical approach. Here are some of them. In which cases the pro¬portion of winning bets (or hit ratio) is a pertinent measure of the efficiency of a dynamic strategy? Which dynamic strategies like or don’t like volatility? What is the best and the worst configuration for a given dynamic strategy? What is the impact of the length of a moving average in a trend-following strategy? What is the theoretical distribution of the strategy returns? Why long-term CTA differs from short-term CTA? What are the risks of a mean-reverting strategy? By answering to all these questions, we provide some insights to understand why and when some strategies perform or not and what are the good metrics to evaluate their performance. We hope that you will find the results of this paper interesting as well as useful in practice.

Thierry Roncalli
Head of Research and Development
Lyxor Asset Management