Journal of Investment Strategies

Welcome to the first issue of the third volume of The Journal of Investment Strategies. In this issue you will find four papers, covering investment performance analysis, alternative investment strategy design, optimization of derivatives strategies, and the empirical analysis of credit markets.

In the first paper of the issue, "Reward-risk ratios", Patrick Cheridito and Eduard Kromer introduce several new families of reward-risk ratios that are designed to address the perceived flaws in the existing large taxonomy of such ratios, of which they also give a comprehensive review. The main methodological requirement that they impose on these new ratios is that they must be monotone and concave, ie, they must prefer more to less and to encourage diversification. It is true that not all industry-standard metrics comply with these simple requirements: the most broadly used Sharpe ratio does not, and neither do most other such ratios based on the ratio of a return metric to some deviation metric.

The reward-risk ratios that the authors propose can satisfy scale invariance (ie, a pure costless leverage should not change the ratio) as well as the monotonicity and concavity requirements, and furthermore they might also satisfy the requirement that they are solely based on the distribution of returns under a given probability measure. The authors give an extensive list of properties of some well-known (and not so wellknown) reward-risk ratios and demonstrate that only a few of them satisfy all four requirements.

Despite what might appear to be a purely theoretical study (I admit that seeing the words proposition and corollary does give that impression!), I would suggest that practitioners nevertheless expend some effort trying to understand the subtle differences in performance measures. Often, we go on using common reward-risk ratios and even managing large amounts of money on that basis without questioning their limits of applicability. This paper and the previously published paper by Pezier in the Summer 2012 issue of our journal will be useful in sorting through different choices and finding the one that best fits the investment objective.

In the issue's second paper, "When you hedge discretely: optimization of the Sharpe ratio for the Delta-hedging strategy under discrete hedging and transaction costs", Artur Sepp tackles a difficult topic: the optimization of the hedging strategy for vanilla options when the underlying price process is different from the Black Scholes lognormal assumption. Taking into account all aspects of the problem - namely, the discreteness of the hedging times, the residual risks and the transaction costs incurred while hedging - Sepp derives a general framework for optimizing delta-hedging strategies and computes specific solutions in the cases of lognormal diffusion (the base Black-Scholes case), jump diffusion, stochastic volatility and stochastic volatility with jumps.

Since these generalizations of the Black-Scholes model are often used in industry, it is very instructive to see their implications for the performance of the delta hedging strategy. The results presented in the paper will guide practitioners in their selection of a hedging model and in its fine-tuning for the particular trading setup.

Furthermore, the presented estimates of the residual risk after the optimal hedge can help in pinpointing the possible sources of market pricing deviation for each model, since these risks will remain on the traders' books and will therefore need to be covered by risk reserves - and they would ultimately influence the market maker's appetite for risk and, consequently, the supply of that risk to the market. There is ample evidence in the literature that such analysis can yield reasonable estimates for effects like volatility smiles and smirks.

Our third paper, "Hedge fund replication: putting the pieces together" by Vincent Weber and Florian Peres, takes a close look at factor-based hedge fund replication techniques, using the dynamic macro factors obtained from tradable futures prices and a framework for explanatory variable selection and validation. Unsurprisingly, the authors find that such a methodology works best for replicating systematic liquid strategies.

The authors performed a very large empirical study of actual hedge fund returns, encompassing more than 7000 hedge funds over a six-year period (2006-12). The scale of the study allows them to weed out many outliers and zoom in on the best common driving factors of hedge fund returns. The authors primarily use statistical techniques (principal component analysis, information entropy measures, cluster analysis) rather than fundamental selection of the explanatory variables. While this can potentially lead to data overfitting, especially in large data sets with many explanatory factors, it is the stability of the resulting factor set that allows meaningful conclusions to be drawn in the case of liquid systematic strategies.

From an alternative investor's perspective, the power of this study is twofold: it allows us to understand the driving forces behind the predominant part of hedge fund returns (alternative betas), and it allows us to extract, within the assumptions of the methodology, the estimate of the "true alpha" of particular hedge funds. These are both very useful for decisions regarding capital allocation and for manager/fund selection
in fund of funds portfolios.

The Investment Strategy Forum paper in this issue is "Credit portfolio management in a turning rates environment" by Arthur M. Berd, Elena Ranguelova and Antonio Baldaque da Silva. The authors reprise their studies from ten years ago regarding the impact of a change in interest rate regime, such as the onset of a rising rates cycle, on credit portfolios and they find interesting new patterns that have emerged in the past few years. The relevance of the study is sharpened by the ongoing discussions in both the Federal Reserve and the markets about the need (or likely need) to end the quantitative easing program, which will potentially cause a rise in interest rates and changes in the shape of the rates curve. We have already seen such cycles before (most notably in 2003-4, after the end of the previous recession), but this time it might be even more important, given how low rates got and how long they have stayed so low.

The authors show that, in general, rising rates are associated with a better credit environment and compression of credit risk and spreads. They break down the results by industry sector and credit rating and introduce a simple metric, the effective duration multiplier, that allows the effects of the rates-spreads correlation to be efficiently taken into account when managing a credit portfolio for interest rate risk. They show that the statistical patterns observed more recently are somewhat different from those seen previously, especially when it comes to the correlation of yield curve steepness and credit spreads. The authors present the results obtained from the Barclays POINT Global Risk Model as of June 2013 and as of December 2003 and warn readers that the most recent statistic might be transient if the Federal Reserve does indeed change its policies.

Arthur M. Berd
General Quantitative LLC