Welcome to the second issue of the third volume of The Journal of Investment Strategies. In this issue you will find four papers, covering topics ranging from asset allocation and efficient portfolio construction techniques, to the hedging of economic risks, to the optimal execution of algorithmic strategies.
In the first paper of the issue, "Optimal starting times, stopping times and risk measures for algorithmic trading: target close and implementation shortfall", Mauricio Labadie and Charles-Albert Lehalle undertake a detailed study of risk measures associated with the execution of algorithmic strategies. This topic, which has been one of the hottest areas of research in recent years, originated approximately fifteen years ago, as the rise of institutional algorithmic trading necessitated a much deeper understanding of the impact that such trading has on the markets and on the investor's portfolio performance and risks.
The authors focus in particular on defining and modeling the risk metrics associated with the execution of strategies. As they explain, the definition of the proper risk (cost) metric is a nontrivial task and they take the phenomenological approach, parameterizing a wide class of models in such a way as to make the calibration to observable characteristics of the strategy possible.
They proceed to define the target close and implementation shortfall algorithms and derive the optimal execution for them under nonlinear market impact and additional constraints on the maximum participation rate. The results obtained in this paper should be of importance to both the sell-side algorithmic trading groups that execute client orders and to buy-side investors who try to optimize their trading to minimize the market impact and slippage versus the target execution price.
In the issue's second paper, "Are commodity futures a good hedge against inflation?", Laura Spierdijk and Zaghum Umar address a topic that has had great importance in recent years: the risk of rising inflation and ways to manage it. The unprecedented measures taken by many central banks - from the Fed in the US to the ECB in Europe and the Bank of Japan - have brought the specter of potential inflation to the forefront of many investors' concerns. Even though this inflation has not yet apparently materialized, the risks of it igniting due to the prolonged period of aggressively easy monetary policy cannot be dismissed.
Commodities have traditionally been the instrument of choice for hedging inflation risk, under the assumption that their prices reflect the "real asset value" and are therefore intrinsically protected from "nominal price inflation". The authors demonstrate that commodity futures can indeed be used to hedge inflation risk, but they note that the efficiency of such a hedge is variable in time and, correspondingly, the residual risks may not be as contained as one would wish. Furthermore, they warn that the reduction in the volatility of real rate of return does not come for free and is also associated with a reduction in the expected real rate of return.
The authors offer a detailed analysis of the hedging efficiency of different segments of the commodity futures market: energy, precious metals, industrial metals, agriculture and livestock. Interestingly, and perhaps surprisingly for many pundits, they find that precious metals do not actually offer a significant inflation hedging capacity. The most efficient choice for inflation hedging is found to be the energy commodity futures. Perhaps this is due to the dominant role that energy prices play in driving inflation in normal times. I would suggest that readers interested in this topic also cross-check these empirical findings with those in the paper by Fulli-Lemaire that was published in Issue 3 of Volume 2 of our journal, where a fundamental economic model of pass-through inflation was investigated.
In our third paper, "Optimal diversification", George Chacko, Robert McMillan and Karl Neumar offer yet another take on the risk-driven portfolio construction problem. This journal has published several papers on this important topic and this one further expands the horizon by focusing on the diversification side of the puzzle.
The authors propose a correlation-based criterion of optimal diversification: namely, that the portfolio is considered to be maximally diversified if it is equally correlated with each of its components. The oft-discussed risk parity framework is considered a logical underpinning of the author's methodology, in that the paper follows the same path of abstracting from the use of expected returns (means) and focuses on building a balanced risk portfolio.
The authors compare the equicorrelation portfolio with the equal weight and mean- variance optimized portfolios (with and without constraints), and show that it fares better under most common measures of quality of returns. While there is no proof that this approach is guaranteed to outperform (in nominal or risk-adjusted terms) all other possible portfolio weighting schemes, it certainly appears to be a reasonable alternative to consider. For other alternative risk-balanced portfolio construction approaches, readers can refer to many works cited in the bibliography of the paper.
In the fourth paper in the issue, "Robust Bayesian allocation", Attilio Meucci offers a brief but comprehensive examination of the problem of optimal portfolio choice when the source of risk is the parameter uncertainty and errors in the estimation of means and covariances. The proposed robust Bayesian allocation approach seeks to ensure an acceptable level of portfolio risk in a broad range of market realizations.
It combines insights from Bayesian frameworks (such as Black-Litterman), which elegantly combine investor beliefs and market uncertainties, and from robust allocation methodologies, which deal with parameter uncertainties, including those in the beliefs of investors. The Bayesian approach allows us combine both objectives and, in addition, to give a precise meaning to the uncertainty range of parameters as the Bayesian location-dispersion ellipsoid.
Following a detailed and highly pedagogic exposition of the methodology, Meucci proceeds to demonstrate its efficacy on an example of cross-sector allocation for the S&P 500 and shows that the new approach results in a significant improvement of performance versus drawdowns.
Arthur M. Berd
General Quantitative LLC