Welcome to the first issue of the sixth volume of The Journal of Investment Strategies. With this issue, which marks more than half a decade in print for the journal, comes a sense of maturity in our quest to serve the buy-side quant community. I believe that The Journal of Investment Strategies has found its voice and style, and it has shaped the audience it was trying to cultivate: an audience that spans industry and academia, representing both active money managers and researchers. We cover both statistical forecasting and systematic risk management, both long-run portfolio management and high-frequency trading strategies. This issue is a good example of how all these diverse issues come together in The Journal of Investment Strategies.
In the issue's first paper, "Insights into robust optimization: decomposing into mean-variance and risk-based portfolios", the BNP Paribas team of Thomas Heckel, Raul Leote de Carvalho, Xiao Lu and Romain Perchet share their knowledge about the robust optimization of portfolios. They show how recognizing the uncertainty of the optimization procedure allows us to naturally see the connection between the classic mean-variance portfolios and the purely risk-driven portfolio constructs that have become popular more recently. The premise of the paper is highly intuitive: if the predicted/expected means are well known and have little uncertainty about them, then the assumptions of mean-variance theory should be essentially valid, and the corresponding Markowitz style portfolios should be optimal. However, if the uncertainty around the means is very large, then those mean predictions are essentially useless, and the best we can do is optimize on risk alone. It is difficult not to agree with that. Interestingly, this insight is, in some ways, complementary to the manner in which the mean-variance model was made more robust in the Black-Litterman framework. There, equilibrium considerations were used to anchor the mean estimates and, thereby, make them less prone to error. This paper presents a viable alternative to the Black-Litterman framework, and it is very important that portfolio managers understand it and consider using it.
The only issue is this: how do we ever know how much uncertainty there is around our expected means? Some portfolio managers disclaim any insight regarding this question and consequently feel justified in using the risk-driven approach. Others think of mean expectations from a fundamental perspective and do not even see a source of uncertainty, so they feel equally justified in using mean-variance theory. A third group use statistical techniques with specific forecasts, and specific forecast error estimates, and are able to pinpoint the intermediate point between those extreme views. The adherence to any of these views depends on your interpretation of the source of uncertainty. In any case, knowing that it exists and being able to formulate a coherent action plan to deal with it are extremely important for any portfolio manager.
In Boris Gnedenko and Igor Yelnik's "Equal risk allocation with carry, value and momentum", our second paper, we find an in-depth discussion of risk factor-based investing that goes beyond the often-restricted view of equity-based risk factors. The authors present a detailed analysis of cross-asset and cross-regional risk factors: specifically, the value, carry and momentum factors, which are well known both in the academic literature and in practice by active portfolio managers. Following the work of Andrew Ang and others, they argue that it is more suitable to think about allocations to risk factor portfolios than to think about allocations to asset classes and regions.
However, this change in focus also causes a change in portfolio construction methodology. Instead of optimizing the mean-variance portfolios built from assets, the authors vote for building equal risk allocation portfolios of risk factors. Why equal risk? Well, if we are not confined to asset classes, then we are not bound to asset class market weights, and therefore there is no real anchor around which we can build a stable portfolio. Hence, equal risk allocation seems a natural choice: that is, if we assume no special knowledge on the specific forecast for the performance of specific risk factors. Further, the authors demonstrate how these portfolios exhibit desirable performance and risk profiles, which are markedly better than most asset-based portfolios that do not include a lot of fine tuning and trading. For this reason, I am sure that our readers will feel intrigued to read the paper carefully, and to see if its recipes and suggestions make sense for their own investment objectives.
In the issue's third paper, "On optimizing risk exposures with trend-following strategies in currency overlay portfolios", Kai-Hong Tee presents an investigation into the optimization of risk exposures of currency overlay portfolios. While this appears to be a narrowly defined topic, it is actually a hugely important one, due to the massive amounts of cross-currency risks in investors' portfolios, which are often managed semi-passively via just such currency overlays. Of course, any deviation from passive currency overlays is equivalent to running a separate investment strategy, even if the strategy's original aim was strictly risk reduction. Once we have the freedom to undertake risk reduction on an active basis, it means we must at the very least try to perform better than the passive currency hedge.
Tee suggests that using certain flavors of trend-following strategies within such currency overlays will markedly improve their risk and return profiles. It is not all that surprising that this is the case, given the fact that many fund managers have historically been able to generate positive returns with fairly attractive risk profiles while exclusively trading in foreign exchange spot and futures markets. It stands to reason that a somewhat similar approach should also work for currency overlays.
In "Optimal closing-price strategy: peculiarities and practicalities", the fourth and final paper of the issue,Yu Hang (Gabriel) Kan and Sanghyun Park develop a specific short-term optimal trading strategy that delivers the closing price to the buyer of a stock. The closing price and the closing auction that delivers it are important for institutional investors. Most of them use closing prices to mark their valuations, net asset values and in the pricing of contributions and withdrawals. Therefore, getting a large block trade executed as close as possible to the closing price is often highly desirable, because any deviation from it remains as uncompensated additional risk to such institutional investors and funds.
Following the well-established methodology of market-impact modeling, Kan and Park estimate the slippage risk and are able to formulate an optimization problem to minimize the residual trading risk. Depending on the parameters of the optimization problem, they recover a strategy that interpolates between a classic volume weighted average price and a simple sell at the closing auction. Further, they showan unambiguous method of estimating the risk aversion parameter for the optimization problem. The results appear quite intuitive and should be useful to many portfolio managers and execution traders at mutual funds and other open-investment vehicles.
I would like to thank our readers for their support during the past five years, and I look forward to many more years of bringing cutting-edge and insightful papers to your attention.
Arthur M. Berd
General Quantitative LLC
The authors of this paper analyze an equal-weight portfolio of global cross-asset-class risk factor exposures.
The authors of this paper aim to demystify portfolios selected by robust optimization by looking at limiting portfolios in the cases of both large and small uncertainty in mean returns.
This paper proposes using an optimization mechanism in the currency overlay portfolio construction process.
The authors of this paper derive an optimal trading strategy that benchmarks the closing price in a mean–variance optimization framework.