Journal of Investment Strategies

Welcome to the second issue of the sixth volume of The Journal of Investment Strategies.

We have a very interesting issue for our readers this quarter, with a focus on portfolio construction techniques. The featured papers include a comprehensive risk modeling exposition, a perspective on multiperiod tactical risk allocation, an examination of the explanatory factors of portfolio risk, and a study of the impact of transaction costs on portfolio optimization.

In “Statistical risk models”, the first paper in this issue, Zura Kakushadze and Willie Yu provide a comprehensive methodology for building statistical multifactor risk models for diversified markets, such as stocks or, more generally, multiple trading strategy returns. While purely statistical multifactor models are often shunned by equity risk modelers when it comes to modeling long-term portfolio applications, they are seen from a different perspective in short-term risk modeling. In this case, the variability of returns is often noisier and more difficult to characterize using common driving factors such as industry and style loadings. Conversely, less intuitive and less stable but statistically more significant models, such as principal components analysis, perform quite well in this setting. The authors present a calculation procedure that can be optimized so it is both accurate and fast, especially when the number of stocks is large. As an added bonus, they demonstrate a regression setting for defining the weights of the optimal portfolio. I believe many readers will find this paper both highly educational and very useful, given the clarity and detail of the exposition as well as the included sample code for implementation of the methodologies.

In our second paper, “Investing across periods with Mahalanobis distances” by Edouard Sénéchal and Brian Singer, we find an illuminating discussion of intertemporal tactical risk allocation. The authors use the Mahalanobis distance between longterm and short-term investment opportunities to formulate a consistent methodology to define and solve the problem of tactical risk allocation: in other words, the problem of when to take active risk, and how much to take, compared with passive static benchmark weights. Indeed, this is a relatively uncommon angle from which to look at investment problems. When considering long-term investments, the usual approach is to set a fixed risk budget with respect to a given strategic benchmark – whether that is a market benchmark, policy allocation or just cash – and then set out to deliver the best risk–return profile given this preset risk budget. But, as the authors correctly note, this need not be so; investors can and sometimes should vary their risk budget amount. It makes intuitive sense that doing this systematically when investment opportunities are at their most ex ante promising should improve overall performance. Of course, this would only happen if we had the predictive ex ante metrics of the attractiveness of the opportunity set. Sénéchal and Singer show how to construct such metrics in certain cases as well as how to build an improved long-term investment portfolio following this approach. I found this paper easy to read and understand, and I am sure many readers will too.

“Interconnectedness risk and active portfolio management”, the third paper in this issue, sees Eduard Baitinger and Jochen Papenbrock consider a novel metric for estimating the risk of investment portfolios: interconnectedness. Unlike a more familiar metric, such as a covariance matrix of returns (or a combination of volatilities and correlations), interconnectedness exposes clusters of common behavior using the graph theory approach. The idea behind using this approach is that it should better highlight risk concentrations, and therefore allow for better and more robust construction of truly diversified portfolios. While the authors demonstrate interesting calculation techniques and discuss their relative merits, when it comes to the empirical applications of this methodology to portfolio construction, the benefits appear to be somewhat limited. Although some improvement in risk–return characteristics is found, it is far less than can be achieved in a less sophisticated manner. This should not discourage the authors or those readers who find this mathematical technique intriguing. I am certain that having a better handle on the risk structure of the portfolio is a good thing, and one can certainly derive substantial benefit from it, both in terms of risk management and improving net return.

Finally, in “Risk constraints for portfolio optimization with fixed-fee transaction cost”, Michael J. Hirsch and Nicole Navarro study the effect of fixed transaction fees on the problem of optimal rebalancing of investment portfolios. While transaction costs alone are not typically the dominant slippage component in portfolio rebalancing (market impact often plays a far more important role), this setting nonetheless applies in the case of retail investors managing their retirement or personal funds in a mass market brokerage. Many of these brokers, including Charles Schwab, Fidelity and TD Ameritrade, offer fixed transaction cost models, and they are popular with many individual investors. Following previous approaches, the authors reformulate the nonlinear optimization problem as a linearized problem with constraints, which is computationally easier to solve using linear programming methods. Using both conditional value-at-risk and mean absolute deviation as risk measures, the authors obtain a significant reduction in the number of unnecessary trades, while maintaining or even improving the performance of the model portfolios. This is as it should be, especially when the transaction costs are large compared with the initial portfolio (which is, again, the case that applies to many individual investors). While I believe its lack of market-impact modeling makes this methodology nonapplicable to institutional portfolio management, it nonetheless might very well be useful for managing smaller individual portfolios.

In conclusion, I would like to express my hope that our readers find the topics covered in this issue of The Journal of Investment Strategies both intellectually stimulating and practically useful, including techniques that can be applied in their own businesses.We look forward to receiving and presenting equally engaging papers in future.

Arthur M. Berd
Founder and CEO, General Quantitative LLC