Journal of Investment Strategies

Welcome to the spring 2013 issue of The Journal of Investment Strategies. You will find four papers in this issue: three research papers and one in the Investment Strategy Forum section. The research papers cover topics from high-frequency trading to portfolio construction to econometric modeling. The paper in the forum section continues the ongoing debate on the topic of risk parity.

RESEARCH PAPERS

In the first paper of the issue, "High-frequency trading and long-term investors: a view from the buy side", Nataliya Bershova and Dmitry Rakhlin present an extensive overview of the impact of high-frequency trading on long-term investors. High-frequency trading has attracted a great deal of attention in recent years, and especially so in the aftermath of the flash crash experience of May 6, 2010. Some see high-frequency trading as a useful and integral part of the market, providing liquidity to other investors, while others view it as being predatory in nature, "stealing ticks" ahead of slower investors and causing increases in both the cost of trading and volatility. As always in such situations, opinions usually vary according to the market perspective of the analyst.

It is therefore particularly welcome to see a serious and deep study focused not only on high-frequency trading itself, but more specifically on its impact on long-term investors. Bershova and Rakhlin's paper offers a broad overview of the field and a well-designed methodology for gauging such impact. The authors are careful to look across both mature markets, exemplified by the London equity markets, and markets that are undergoing significant structural changes, exemplified by the Tokyo equity markets. Their study dispels many misconceptions about the impact of high-frequency trading (such as its perceived predatory function) by showing that, while it does indeed cause a rise in intraday volatility, the adverse effect on trading costs is more than offset by the compression of bid-offer spreads. Given the provenance of these findings and the wealth of data that went into the research, I believe that the Bershova-Rakhlin study will be a welcome dose of sober analysis in this area filled with too much passion, sometimes at the expense of precision.

In the issue's second paper, "Properties of the most diversified portfolio", Yves Choueifaty, Tristan Froidure and Julien Reynier step into the important debate over what should be considered to be the "best constructed" equity portfolio. They introduce the "diversification ratio": a ratio of the weighted average return volatility of the constituents of a portfolio to the portfolio's overall return volatility. They define the maximum diversified portfolio as the one that maximizes this ratio.

The authors also introduce a number of invariance principles that well-designed portfolios must respect. They argue that while the maximum diversified portfolio satisfies all of them, conventional alternatives such as equal-weighted portfolios, equal-risk-contribution portfolios and minimum-variance portfolios do not. We refer the interested reader back to previous issues of our journal for more discussion on this subject: see "Understanding risk based portfolios" by Taliaferro from Volume 1, Issue 2; "Balanced baskets: a new approach to trading and hedging risks" by Bailey and Lopez de Prado from Volume 1, Issue 4; "Alternative indexing methods: point of reference - does it matter?" by Gander et al from Volume 2, Issue 1; and finally the discussion paper by Goldberg and Mahmoud in this issue.

One important limitation that is partially responsible for the results in this paper is the constraint of having a long-only portfolio. When portfolios can hold both long and short positions, the maximum diversification requirement may lead to unintended consequences. Alternatively, when it is the relative performance of the portfolio that is relevant and it is the active weights of the portfolio compared with its benchmark that are therefore being optimized, having the maximum diversification portfolio as the benchmark can also lead to portfolios that might be less intuitive.

Before moving on - and just as we said about the journal's earlier publications on this topic - while optimality of risk-based portfolios such as the maximum diversified portfolio can be studied and established under the assumption of certain volatilities and correlations between assets, in practice those parameters are not known precisely, and the nonlinear optimization criteria, such as maximizing the diversification ratio, will surely need to be adjusted for the uncertainty of the future forecasts. That is an entirely separate topic, however, and it could possibly lead to yet another definition of "risk optimal" portfolios, ie, portfolios that are optimal under future uncertainty about the risks.

In our third paper, "Time-bridge estimators of integrated variance", Alexander Saichev and Didier Sornette present a novel approach to empirical estimation of variance in a setting when a set of consecutive open-high-low-close bars are known. This is a very practical setting as most financial data providers offer this type of data, and it is very widely used by practitioners.

Saichev and Sornette compare their bridge estimators with well-known Garman-Klass and Parkinson estimators and show that they are more stable with respect to the unknown drift. Given that these estimators are typically used for shorter-term volatility measures, the unknown realized drift can actually be quite significant, and therefore the stability property with respect to this factor is quite important.

The main improvement achieved by the authors is to suggest that the so-called time-bridge estimators take into account not only the high and the low within the bars but also the timing of these extremums. As it turns out, this relatively modest amount of additional information leads to a significant improvement in the efficiency of the variance estimators. Hence, the authors argue that addition of this information to the coarse-grained data would be very useful for practitioners - a sentiment with which I completely agree.

INVESTMENT STRATEGY FORUM

Our forum paper in this issue is "Risk without return" by Lisa R. Goldberg and Ola Mahmoud. It continues the theme of risk-based optimal portfolio construction methodologies. As its title suggests, the authors are taking a somewhat skeptical view of these techniques and study not only their selling points but also their hidden assumptions and pitfalls.

Importantly, Goldberg and Mahmoud emphasize that all of the mainstream risk based strategies - namely, those based on risk parity, minimum variance and low beta - differ from the so-called balanced approach (the famous 60/40 policy portfolio) in having a higher allocation in defensive investments. That fact alone drives their higher Sharpe ratio and also explains the fairly high correlation that all these strategies have with each other.

It is important to evaluate the other differences between the risk-based strategies in the context of the induced turnover, which of course depends on the market environment. In particular, during turbulent market conditions, risk metrics also fluctuate a lot, causing large turnover and potentially large trading costs. Whether or not these increased trading costs are justified by subsequent performance is, in my opinion, a function of the type of market environment. Obviously, when rebalancing the bulk of the portfolio based on backward-looking risk metrics, one can potentially get whipsawed quite badly. But in recent history, what has more often happened has been that the monthly rebalancings have proved fortuitous and the market has on average turned at roughly the same frequency.

Goldberg and Mahmoud also introduce their version of the risk diversity index. Their index improves on the Herfindahl-Hirschman index, which focuses on capital diversification, by focusing on the diversification of risk contributions. Readers can see certain parallels between the risk diversity index definition in this paper and the definition of diversification ratio in the paper by Choueifaty et al in this issue. The critical difference is that Goldberg and Mahmoud define their diversity metric in differential form: I believe that this is likely to be better behaved than the integral form used in the Choueifaty et al and will be much easier to use in the long-short portfolio context.

On behalf of the Editorial Board I would like to thank our readers for their keen interest and positive feedback. I look forward to sharing with you the growing list of excellent papers on a broad variety of topics related to modern investment strategies that we have been receiving from both academia and practitioners. I hope you find them as fascinating and illuminating as I do.