Canadian Investment Review

A Streetwise Black-Litterman

Written by Lior Menzly, Ph.D. on Thursday, October 7th, 2010 at 9:41 am

story_images_Wall-StreetThe Black-Litterman (BL) model provides a framework for incorporating portfolio managers’ views into portfolio optimization. It is the bread and butter of MBA investment courses, yet it is seldom used in practice as it does not correspond well to real-world investing.

Although the BL framework results in a stable intuitive optimal portfolio, it is costly to use from an operational standpoint. The framework asks for too much information in a form that is not very intuitive. The manager has to specify all views and express them through securities in the portfolio, and the challenge is to translate the manager’s views into views that are in line with the BL framework

However, two recent enhancements in financial engineering allow us to bring this theory to the real world of investment by exploiting the strengths of the BL framework while avoiding its weaknesses.

The first application reverse engineers the BL portfolio optimization to perform concentration analysis. Unlike traditional risk management tools, this application allows risk managers to take an active role in shaping the portfolio by finding concentrated positions and cheap hedges. The resulting concentration measure, as constructed by Menzly and Greenberg (2009), uncovers embedded manager views in the current portfolio. Implied views that are too extreme are indicative of highly concentrated positions. The risk manager can then ask the trader to trim down the position on the basis that information ratios higher than 2 rarely occur in practice. In addition, a negative implied view may indicate a cheap hedging opportunity, especially if the portfolio manager is known to be bullish on that asset. The authors also provide a special case approximation for their concentration measure, which can be calculated with a few iterations of a risk model. This approach allows us as risk managers to be actively engaged in the construction of the portfolio, instead of taking a passive role.

The second application is strategic allocation, which incorporates a forward-looking macro scenario analysis into the BL framework. Post-Lehman, volatility in the financial markets has been dominated by macro factors. The main challenge for many bottom-up portfolio managers has been avoiding unintended macro tail bets and incorporating investment committee macro views. An extension of the BL framework along the lines of Meucci (2009) and Cheung (2009) provides the least distorted way to embed the top-down scenarios of the investment committee. With this application the scenario analysis — a table that provides the movement of aggregate risk factors like the S&P 500 across different scenarios and the associated probability of each scenario — is the input. The output is a recommendation of how to change the current portfolio so that it will maximize the expected returns in base scenarios, and minimize losses in tail events while maintaining the idiosyncratic bets intact.

Lior Menzly, Ph.D. is head of quantitative research and risk management, Nomura Asset Management U.S.A. Inc.

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