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Investing in Turbulent Times: Applying Dynamic Portfolio Theory

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by Professor John M. Mulvey, Ph. D.
Princeton University

Introduction

The 2008-2009 market crash and October 19, 1987 are the most violent episodes in modern economic market history. Undoubtedly, similar to the 1987 event, the 2008-2009 crash will be the focus for much future research. Nevertheless, several immediate lessons can be learned from recent events:

Traditional diversification approaches did not achieve intended benefits (due to extreme levels of contagion, among other causes);
Alternative investment categories, such as private equity, hedge funds, and venture capital, did not protect the investor;
Volatility increased to unprecedented levels; and
Most investors did not take correction action in time to protect their wealth.

To illustrate the first point, we measured the average correlation among standard equity benchmarks (size – large, mid, small; and style – value, growth) in developed countries. These correlations have steadily increased over time, to the point that diversification benefits of traditional equity asset allocation are largely diminished. Exhibit 1 shows these trends to 2007. The situation became critical in late 2008, when contagion became extreme with correlation approaching unity.

Exhibit 1: Average Correlation of Traditional Equity Style Indices

(ICB = 10 sectors as defined by Datastream, level 2; ST6-A= 6 adjusted Russell asset categories with minimum overlay; ST9-A= 9 standard Russell asset categories; RND= Randomized indices; and OPT= optimization model designed to maximize diversification benefits)

Despite the plunge in asset values, select institutional investors (mostly multi-strategy hedge funds) were able to achieve superior performance in 2008 - 20% to 30+%. Some of these investors, such as global-macro funds, anticipated the dire times ahead and shorted assets – leveraged equity, high-yield bonds, and commodities. I will ignore these discretionary investors. Instead, I will discuss systematic concepts that have proven effective at protecting investor wealth over many decades. I call this domain “dynamic portfolio theory” since the investor must respond to (changing) market conditions in a timely fashion (Mulvey 2009).

Highlights of Dynamic Portfolio Theory

The starting point for dynamic portfolio theory is the interpretation of the investor’s environment as a long sequence of investments (bets) similar to the playing of a game of chance such as blackjack. Several points are worth noting:

Investor circumstances change daily as a function of the investor’s wealth, goals, and underlying economic conditions. Taking the blackjack analogy, an investor interested in growing her wealth over time must consider the odds and current wealth before placing a bet. For example, the Kelly strategy (growth optimal) requires a reduction in the underlying dollar value of the bet as wealth decreases. Conversely, larger bets are made when the investor’s wealth increases (all else being equal).
The development of optimal investment strategies must account for transaction and market impact costs, especially during periods of extreme turmoil. To accomplish this, I advocate multi-period asset allocation (or asset and liability management) models. Transaction costs can be readily included in the framework as a function of current economic conditions. Also, changing correlations and volatilities can be directly added.
Given (1) and (2), the investor can protect her wealth against adverse circumstances. There are two fundamental ways to accomplish this goal: a) maintain investment strategies that produce strong positive returns when other strategies are performing poorly, and b) reduce risk capital during drawdown periods.

Two reliable examples of achieving higher returns during stressful market conditions are duration-enhanced overlay strategies (Mulvey and Kim 2008) and rebalancing a large set of relatively independent investment strategies - to achieve rebalancing gains during extreme turbulence (Luenberger 1998). The longstanding MLM trend-following index partially fits the latter requirement (Mulvey et al. 2004). Here, performance is best when volatility increases; 2008 was no exception with an over 15% return.

The steep market plunge during September-December 2008 was preceded by and accompanied with high turbulence and massive trading volume. Investors who saw these conditions and were able to act accordingly were able to reduce their risk exposure and protect their capital base. Buy-and-hold investors suffered severe losses.
An investor interested in protecting her wealth must be able to take corrective action in a timely fashion. Thus, in 2000 at the height of the tech bubble, our investor must be aware of the potentially large imbalance in her asset mix with high tech stocks (or equivalent venture capital). Andrew Golden, head of Princeton’s investment management company, has recounted such an event. At the time, he decided to rebalance Princeton’s portfolio through pubic markets since he could not drawdown the private venture funds. While this hedge was incomplete, it did partially protect against subsequent losses in 2000-2002.

Applying DPT with Alternative Investments

Leading university endowments in the United States have switched to alternative investments over the past decade. David Swensen at Yale University has had an important impact on this trend. A key argument favoring these is greater expected returns in private investments; performance had been quite good up until 2008. Unfortunately, these investments underperformed in 2008 despite the shelter of non-public investments. In fact, illiquidity has worked against the investor since standard contracts for private investments largely limit access to funds for rebalancing or cashflow needs.

Exhibit 2: Performance of Fundamental Replicating Strategy and Related Series

There are significant limitations for measuring the temporal returns of private equity markets. The Cambridge Associates results should be carefully evaluated in this context.

To assist in applying DPT with alternative investments, we have developed a fundamental replication strategy for private equity (the strategy works best for funds with a focus on mature firms). By fundamental, we refer to strategies based on the basic premises of private investors – including leverage, selection of industries, and cashflow decisions. A fundamental approach can largely capture the returns of the median private investment. Exhibit 2 shows the wealth path of the median performance of private equity (as measured by Cambridge Associates) over the period 1995-2008 (along with S&P 500). In comparison, we plotted the fundamental replication strategy, including the recent time period. Note that the Cambridge data is only available quarterly. Based on these tests, we estimate that the median private equity fund dropped by roughly 25% during the fourth quarter 2008.

Conclusions

Most investors lost a substantial portion of their investible wealth in 2008. Could these investors have rightly expected to protect their wealth? Of course, this issue cannot be fully answered. However, several strategies exist that perform best during high turbulence. For example, the mentioned duration enhanced and trend-following overlay strategies promise to excel during high volatility and market crashes. Experience has shown that these strategies can be implemented over longer time periods without the excess costs of purchasing puts and other traditional protective securities.

The challenge for the future is to understand the preconditions of economic distress and to take quick action when the investor’s overall wealth is threatened. We have seen that the definition of “quickness” is now much shorter than it was before 2008. Investors should take note and develop rapid response teams and anticipative strategies to protect their wealth against future turbulent episodes.

Selected References

Luenberger, D., Investment Science, Cambridge University Press, 1998.

Mulvey, J.M., Simsek, K., and S. Kaul, "Evaluating Trend-Following Commodity Index for Multi-Period Asset Allocation," Journal of Alternative Investments, Summer 2004.

Mulvey, J. M. and W. Kim, "Evaluating Style Investment: Does a Market Defined along Equity Styles Add Value?," Princeton University Report, October 2008. (Recently accepted by Quantitative Finance - expected to appear as a feature article later in 2009.)

Mulvey, J. M. and W. Kim, "Duration Enhanced Overlay Strategies for Defined-Benefit Pension Plans," submitted to Journal of Asset Management, Special issue on Pension Trusts, 2009.

Mulvey, J.M., and S. Ling, "Replicating Private Equity Return Using Leveraged Exchange Traded Funds", Princeton University ORFE Report, January 2009.

Mulvey, J.M., "Dynamic Portfolio Theory," Princeton University ORFE Report, February 2009.

Swensen, D., Pioneering Portfolio Management, The Free Press, 2000.