What we've learned about portfolio construction from the first decade of hedge funds.

    Rarely has the development of a diversified portfolio, which combines traditional assets and hedge fund strategies in a way that should meet a taxable investor's objectives for both return and risk, been more important to investors than it is today. In a world of modest returns on financial assets and an ever closer correlations between different markets around the globe, the search for uncorrelated returns has become intense.
    This article is divided into two parts and builds on the insights from our previous articles on performance and risk1,2 in hedge fund strategies [Financial Advisor, March 2005 and May 2005]. The first part will develop a general asset allocation framework that begins by examining only traditional assets. Particular emphasis is placed on the realization that return distributions are not normally distributed, and that loss of wealth over a period of time may be more of a concern to an investor than the volatility of returns from period to period. We also introduce hedge fund strategies toward the end of Part I to examine the improvement an investor may be able to achieve by including such strategies. In Part II, we will delve deeper into the process to select specific hedge funds to populate one of the hedge fund strategies identified in part I. While we will emphasize the use of quantitative tools to assist in the construction of the portfolio, we acknowledge from practice that portfolio construction is more of an art than it is a science.

Part I
The Investor's Objective
    In any given investment program the first and perhaps most important step is to determine the investment goal. Remember that this is not a one-size-fits-all exercise. While investment goals and objectives are personal, key considerations are common to most investors. These include a desired rate of return; quantifying the "pain" associated with economic loss; investment time horizon; liquidity requirements; and the investor's tax status. Each of these key considerations must be reviewed, understood and defined before portfolio design can begin.
    For our portfolio construction exercise, we assume the investor:
    must pay taxes on the investment portfolio;
    has a five-year investment horizon;
    will have grave concerns if there is a loss of portfolio assets of greater than 10% over any time period within the five-year period;
    must be confident that 60% of the value of the portfolio can be liquidated at any time;
    requires a 7% to 9% compound return after taxes and fees;
    is willing to consider some limited investment in hedge funds, if a good case can be made and appropriate funds can be found.
    Portfolio construction is largely an art, but as with any art there are valuable tools of the trade. These include the use of optimization and stress testing. Key elements of each of these tools are return distributions and how returns vary over time with each other, i.e., correlations. As we pointed out in prior articles,3 serious problems are associated with each of these tools. In developing the portfolio for the hypothetical investor, we will show how these problems may be addressed to arrive at a solution that has a greater likelihood of meeting the investor's expectation.

The Analysis
    To begin the analysis, we start with performance data for six traditional asset classes where the asset returns have been adjusted for ETF (exchange-traded fund) or mutual fund fees for each asset class. All returns were estimated on an after-tax basis, assuming 15% capital gains and dividend taxes and a 40% effective tax rate on current income. A two- to three-year holding period was assumed for calculating capital gains. The data was collected from January 1, 1990, through December 31, 2003. Figure 1 shows the average annualized returns and standard deviations of the data used.
    To illustrate problems associated with portfolio optimization using historical mean returns and standard deviations, we developed an efficient frontier6 using the traditional assets in shown in Table 1 and the associated correlations. There were no constraints placed on any of the assets, meaning that the investor could choose any investment option and weight that investment between 0 and 100%. Shorting and leverage, however, were not permitted in this exercise. This efficient frontier is shown in Figure 2 and the associated asset mix for varying returns in Figure 3.

What Does The Efficient Frontier Suggest?
    For starters, it becomes apparent that the high end of the 7% to 9% after-tax return objective may be difficult to achieve. To obtain a portfolio with returns of greater than 8% would require an equity investment in excess of 75%. If that were the case, the standard deviation of the portfolio would be 11%. This level of risk would imply that in any given year the portfolio could realize a return of +19% to -3% two-thirds of the time.7 Furthermore, it is possible that the returns could range between a gain of 30% and -14% with 95% probability. Perhaps a "reasonable" portfolio would be one with 60% S&P and 40% Municipals that has a return of 7.7% and a standard deviation of 9.0%. A two-standard-deviation downside return would be a loss of 10.3% with this portfolio. This result would appear to be close to the low side of the investor's objective. Overall, it does not appear that the investor's objective can be fully met with traditional assets. Before we go searching for other assets, however, we will stress test this solution to see how well the portfolio offering a return of 7.7% meets other criteria set up by the investor.

The Problem With Traditional Mean-Variance Optimization
    As we noted in the earlier articles, mean-variance optimization is based on the assumption that asset returns are normally distributed. Figures 4, 5 and 6 show that this is not a good assumption, even for traditional assets. These charts provide the histogram of the returns for the Lehman Aggregate Bonds, S&P 500 Equities and Municipal Bonds, and a normal distribution curve that has the same mean and standard deviation. The exhibits also show the probability distribution that is the "best fit" for the returns. The best-fit curves are obviously a much better representation of the return distribution than the normal curve, when compared to the histograms. It should be noted that the best-fit curves are negatively skewed, and have "fat tails."8 The problem with a distribution with fat tails is the element of surprise. In looking at the exhibits, one may wonder if the distributions are really that much different. Keeping in mind that the returns shown are monthly returns, there is 2.5% probability of a loss of greater than 2.1% for Municipals if the normal curve is used but a loss of greater than 2.5% if the "best-fit" distribution is used, or almost 20% greater. The increase in possible losses for the S&P 500 and the Lehman Aggregate Bonds are 15% and 18% respectively. Thus while the distributions do not appear dramatically different, if losses are a concern, the difference is relatively large.
    Another constraint with mean-variance optimization is that it is a single period optimization. Our investor's goal, however, has a five-year objective and includes not realizing a loss of 10% at any time within the five years. We developed a Monte Carlo9 simulation to test the 7.7% optimized portfolio and evaluate how the optimized portfolio might perform over the five-year period, with return patterns that are the best-fit distributions. The simulation consisted of 1,000 iterations over a random 60-month period. The portfolio is rebalanced monthly. The simulation preserved the correlations of the returns and used the best-fit distributions. The results of the simulation are shown in Figure 7.
    One statistic that was captured by the simulation was the maximum drawdown in any 60-month period. This drawdown could have been the result of several months of poor performance and was independent of the calendar, e.g., it could have been over the year-end. The average of the maximum drawdown over the 1,000 iterations was 16.6%, but there was one 60-month period out of the 1,000 that had a drawdown of almost 50%. This is clearly outside of the investor's objectives. It is interesting to note that the average compound return was 7.1%-below the investor's objective and less than would have been expected from the mean-variance optimization, which is a result of the negative skewness described above and shown in Figures 4, 5 and 6. This suggests that this portfolio was doomed to disappoint the investor because it is highly likely to have never returned the expected 7.7%. The portfolio had negative skewness (greater downside events) and slight positive excess kurtosis (fat tails indicating performance events that are outside normal expectations).

Can We Improve The Results?
    While the traditional asset portfolio may meet some of the investor's goals, the drawdown is too large and the returns will be at the low end of the range. Thus, it would appear to be desirable to look for other strategies, including hedge funds, which have low correlations to traditional assets in order to develop a portfolio that will be more consistent with the investor's objectives.
    Hedge funds diversify overall portfolio risk by generating returns that for the most part have low correlations to traditional equity and bond indexes. However, before adding other, noncorrelated strategies like hedge funds to the mix, it is worth examining a more robust approach to building a more "efficient" portfolio.
    The major objections of traditional mean-variance optimization techniques include the assumption that returns are normally distributed and are best viewed as a one-year probabilistic outcome. To incorporate more realistic factors, we use a simulation model and optimize the asset mix to minimize the average maximum drawdown at a given level of return. Figure 8 shows the results of this optimization approach when we set the target return to 7.1%, which was the result of the simulation of the original mean-variance optimization. There were no constraints placed on any asset class for this optimization.
    Even though the compound return is still 7.1%, the asset allocation indicated has characteristics that are more in line with the investor's objective. The average maximum drawdown is 11.1%. The largest drawdown recorded over the 1,000 iterations of the five-year period is only 30.8%, or almost 20 percentage points less than the portfolio created using mean-variance optimization. On average, we are much closer to the investor's objective of no drawdown in excess of 10%, but must improve because there is still a 5% chance that the portfolio will have a drawdown greater than 19.3%. The portfolio has less negative skewness (smaller downside potential with only slightly larger fat tails). The resulting asset mix changed significantly, and is mostly comprised of municipals and emerging market equities and large-cap stocks. As a result of this shift, the standard deviation of the portfolio is reduced to 7.2%. Clearly, this illustrates how the use of more representative distributions, which do not appear dramatically different from normal distributions, can affect the compositions of the optimum portfolios and can lead to portfolios that are more responsive to the investor's objective.
Why is the allocation to municipals so high? For a taxable investor, municipals offer the best risk-weighted, after-tax return. This high allocation to municipals would be quite different for a nontaxable entity like a pension fund. Other assets, like emerging markets equity, help diversify and add return so that the portfolio is closer to achieving the investor's objective.

Adding Hedge Funds To The Mix
    While we are closer to the investor's drawdown objective, it has not been met and returns are on the low side. If we include alternative strategies, like hedge funds, it may be possible to improve the results. The first question we will analyze is which hedge fund strategies are most complementary.
Keep in mind that the investor exhibited some concern about the use of hedge funds, but indicated some willingness to include them at a modest level. The investor's objective also included a requirement to be able to liquidate 60% of the portfolio at any time. Since most hedge funds have limited liquidity13, we will include hedge funds in the optimization process but limit the allocation to 25% of the total and limit the maximum investment to any one strategy to 10% or less. We also will set the target return to 8%, the mid-range of the objective, and optimize to minimize the average maximum drawdown over the five-year period. The allocation and relevant statistics are shown in Figure 9.
    At the 8% average compound return over the five-year period, the average maximum drawdown is reduced to 6.3%, which is well within the investor's objective. The maximum drawdown (19.1%) is still somewhat above the 10% objective but there is only a 5% chance that the maximum drawdown will be greater than 10.9%. Thus, it is likely that this portfolio is close enough to the investor's objective to be acceptable.

Conclusion For Part I
    Actual re-turns are not normally distributed.
    While differences between best-fit distributions and normal distributions appear small, the differences in performance, drawdowns and portfolio allocations can be large.
    The use of simulations using best-fit distributions can identify potential areas of investor concern and provide a better method to evaluate the likelihood of meeting the investor's objectives.
    Optimization, combined with simulations, provides a means to select portfolio allocations that can come closer to meeting investor expectations.
    The inclusion of hedge funds provides an opportunity to increase returns and reduce risk to the investor. In comparing Figure 9 to Figure 7 (the simulated results of the optimal portfolio developed through mean-variance optimization), higher returns are apparent with significantly lower drawdowns and volatility.
    It also is apparent that for the taxable investor, municipals play an important role.
    The taxable investor may need an unconventional asset allocation, but by adding uncorrelated assets like hedge funds, an investor can achieve better potential results.

Part II
Identification Of Specific Hedge Funds
    The hedge fund strategies indicated in Figure 9 include Managed Futures, Event Driven, Long/Short Equity and Macro Funds. No hedge fund strategy is greater than 10%, and the total hedge fund allocation is 25%.
Which hedge funds should one consider?
    The first step in identifying hedge funds is to use screening criteria to reduce the field of well over 7,000 funds contained in hedge fund databases.         The screens used are designed to identify those funds that appear to have characteristics that suggest they:
    have the financial ability to retain staff;
    are viable businesses that will remain in existence;
    have indications of a risk management process that controls drawdowns and are risk/return efficient;
    have returns that are reasonable, but not necessarily in excess of the investor's objectives for the portfolio;
    have product descriptions that suggest a well thought out process and a viable investment philosophy;
    are available to U.S. taxpaying investors.
    The screens identify around 20 to 30 funds in each strategy. This is a reasonable number to start the qualitative due diligence process. Added to this field are funds suggested by the investor, and others that have been previously evaluated, but may not be in databases.
    Phone calls are made to the marketing contact to determine if the funds are open, and to get a description of the investment process, investment staff background and other basic information to determine if further review is warranted. This step usually eliminates a third of the identified funds.
Marketing presentations, due diligence questionnaires, fund prospectuses, financial statements and subscription agreements are obtained from the remaining funds and are thoroughly reviewed. Internet searches, including the SEC's records, are also conducted to determine if there is any relevant information to assist in the decision process. Information obtained from this document review can provide reason to eliminate half or more of the remaining candidates.
    The next step is to have telephone interviews with investment staff to develop a greater understanding of the research process, portfolio construction, and risk management discipline employed by the funds. The most promising prospects are then visited for an onsite review.
The onsite visits are used to expand the understanding of the investment and risk management activities, inspect the facilities and confirm their existence and to evaluate the interaction of the staff to determine how well they work together and the likelihood of defections of major players. Frequently, discussions with the receptionist or new hires can be as insightful as those with the managing partners.

Selection Of Specific Funds
    We now have built a file for each strategy that includes monthly performance net of fees and taxes, volatility measures and a correlation matrix, which describes in one number how each fund's performance varies relative to all other funds.16 A portfolio built with funds that exhibit low correlations to each other is ideal, as performance for the overall portfolio will be more predictable over time with fewer painful surprises.
The remaining candidates for each strategy are evaluated to determine which ones make the "best" strategy portfolio.

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