Thu, 27/01/2005 - 06:06
Marc S. Freed of Lyster Watson & Company examines the evolution of the latest generation of tools for evaluating hedge fund performance.
Among the many offspring spawned by Markowitz's  seminal work on portfolio construction, performance measurement ranks among the oldest. Following Markowitz, Sharpe [1964, 1965, 1966, 1968], Treynor , and Jensen , made notable contributions to the literature. By the late 1970's, many others had enriched their fundamental insights.
In the generation since these pioneers of modern financial analysis introduced their ideas, the financial services industry has adopted them as core principals of academic and applied finance. Powered by decentralized computing power beyond the imaginations of these early students of financial markets, the deregulation of the financial markets, and the growth of securities' markets, many of the once theoretical ideas of performance measurement have evolved into common statistics available at the click of a mouse to investors everywhere. In many instances, investors attribute to these measures degrees of accuracy and insight into the behavior of markets that they may not merit.
While the most common measures of fund performance can trace their origins to academic research conducted more than 35 years ago, changes in the financial markets have created new kinds of funds not envisioned in the original work on fund performance. Specifically, the emergence of hedge funds as a significant component of asset allocation raises new questions about the utility of conventional measures of fund performance.
This note explores the properties of hedge funds and proposes a new measure of performance valuation that extends the traditional paradigm in ways that reflect more accurately the distinctions between long-only investing and hedge fund investing.
We use a two-step quantitative approach to evaluate hedge fund performance.1 First, we discuss the idea of the Orthogonal Index Score ("OIS") as a method for rating and ranking investment fund performance.2 Analysts may use the OIS methodology to calculate TRUE ?? (TRUE ALPHA?)3. While clearly based on previous research on this topic, the OIS method has attributes that make it superior to existing methods of evaluation. OIS embodies the fundamental principles of modern finance more accurately than other measures of managerial skill for two reasons:
1 It assesses the performance of fund managers for fixed periods in the context of the opportunities available to them in those periods.
2 It rewards both risk reduction and return enhancement.
Second, we introduce the concept of a Portfolio Possibility Set ("PPS") as a means of identifying a market risk and return for asset classes for which no clear market exists. Calculation of the PPS for hedge fund strategies reveals the behavior of "markets" characterized by trading strategies rather than by specific assets.
Conventional Measures of Performance
While modern financial theory has spawned incredibly complex tools for money management, investors still focus primarily and properly on two attributes of any investment: the volatility of its returns over time, from which one can compute a probability probability of loss, and its percentage return. Good investments compensate investors fairly for the risk of loss they bear with substantial positive returns in excess of those available on investments that pose no risk of permanent loss of capital such as US Treasury securities. Poor investments compensate them poorly or not at all for risking loss of principal.
Many existing measures of relative financial performance tend to focus solely on one attribute or the other, usually the return. A slightly more complex measure known as the Sharpe Ratio, developed by the Nobel Prize-winning economist William Sharpe, calculates a modified ratio of return earned to risk taken. While this measure has at least the virtue of combining two key factors, risk and return net of the return on a risk-free asset, into a single number, it ignores an even more important factor affecting investment returns: the performance, i.e. the risk and return, of the market in which a fund operates. True ?™ quantifies the relationships between the performance of investment portfolios and that of the markets in which they occurred.
Calculation and Interpretation of True Alpha™
Specifically, OIS measures the extent to which a fund manager has improved the tradeoff between risk and reward of an investment relative to the comparable tradeoff available in the market in which the fund operates. One measures a market's terms of trade by taking the ratio of its return net of the return on a risk-free asset to a quantitative measure of its riskiness. In other words, one calculates the Sharpe Ratio of the market as a whole. One calculates True ?™ as the perpendicular distance from the performance of a fund to a strategy market line connecting the risk-free rate of interest and the performance of the market in which the fund operates.
The calculation of True ?™ is relatively simple. In simple algebraic terms, it is the length of the hypotenuse of a triangle whose sides measure the incremental risk and return of a fund relative to a point on the strategy market line. For each individual fund, that point is the orthogonal intercept between the fund and the line.
This calculation produces a number with properties that make it attractive for comparing performance:
1) The sign of True ?™ indicates performance relative to the strategy market in which a fund operates:
a) it is always positive for funds above the market line
b) it is always negative for funds below the market line
c) It is always zero for funds on the market line
2) Positive True ?™ scores always correspond to above-market returns and below-market volatility while negative ones always correspond to the opposite.
3) True ?™ neutralizes the effects of implicit leverage used by managers to enhance performance.
The Strategy Market Line
The Strategy Market Line is a variation on the term capital market line that Sharpe (1964) coined in his Nobel Prize-winning research, to describe the set of returns available to an investor who allocates his investment exclusively between the risk-free asset and the market index. The Strategy Market Line that describes the returns available from combinations of the risk-free asset and a diversified portfolio of hedge funds implementing a single hedge fund strategy applies this notion to the world of hedge fund investing.
By incorporating both a risk-free rate of return and a risky market rate of return with both the risk and return of a fund, OIS informs investors about the actual contribution of the manager to the performance of its fund. Investors may benefit from this if it enables them to choose managers who truly add value rather than managers who simply mimic the markets in which they operate. It may also help them to avoid managers who produce substantial returns only by taking excessive amounts of risk.
Comparison of OIS to the Sharpe Ratio
Both the Sharpe Ratio and the Orthogonal Index Score measure out-performance or under-performance of investments relative to other investments. By incorporating only the risk-free rate and the performance of the asset under review in its calculation, the Sharpe Ratio ranks investments only in order of their performance relative to the risk-free rate. In contrast, by incorporating both the risk-free rate and market performance in its calculation, the OIS provides a measure of investment performance that permits an analyst to rank investments in order of their performance relative to both the risk-free rate and to the performance of the market to which it belongs. Because both True ?™ incorporates the parameters of the Sharpe Ratio, it produces rankings that are similar but usually not identical to those of Sharpe Ratios. In economic terms, True ?™ captures information about an investment that the Sharpe Ratio ignores, the opportunities provided to it by the market to which it belongs.
Portfolio possibility sets
To calculate the performance of the market for a specific hedge fund strategy, we put return data from a sample of funds practicing the same single strategy through a Monte Carlo process to simulate the performance of highly diversified portfolios of the sample funds. We base this approach on a hypothesis that collectively a group of managers in a strategy capture all the opportunities available at any given time. This process produces a cloud or "blob" of datapoints clustered around a mean risk and return. The size of the blobs reflects the dispersion of returns in each strategy and reveals much about both the nature of each strategy and the variations in skill of its practitioners. The northwest edge of each blob is an observation of the efficient frontier of the strategy.
While we could use a point of tangency between the risk-free rate and the blob to select an efficient allocation among funds as a proxy for the market, we use instead the arithmetic mean of the observations. This reflects more accurately, we believe, the likely outcome of a naïve investment strategy of investing in a large number of managers of a particular type.
Hedge fund investors seek to identify managers who generate positive returns when markets present opportunities to do so, and who protect capital when markets are less favorable. In the absence of accepted standard indices for hedge fund strategies, it is difficult to identify such managers by comparison to a common reference point.
Lyster Watson True ?™ addresses this problem by calculating an observable measure of performance for a single strategy and ranking funds in that strategy on the basis of their relative out-performance or under-performance of a diversified portfolio of funds in a single strategy. True ?™ is easy to calculate and interpret. While hardly a crystal ball, it does serve as a useful screen for sifting managers within a single strategy.
1 As the reader will see below, these techniques work for conventional fund analysis as well.
2 Lyster Watson & Company and the author have filed a patent application with the United States Patent Office for the methodology employed to calculate the Orthogonal Index Score.
3 The marks True ? and True Alpha are trademarks of Lyster Watson & Company.
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