Hedge Funds: Insights in Performance Measurement, Risk Analysis, and Portfolio Allocation
I enjoyed the October 30 Hedge Fund Panel Discussion by the authors of, “Hedge Funds: Insights in Performance Measurement, Risk Analysis, and Portfolio Allocation“, sponsored by the Chicago GSB Alumni Club of Greater New York. Heidi Christensen Goldstein did pre-introduction Then Cyrus Claffey, President Chicago GSB Club of NY, made formal introduction Moderator:
David K.A. Mordecai President Risk Economics Limited, Inc.
Mark Shore Former COO of VK Capital Inc.Morgan Stanley, New York
Hilary Till Co-Founder & Portfolio Manager Premia Capital Management, LLC, Chicago (Premiacap.com) Formerly Chief of Derivative Strategies at Putnam, and formerly at Harvard Management Company. BA Statistics UChicago. Fulbright Fellow LSE. Advisory board of natural resources hedge fund/fund of funds Now editing a book on commodity investing
Fabrice Rouah Ph.D. Candidate McGill University, Montreal Institute of Financial Mathematics Studies CTAs/hedge funds in general
Jacqueline Meziani Senior Director Standard & Poors, New York hedge fund indices. Chemical Bank, Citigroup MBA Stern 10 years at S&P Product Manager: Ops, marketing, licensing, research. My job is to catch things if they fall.
Mark Shore Book excerpt and Slides Ch. 25 Study: modern portfolio theory assumes returns to be normal-but is this true?
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Most asset classes are not bell-shaped normal curves. Can higher statistical moments (skewness, kurtosis) offer a clearer picture of risk-adjusted returns?
How do hedge funds and managed futures perform individually and simultaneously as diversifiers in a traditional portfolio?—expanded Harry Kat 2002 study of hedge funds and managed futures Sharpe ratio is widely misused — Sharpe Ratio = (returns-RF rate)/std deviation Assumptions: – historic results have some predictive ability – mean and variance are sufficient statistics for evaluating a portfolio – Distribution is symmetrical….BUT many studies have shown that time-series distributions are asymmetrical – An investment with lower correlations (such as alternative investments) may add greater value with a lower Sharpe ratio Sortino Ratio —– (return-MAR)/downside deviation —- is a better concept of downside risk.
If Standard Deviation goes up, does that mean risk has increased? Not necessarily. Schneeweis & Spurgin (2002): the independent returns of alternative investments are not as important as how they may benefit the overall portfolio. Consider co-skewness of each portfolio component.
Co-skewness may be utilized to reduce “volatility shocks’ or tail risks Kurtosis- the fatness of the tail by the peakedness or flatness of the returns distribution Beckmann and Scholz (2003) Kraus and Litzenberger (1976) support a rational investor’s preference for positive skewness and reducing volatility Till (2002): mean-variance metric is most appropriate when returns are symmetrical.
Thus using it for asymmetrical returns assumes the investor is indifferent between upside volatility and downside volatility Kahneman and Tversky Kat study (basis of Mark Shore work): asked if hedge funds and managed futures complement each other? Answer: yes, when managed futures receive >45% of alternative investment allocation.
Indices for Kat study: S&P 500 index, 10 yr Salomon Bros govt bond index, and a portfolio of 20 funds, and the Stark 300 index of managed futures Shore study: S&P 500 index, Citigroup Corporate bond index, HFR fund of fund index, and CISDM Conclusion: Sharpe ratio may overestimate the risk-adjusted returns by de-emphasizing the downside volatility of investments with negative skewness.
Sharpe ratio may understate the risk-adjusted returns of investments with positive skewness by penalizing positive volatility. S-ratio is a good ratio to use.
Ms. Hilary Till Slides Hedge Funds: Quantitative Insights
1. Return Sources
A. Inefficiencies What is capacity of hedge fund industry (with an alpha advantage) ? (based on argument in Foss (2004)) If hedge funds are exploiting inefficiencies, someone must provide them. Assume: Maximum tolerance of average investor supplying inefficiencies: -50 basis points (assumption based on size of inefficiency in global fixed income markets) Size of global capital markets: $55 trillion Required excess return for hedge funds: 10%. Ergo: implies the hedge fund industry could go to $2.75 trillion under management.
Caveat 1: prop traders also are fighting with hedge funds to exploit these inefficiencies
Caveat 2: many strategies are based on earning risk premia, not on exploiting inefficiencies.: Relative-value bond funds, equity risk arb, value vs. growth, small cap stocks, high-yield currency investing. Examples drawn from Cochrane 1999ab, etc.) I.
Return Sources C. Illiquidity Reason: tick-by-tick evaluation of a good investment is painful. Nassim Taieb (2001), Fooled by Randomness, Table 3.1: An investment of 15% return, with 10% volatility/year, implies: Scale Probability of Making Money at Different Scales 1 yr 93% 1 q 77% 1 mo 67% 1 day 54% 1 hr 51.3% 1 min 50.17% 1 sec 50.02% So on a tick-by-tick scale, you’ll suffer about half of all days from a feeling of losing money
Fabrice Rouah Review of the Academic Hedge Fund Literature (Ch. 13) Slides
1. Performance Persistence-do winners repeat? 3 methods to analyze this: + 2×2 contingency tables + binomial model (multi-period) + regression of current performance returns on past rerturns Summary: Little evidence of persistence, especially long-term Most persistence is due to losers continuing to lose Some losers increase volatility in attempt to boost returns.
2. Factor modeling No transparency, so investors attempt to identify factor exposures.
Important for anyone holding several funds (pensions, FoFs) Helps to eliminate funds with similar strategies.
Linear models are difficult because of the non-linear relationship between HF returns and asset returns (options, short-selling).
R squareds for hedge funds are dramatically lower than those for mutual funds (which are typically 0.8-0.9), i.e., these conventional factors have low explanatory power.
Particularly important study: Agarwal & Naik 2004 Non-linear returns make linear modeling difficult
3. Portfolio diversification Many styles have low correlation with equity & bond indices. Stress testing indicates they hold up well during market downturns.
Funds should not be co-integrated with markets or with themselves Adding hedge funds to a traditional portfolio increases its risk-return profile Simulation indicates 5-20% allocation Correlations: tend to be low (0.37 vs. S&P 500).
High p value means there’s not enough evidence to show that correlation is anything other than zero.
4. Survivorship bias Compares returns of portfolios.
This is the bias you will experience if you analyze a portfolio that contains only live funds. Usually about 300 bps.
In Mutual Funds, it’s usually <100 bps.
This is the most important of all biases.
5. Survival analysis how long can HFs be expected to survive, and how fast do they die? New area of research New inflows are from institutional investors They wish to invest long-term, but are worried about high attrition rates.
Seek funds with longevity Factors driving survival are the same factors driving survivorship bias. 50% survival time (i.e., half-life)= one-half funds die before this date, and one-half die after.
Estimates are of 5-6 years. Most of these studies are very biased because they usually only use funds born after 94. But one of the better studies says >10 years. No surprise: low returns, small asset base, young manager age all correlate with high mortality
Jacqueline Meziani Disclosure: “I am not a quant.” Edward Blum, my former colleague, is the major researcher on this chapter Studied equity long/shorts Short position serves following purposes: alpha generation, hedging of market risk, earning interest on short position while collecting short rebate Managers may use futures and options to hedge their positions. Overall, net exposure of E L/S funds tend to have a positive bias.
High beta funds usually have high net market exposure are often concentrated.
Moderate beta funds hold proportionately more short positions that would lower net market exposure.
High beta variability may indicate several things: manager consistently includes securities different from those in benchmark. A market-timing fund manager is controlling beta.
A stock-picking fund manager does not manage beta b/c he is concerned primarily with fundamentals of stocks in the portfolio Investable E L/S indices are fairly clustered Managers tend to go long small cap stocks and go short large cap stocks. Managers want more liquidity on short side.
Negative relationships with value premium.
These managers were taking long positions with growth stocks and short positions with value stocks (although this finding is less robust).
On average, E L/S hedge funds returns are drivne by returns of the global equity market, size premium, and the value premium.
Published on November 22, 2006, Updated on December 28, 2012. Public Equities
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