Performance measures Nicolas Papageorgiou AQF-2005 Measuring hedge - PDF document

Performance measures Nicolas Papageorgiou AQF-2005

Measuring hedge fund performance • What is the best method? • Risk adjusted performance measures • Multi-factor models – Peer group factors – Return based factor – Asset based factors – Option returns and other non-linear factors

Risk-adjusted performance measures • The Sharpe ratio • Downside risk performance measures – Sortino – Upside potential ratio – Sterling and Burke ratios – RoVaR • The Treynor ratio and Jensen alpha

The Sharpe ratio • Three caveats to keep in mind – Inferred from past data. Backward looking therefore deceptive for investments in assets that have changing volatility • Susceptible to frequency and horizon – No straightforward interpretation of the number • Graham/Harvey and M2 (1997) – Compute portfolio of the levered position in the fund and the risk free rate such that standard deviation equal that of benchmark (Bridgewater) – The denominator is a measure of total risk • We would prefer a systematic risk measure – Treynor ratio?

Sortino ratio Sd Dd Shr Sor • Accounts better for assymetry of 1.21 0.78 .24 .46 Arb distribution 4.87 2.62 .18 .4 Cta – Similar to sharpe, but 4.41 3.91 .39 .78 DD replace standard 1.78 1.14 .24 .2 ED deviation by downside deviation 2.58 1.93 .34 .5 FI – All strategies with 3.75 2.14 .17 .44 Lse negative skew are hit 3.49 2.33 .15 .26 by sortino… Mc 3.85 2.27 .23 .22 rv

Jensen and Appraisal • Jensen JwB JwSB AR – Proper estimation of beta .32 .28 .21 Arb coefficient becomes important .79 .79 .17 Cta – Serially correlated hedge funds will lead to 1.44 1.51 .43 DD underestimation of beta .61 .66 .28 ED – Dimson (79) – use lagged as well and sum them up .71 .73 .37 FI – Does not account for leverage however .70 .72 .20 Lse – AR – Jensen divided by standard deviation of non- .51 .50 .15 Mc systematic risk .59 .56 .22 rv

Unconditional Factor models • Market portfolio (CAPM) • Fama French • Carhart – FF + momentum • Elton, Gruber, Blake – FF + Momentum + bonds

Conditional performance measurement • Ferson and Schadt (1996) – Expected returns and risks vary over time – Beta should be conditioned to market • Christopherson, Ferson, Glassman – Alpha should also be conditional to market

Other factors • Asset backed factors – Commodities, MBS, International and emerging equities, Currencies… • Option based buy and hold strategies – Agarwal and Naik (2000)

The idea behind option based factors • Hedge funds exhibit non-linear (option- like) exposures to standard asset classes • Linear factor models offer limited help in evaluating performance of hedge funds • Agarwal and Naik find that simple option writing/buying strategies are able to explain a significant proportion of the varations in hedge fund returns

Three sources of returns Trading Strategy factors – Option-like payoffs • Location Factors – Buy-and-hold strategies on different equity, bonds, currency, commodity indexes, FF factors, momentum, default spreads. • Leverage factors

Option-based factors • First proposed by Glosten and Jagganathan (1994) • Motivation: – Hedge fund manager’s compensation involves an explicit sharing of the profits, hence even if pre-fee returns do not exhibit option like behavior post-fee returns will. – Hedge fund managers frequently trade in derivatives or implement dynamic trading strategies – Many hedge funds make state contingent bets (opportunistic strategies)

Other advantages of AN approach • Less susceptible to manager manipulation • Managers can increase traditional performance measures such as Sharpe and Treynor by selling call options • This will be controlled for with the option factors

AN results • Non-Directional strategies display more significant loadings on Trading Strategy factors • Directional strategies display more significant loadings on Location Strategy factors

Hedge fund studies Emerging International International R 2 Reference U.S. Equities Markets U.S. Debt Currencies Commodities Cash Equities Debt Equities US Fed Euro$ Liang (1999) S&P500 MSCI-W MSCI- EM SBG SBW Gold 0.20 to 0.70 TW Dep Fung & Hsieh US Fed Euro$ 48% below ⎯ MSCI MSCI-W JPM US JPM NonUS Gold (1997) TW Dep 0.25 Agarwal & Naik US Fed ⎯ S&P500 MSCI-W MSCI-EM LEH-HY SBW Gold 0.10 to 0.84 (2000b, 2000c) TW RUS3000, FF, SBG, Agarwal & Naik ATM and LEH-HY, US Fed ⎯ MSCI-W MSCI-EM SBW GSCI 0.33 to 0.92 (2004) OTM calls & Change in CW puts on DEFS S&P500 Edwards & S&P500, TERM, ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ Caglayan FF, WML DEF (2001) Fung & Hsieh 0.134 to ⎯ ⎯ ⎯ ⎯ ⎯ WIL1750 IFC CSFB-HY (2002) 0.890

Peer-group based factors • Lhabitant (2001) proposes to use peer- group based factors, that is, hedge fund indices. • The problems: – classification of funds over different databases is not consistent. – Style drift

Performance Persistence • Do some hedge funds systematically outperform their investment category peers • Do hedge funds portfolios formed on the basis of hedge funds’ past average returns rankings display short- and long-term performance persistence

How to measure persistence • The most common measure of performance is risk-adjusted returns (Sharpe ratio), but other measures have been used, such as the alpha obtained from a linear model, the appraisal ratio… – Conduct contingency table analysis, by grouping funds as either “winning” or “losing” . • CPR • The other common method is to regress current performance on past performance, and determine whether a positive and significant slope coefficient is observed.

Performance persistence • The results of studies on performance persistence published prior to 2000 have brought conflicting results, due to the time frame and database used. – Brown & Goetzmann (95) – Brown, Goetmann and Ibbotson (99) • use annual returns from the U.S. Bernheim offshore hedge fund database to investigate performance persistence during the 1989-1995 period. • The authors find persistence to not exist in their sample, • They attribute the performance to the strategies employed by the hedge fund managers, rather than to manager skill alone. • They find no evidence that past performance forecasts future performance, nor do they find managerial skill in any particular hedge fund classification. – Agarwal & Naik (2000) • Use quarterly onshore data for 167 funds • Break it down into styles • Find plenty of persistence • AgarwalNaik1999.pdf • One recent study, however, has found strong performance persistence (Kosowski, Naik and Teo, 2004). – Using bootstrap analysis, the authors conclude that the performance of top hedge funds is not only due to luck, after adjusting for backfill bias and serial correlation

Kosowski,Naik and Teo (2004) • Perform AN (2004) style regression • The regression alpha is the value added by the manager after controlling for linear and non-linear market exposures • Non-parametric bootstrap method – No distributional assumptions about alphas

Dominating FOF with simple hedge fund strategies • A study of persistence and the value aded of FOF managers • Do we pay too much for managers DD?

Biases that must be addressed • Backfilling bias – Fung and Hsieh (2000) show that this type of bias can add up to 1.4% to the yearly returns. • Survivorship bias (Liang 2003) – 2.32% for hedge funds – FOF 1.18% – CTAs 5.89%

Survivorship and attrition rates • Attrition ratesfor HF and FOF – 13% in up markets – 17% in down markets • Attrition ratesfor CTAs – 23% in up markets – 20% in down markets