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

Performance measures

AQF-2005 Nicolas Papageorgiou

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

• Accounts better for

assymetry of distribution

– Similar to sharpe, but replace standard deviation by downside deviation – All strategies with negative skew are hit by sortino…

.22 .23 2.27 3.85

rv

.26 .15 2.33 3.49

Mc

.44 .17 2.14 3.75

Lse

.5 .34 1.93 2.58

FI

.2 .24 1.14 1.78

ED

.78 .39 3.91 4.41

DD

.4 .18 2.62 4.87

Cta

.46 .24 0.78 1.21

Arb Sor Shr Dd Sd

Jensen and Appraisal

• Jensen

– Proper estimation of beta coefficient becomes important – Serially correlated hedge funds will lead to underestimation of beta – Dimson (79) – use lagged as well and sum them up – Does not account for leverage however – AR – Jensen divided by standard deviation of non- systematic risk

rv Mc Lse FI ED DD Cta Arb

.22 .56 .59 .15 .50 .51 .20 .72 .70 .37 .73 .71 .28 .66 .61 .43 1.51 1.44 .17 .79 .79 .21 .28 .32

AR JwSB JwB

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

• r 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

0.134 to 0.890 ⎯ ⎯ ⎯ ⎯ CSFB-HY IFC ⎯ WIL1750 Fung & Hsieh (2002) ⎯ ⎯ ⎯ ⎯ ⎯ TERM, DEF ⎯ ⎯ S&P500, FF, WML Edwards & Caglayan (2001) 0.33 to 0.92 ⎯ GSCI US Fed CW SBW SBG, LEH-HY, Change in DEFS MSCI-EM MSCI-W RUS3000, FF, ATM and OTM calls & puts on S&P500 Agarwal & Naik (2004) 0.10 to 0.84 ⎯ Gold US Fed TW SBW LEH-HY MSCI-EM MSCI-W S&P500 Agarwal & Naik (2000b, 2000c) 48% below 0.25 Euro$ Dep Gold US Fed TW JPM NonUS JPM US ⎯ MSCI-W MSCI Fung & Hsieh (1997) 0.20 to 0.70 Euro$ Dep Gold US Fed TW SBW SBG MSCI- EM MSCI-W S&P500 Liang (1999) R2 Cash Commodities Currencies International Debt U.S. Debt Emerging Markets Equities International Equities U.S. Equities Reference

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
• utperform 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

• btained 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
• f 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