Harry Kat · Title: Microsoft PowerPoint - Harry_Kat.ppt Author: sekret.r Created Date: 5/5/2006...

5/5/2006 Copyright (C) 2006 Harry M. Kat. All rights reserved 1

Hedge Fund Risk and Performance

Harry M. KatAlternative Investment Research Centre

Sir John Cass Business School, City University, LondonE-mail: [email protected]


The Problem With Hedge Funds

Investors tend to evaluate hedge funds in the same way asliquid stocks and bonds and do not pay enough attentionto the striking differences between them.

Hedge Fund Investment


Problem Areas for Analysis• Survivorship bias: concentration on survivors will

overestimate average return by 2-4% per annum.• Back-fill bias: backfilling will overestimate average return

by 3-4% per annum.• Autocorrelation: smoothing in monthly returns will

underestimate volatility by 20-40%. • High parameter uncertainty: available data cover a short

and exceptional period.• Liquidity: lock-up and exit clauses make for highly illiquid

investment.• Non-Normality: makes use of traditional portfolio selection

and performance measures inappropriate.



The Problem with Mean-Variance Analysis

Because it does not consider (co-)skewness and (co-) kurtosis, mean-variance analysis only looks at the good sideof including hedge funds in a portfolio while ignoring thedownside.




Mean Variance Plot

0.4

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0.8

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1 1.5 2 2.5 3 3.5 4 4.5 5

Standard Deviation

Exp

ecte

d R

etur

nNo Hedge Funds Yes Hedge Funds



Mean-Var. Has Other Deficiencies As Well

• Difficult to incorporate (differences in) estimation error.

• Difficult to incorporate (differences in) liquidity.


The Problem With Alphas

Requires complete and correct specification of return generating factors.

Liquidity risk premium typically ignored.

Result: find alpha where there is probably none.



Relationship Alpha and Illiquidity


Average Alpha Average AC (1) Regression Coefficient

Merger Arbitrage. 1.20 0.13 1.1356 Distressed Securities 0.89 0.25 0.8720 Equity Mkt. Neutral 0.40 0.08 0.3112 Convertible Arbitrage 0.97 0.30 1.2975 Global Macro 0.26 0.03 0.2864 Long/short Equity 0.94 0.09 0.8954 Emerging Markets 0.33 0.15 0.3680


The Problem With Sharpe Ratios

Sharpe ratios of hedge funds tend to be (far) too high because means are overestimated and standard deviationsare underestimated.

In addition, Sharpe ratio does not take higher momentslike skewness and kurtosis into account.



.


Sharpe Ratio

S&P 500 0.2796 Eq. Mkt. Neutral 0.3720

Risk Arbitrage 0.4751

Global Macro 0.3510

Distressed 0.3495

Long/Short Eq. 0.8629


The Question:

How to evaluate hedge fund performance given that hedge fund risk profiles can be highly non-normal?

The Answer:By replicating hedge fund returns and comparing the average fund return with the average replicatedreturn.



Why Replicate Hedge Fund Returns?

- Lack of transparency - Lack of liquidity- Lack of capacity- Hidden risks- Excessive fees- Annoying managers- Style drift- Regulation

Hedge Fund Replication


What Exactly Do We Mean by “Replication”?

Hedge fund return generating processes are extremely complex. Accurate replication of month-to-month returns is therefore not possible.

Fortunately, from an investment perspective there is no real need to replicate month-to-month returns.

It is typically enough to replicate the statistical propertiesof a fund’s returns.



Hedging/Pricing Options

1. Determine option’s payoff function (payoff as a function of the reference index).

2. Design dynamic trading strategy, trading the index and cash, that generates the same payoff as the option under all possible scenarios.

3. Executing the strategy will hedge sale of the option.

This idea is used by banks all over the world to hedge trillions worth of options positions.



Call Option Payoff Function


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From Payoffs to Return Distributions

Payoff function in combination with distribution of the reference index implies a return distribution.

Reverse reasoning: If you can find a payoff function that implies the desired return distribution then you can generate that distribution by generating that payoff.



What Assets to Trade?

Cash - to move money through time.

Reserve asset – the main source of uncertainty.

Investor’s portfolio - to match the relationship between fund return and portfolio return.



The General Replication Procedure

1. Collect return data on fund, portfolio and reserve asset.

2. Analyze data and decide on desired bivariatedistribution.

3. Derive payoff function generating desired distribution. 4. Derive dynamic hedging strategy from payoff function.5. Execute strategy.



Performance: Out-of-Sample Test

Monthly hedge fund return data from TASS database.

Assume first 24 months of data are given.

Assume investor’s portfolio consists of 50% S&P 500 and 50% T-bonds.

Trade S&P 500 and T-bond futures for replication.

Use Eurodollar futures as the reserve asset.



Example 1: A well-known Fund of Hedge Funds





Fund Returns Replicated ReturnsMean 0.0104 0.0123 Standard deviation 0.0409 0.0350 Skewness -1.3014 0.1487 Skewness (robust) -0.1282 -0.0273 Excess Kurtosis 8.6624 0.8153 Excess Kurtosis (robust) 0.2742 0.4719 Correlation with Investor’s portfolio returns

0.713 0.748

Kendall’s tau with Investor’s portfolio returns

0.536 0.597


Example 2: A well-known Convertible Arbitrage fund





Fund Returns Replicated ReturnsMean 0.0083 0.0096 Standard deviation 0.0215 0.0173 Skewness 0.3737 0.7471 Skewness (robust) 0.0367 0.0742 Excess Kurtosis 2.6579 2.2273 Excess Kurtosis (robust) 1.6936 0.9593 Correlation with Investor’s portfolio returns

0.511 0.505


0.337 0.388


Example 3: A well-known Short Seller





Fund Returns Replicated ReturnsMean 0.0082 0.0095 Standard deviation 0.0685 0.0490 Skewness 0.0886 1.5116 Skewness (robust) -0.0234 0.0905 Excess Kurtosis 1.2203 7.3804 Excess Kurtosis (robust) 1.3591 1.4204 Correlation with Investor’s portfolio returns

-0.305 -0.371


-0.179 -0.225


Evaluation of Fund Returns

If we can generate returns with the same risk characteristics but with a higher mean return, then the fund in question is inefficient.

Hedge Fund Evaluation


Volatility Replication of 485 Funds of Funds



Skewness Replication of 485 Funds of Funds



Correlation Replication of 485 Funds of Funds



Evaluation of 485 Funds of Funds



Volatility Replication of 1917 Individual Funds



Skewness Replication of 1917 Individual Funds



Correlation Replication of 1917 Individual Funds



Evaluation of 1917 Individual Hedge Funds



Evaluation over Two Equal Sub-Periods



Conclusions

1. The complex risk profile of hedge funds makes traditional methods of analysis unsuitable and dangerous to use.

2. Hedge fund returns can be replicated by mechanical futures trading strategies, which avoids many of the problems associated with direct hedge fund investment.

3. Using replication to evaluate hedge fund performance confirms that the majority of funds (of funds) do not offer investors superior returns (anymore).

Hedge Fund Conclusions


For research papers visit the Alternative Investment Research Centre website at:

www.cass.city.ac.uk/airc

Harry Kat · Title: Microsoft PowerPoint - Harry_Kat.ppt Author: sekret.r Created Date: 5/5/2006...

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