1. 1 EDHEC Alternative Hedge Fund Indices Lionel Martellini Risk and Asset Management Research Centre, EDHEC Graduate School of Business Marshall School of Business, University of Southern California lionel.martellini@edhec-risk.com © Edhec 2003Edhec Alternative Hedge Fund Indices

2. 2 Outline of the talk I. Why hedge fund indices II. Hedge fund indices are not born equal IV.IV. Edhec alternative indices : construction methodology and management principles III. Why EDHEC alternative indices V. Properties of EDHEC alternative indices VI.Using EDHEC alternative indices in management process © Edhec 2003Edhec Alternative Hedge Fund Indices

3. 3 I. Why hedge fund indices  HF managers often use risk-free rate as a benchmark  This absolute return approach is theoretically valid if and only if  CAPM is an appropriate factor model for HF returns  Hedge fund beta is zero  Recent research has shown that CAPM, a linear single-factor model, is ill-suited to benchmark HF returns, for at least two reasons  Dynamic trading strategies and use of derivatives by HF managers induce non linear dependency w.r.t. traditional asset classes  HFs are exposed to a variety of risk factors, including market risk(s), but also volatility risk(s), credit risk(s), liquidity risk(s), etc.  Right benchmarking is a fundamental problem in the presence of incentive fees © Edhec 2003Edhec Alternative Hedge Fund Indices

4. 4 I. Why hedge fund indices  This calls for the need of a multi-factor model with non-linear factors  Such non-linear factors can be  Derivatives portfolios: the choice of academia (Mitchell and Pulvino (2000), Fung and Hsieh (2000), Agarwal and Naik (2000), Schneeweis and Spurgin (2000))  Hedge fund indices: the choice of the industry  Hedge fund indices and sub-indices are a natural choice for benchmarking hedge fund returns  Reliable HF indices are also needed for  Indexing strategies  Strategic and tactical asset allocation decisions © Edhec 2003Edhec Alternative Hedge Fund Indices

5. 5 II. Hedge fund indices are not born equal © Edhec 2003Edhec Alternative Hedge Fund Indices Universe of Equity (20000+) Wilshire Sub-Universe (5000 approx) Russell Sub Universe MSCI Sub-Universe S&P Indices (value, growth) Russell Indices (growth,value) Composite of world unknown Sub-universe (e.g., MSCI) may or may not represent world index Competing style indices for the same universe Problems with indices in traditional equity universe

6. 6 II. Hedge fund indices are not born equal © Edhec 2003Edhec Alternative Hedge Fund Indices Problems are similar but much worse in hedge fund universe Universe of Hedge Funds (6000+) Zurich Sub-Universe (1300 approx) HFR Sub Universe TASS Sub-Universe Zurich Hedge Fund Indices CSFB/Tremont Index EACM 100 Composite of world unknown Sub-universe (e.g., HFR, TASS) may or may not represent world index Competing indices for the same universe

7. 7 II. Hedge fund indices are not born equal © Edhec 2003Edhec Alternative Hedge Fund Indices Sample of hedge funds in the database used by a given commercial index Population of hedge funds following a given strategy Lack of representativeness Presence of a style bias

8. 8 II. Hedge fund indices are not born equal Various data bases and many indices © Edhec 2003Edhec Alternative Hedge Fund Indices New comers: MSCI and S&P

9. 9 II. Hedge fund indices are not born equal Hedge fund indices offer a contrasted view of hedge fund performance © Edhec 2003Edhec Alternative Hedge Fund Indices Source: Amenc, Martellini (2002a)From 01/98 through 12/2000

10. 10 II. Hedge fund indices are not born equal Return differences can be rather formidable © Edhec 2003Edhec Alternative Hedge Fund Indices Source: Amenc, Martellini (2002a)From 01/98 through 12/2000

11. 11 II. Hedge fund indices are not born equal Fixed Income Arbitrage Market Risk Volatility Risk Interest Rate Risk Slope of the Yield Curve Currency Risk Commodity Risk Credit Risk Liquidity Risk CSFB0.000.120.150.230.420.05-0.38-0.10 HFR-0.160.140.250.190.570.07-0.24-0.18 Van Hedge0.53-0.470.090.02-0.130.14-0.16-0.05 Hennessee0.37-0.370.06O.190.260.12-0.22-0.12 HF Net-0.100.200.220.200.420.03-0.37-0.01 Source: Amenc, Martellini (2002a) Exposure with respect to main risk factors – The Case of Fixed Income Arbitrage Very contrasted exposure to risk factors © Edhec 2003Edhec Alternative Hedge Fund Indices From 01/98 through 12/2000

12. 12 II. Hedge fund indices are not born equal Efficient frontiers can be strongly dependent on the choice of an index © Edhec 2003Edhec Alternative Hedge Fund Indices

13. 13 III. Why EDHEC alternative indices  Option 1 : Build a new index (requires a significant amount of time, resources and know-how) Given that existing hedge fund indices offer very contrasted views of HF returns, an investor seeking a reference index is left with the following three options :  Option 2 : Select one of the available indices (a priori requires little time, resources and know-how)  Option 3 : Build an index (e.g., a portfolio) of indices  Enhances representativity  Reduce biases Options 1 & 2 are based upon the assumption that there exists such a thing as a “best index”. Any consensus on the subject is however very hard to achieve, as evidenced by the number of competing indices and methods. Therefore options 1 and 2 both lead to accept a fair amount of subjectivity. © Edhec 2003Edhec Alternative Hedge Fund Indices

14. 14 III. Why EDHEC alternative indices Theorem 1 : An index of indices is always more representative than any competing index it is based upon Let Card (I j ) be the number of funds in the data base used by index I j HFR MAR Van Hedge Altvest © Edhec 2003Edhec Alternative Hedge Fund Indices

15. 15 III. Why EDHEC alternative indices Theorem 2 : An index of indices is always less biased than the average of the set of indices it is extracted from Indeed, if we assume that biaises in competing indices are independent: where w is the vector containing portfolio weights, i.e. w = ( w 1,……,w n ). We then have : © Edhec 2003Edhec Alternative Hedge Fund Indices

16. 16 A Principal Component Analysis of a time-series allows one to explain the behavior of observed variables using a smaller set of unobserved implied variables. From a mathematical standpoint, it involves transforming a set of correlated variables into a set of orthogonal variables, or implicit factors, which reproduces the original information present in the correlation structure. Each implicit factor is defined as a linear combination of original variables. Construction methodology for Edhec alternative indices The first principal component can be regarded as the “best one dimensional summary” of a set of competing indices, as it accounts for the largest fraction of the information they contain Furthermore, a simple normalization can be performed to obtain an index which can be regarded as a portfolio of competing indices. where λ{i} is the eigenvalue associated with the ith principal component IV. EDHEC alternative indices: construction methodology and management principles © Edhec 2003Edhec Alternative Hedge Fund Indices

17. 17 IV. EDHEC alternative indices: construction methodology and management principles Management principles for Edhec alternative indices An analysis of the risk/return measures for Edhec indices is published on the 3 rd working day of the month M+1 on the www.edhec-risk.com website, with flashes available on the 26 th of the monthwww.edhec-risk.com The composition of different Edhec Alternative Indexes is calculated every three months based on a PCA on the historical performance data (three years) of the selected competing indices Historical performances of Edhec alternative indices are available starting as of January 1997, and do not suffer from ex-post adjustments © Edhec 2003Edhec Alternative Hedge Fund Indices Example: Performance for January is published March 5 th, with a flash available on February 26th

18. 18 Composition of Edhec alternative indices IV. EDHEC alternative indices: construction methodology and management principles © Edhec 2003Edhec Alternative Hedge Fund Indices

19. 19 Advisory board for Edhec alternative indices Decisions related to inclusion or exclusion of one index in the construction of Edhec alternative indices are taken by a dedicated Advisory Board on the basis of IV. EDHEC alternative indices: construction methodology and management principles  The available history  The clarity of its construction method  Its representativity in terms of being a reference index for managers and/or investors as well as whether it takes existing funds into account  The completeness of the provider’s indices  The stability of the composition  The regularity with which the data/index is published © Edhec 2003Edhec Alternative Hedge Fund Indices

20. 20 V. Properties of Edhec alternative indices A better representativity * These portfolios are regarded as representative because they have been extracted from a data base containing 7 422 funds (bases MAR, HFR and TASS, as well as 2 317 which do not report their performance to any data base) © Edhec 2003Edhec Alternative Hedge Fund Indices Correlation coefficients with respect to representative portfolios (*)

21. 21 V. Properties of Edhec alternative indices Edhec indices enjoy a satisfying level of stability * The numbers in the table measure the average weighting evolution over the period January 2001 through December 2002 © Edhec 2003Edhec Alternative Hedge Fund Indices Stability of the composition of Edhec alternative indices (*)

22. 22 Replication of Edhec indices V. Using Edhec alternative indices in management process Tracking Error « in-sample » and « out-of-sample » (*) * In an attempt to illustrate the benefits of Edhec indices from the perspective of replication strategies, we have built replicating portfolios from randomly selected funds in the HF Net data base. The replicating portfolios are designed as the result of a « tracking error » minimization program : © Edhec 2003Edhec Alternative Hedge Fund Indices

23. 23 Using Edhec indices in a strategic asset allocation context V. Using Edhec alternative indices in management process Average turnover for the minimum variance portfolio (*) * In an attempt to illustrate the benefits of Edhec indices from the perspective of strategic asset allocation, we have considered the stability through time in the composition of minimum variance portfolios. The construction of the minimum variance portfolio is obtained from the following optimization program : © Edhec 2003Edhec Alternative Hedge Fund Indices

24. 24 CONCLUSION Edhec alternative indices : benchmarks for HF performance that are  More representative and less biased  Easily replicable  Stable We hope to see you soon on www.edhec-risk.com ! © Edhec 2003Edhec Alternative Hedge Fund Indices  Allow for a better benchmarking (single or multi-regression analysis of hedge funds and funds of funds returns)