The FundCreator Approach to Hedge Fund

The FundCreator Approach to Hedge Fund

Replication, Evaluation and New Fund Creation

Harry M. Kat

Alternative Investment Research Centre

Sir John Cass Business School, City University, London

E-mail: Harry@AIRC.info

3/5/2007 Copyright (C) 2007 Harry M. Kat. All rights reserved

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3/5/2007

Synthetic Funds

Synthetic Funds Would Solve Many Problems

- Excessive fees

- Lack of liquidity

- Lack of transparency

- Lack of capacity

- Hidden risks

- Annoying managers

- Style drift

- Regulation

Copyright (C) 2007 Harry M. Kat. All rights reserved

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Two Different Approaches

1. Traditional: Factor Models

Tries to match the risk exposures of a fund or index. If successful this produces same month-to-month returns and therefore same properties as target fund or index.

2. More Recent: FundCreator

Aims to generate returns with the same statistical properties as a given fund of index, but not necessarily the same month-to-month returns.


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The Factor Model Approach

Several articles and papers written on the subject but none providing realistic backtests of the actual replication strategies.

Second best alternatives:

1. Look at R-Squared of factor model estimates.

2. Look at out-of-sample return predictions.


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Factor Models for Individual Funds

Strategy Group

Convertible Arbitrage

Emerging Markets

Equity Market Neutral

Event Driven

Average Variation Explained

17.3%

19.4%

10.4%

19.5%

Fixed Income Arbitrage

Global Macro

Long/Short Equity

14.9%

14.8%

21.6%

Source: Hasanhodzic and Lo (2006, Table 5).


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Factor Models for HFRI Indices

H F R I In d ex

M an ag e d F u tu re s

E q u ity M ark e t N eu tral

F ix e d In c o m e A rb itra g e

G lo b a l M ac ro

M erg er A rb itrag e

C o n v e rtib le A rb itrag e

V a r ia tio n E x p la in ed

3 4 .3 %

3 5 .3 %

4 0 .5 %

4 9 .7 %

5 2 .9 %

5 4 .0 %

D istre sse d 6 8 .4 %

L o n g /S h o rt E q u ity 8 8 .5 %

S o u r ce : J a eg e r a n d W a g n e r (2 0 0 5 , T a b le 1 ).


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Synthetic Funds

Factor Model for HFR EMN Indices

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Source: Jaeger and Wagner (2005, Figure 8).


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The Merrill Lynch Factor Index: It Works!

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Source: Umlauf (2007, page 7).


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But Who Would Want the HFRI Composite?

S&P 500 vs. HFRI Composite (Jan95 = 100)

400

350

300

250

200

150

100

50

S&P 500

HFRI

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The HFRI Composite is so diversified that it contains nothing ‘alternative’ anymore.


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Merrill Lynch Factor Index Portfolio

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Source: Umlauf (2007, page 9).

The replicating portfolio requires no ‘alternative’ risk factors or dynamic trading. It is simply a very traditional portfolio.


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Conclusion Factor Models

1. Factor models cannot replicate individual funds.

2. Factor models cannot replicate most hedge fund indices.

3. Factor models can replicate the most diversified indices, but these don’t make very interesting investments

Put simply: It works when you don’t really need it to work!

4. When replication is not accurate the statistical properties of the returns generated are unclear.


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Synthetic Funds

The FundCreator Alternative

The FundCreator system designs futures trading strategies that generate returns with predefined statistical properties.

Based on two ideas:

1. The sequence of returns is of no importance for investors as long as they have the desired properties.

2. In the longer run the market pays a return in line with the bottom line risk you have taken.


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An Example

A Zero Correlation Fund

Synthetic fund generating returns with 12% volatility, no skewness or excess kurtosis, and zero correlation with stocks and bonds.

Trade 3M-Eurodollar, 10Y-Note, 30Y-Bond, S&P 500,

Russell 2000, and GSCI futures.

Start fund in 1995 and work forwards to the present, only using information available at that time.


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Zero Correlation Fund: Volatility 1997-2006

Sta ndard D ev iatio n

0.16

0.15

0.14

0.13

0.12

0.11

0.1


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Zero Correlation Fund: Skewness 1997-2006

Skewness

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00


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Zero Correlation Fund: Correlation 1997-2006

Correlation

0.40

0.30

0.20

0.10

0.00

-0.10

-0.20

-0.30

-0.40


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Zero Correlation Fund: Mean Excess 1997-2006

Mean Excess Return

0. 2

0.15

0. 1

0.05

0

-0.05

-0. 1

-0.15

-0. 2


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Same Approach as When Hedging 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.

Not a fantasy idea, but used by banks all over the world to hedge trillions worth of options positions.


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Call Option Payoff Function

14

12

10

8

6

4

20

18

16

2

0


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From Payoffs to Return Distributions

Every payoff function 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 executing the hedging strategy for that payoff function.


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What to Trade?

Cash - to move money through time.

Reserve asset – the main source of uncertainty.

Reference portfolio - to correct the relationship between the reserve asset return and the reference portfolio return.


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The General Procedure

1.

Decide on desired risk characteristics, i.e. the desired return distribution.

2.

Derive payoff function implying desired distribution.

3.

Derive hedging strategy for that payoff function.

4.

Execute hedging strategy.


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Some Out-of-Sample Tests

Monthly hedge fund return data from TASS database.

Assume first 24 months of data are given.

Assume reference 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.


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Synthetic Funds

Example 1: A well-known Fund of Hedge Funds


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Standard deviation

Skewness (robust)

Excess Kurtosis

Excess Kurtosis (robust)

Correlation with

Investor’s portfolio returns

Kendall’s tau with


0.0409 0.0350

-0.1282

8.6624

-0.0273

0.8153

0.2742 0.4719

0.713 0.748

0.536 0.597


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Example 2: A well-known Convertible Arbitrage fund


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Excess Kurtosis






Fund Returns Replicated Returns

0.0215 0.0173

0.0367

2.6579

0.0742

2.2273

1.6936 0.9593

0.511 0.505

0.337 0.388


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Example 3: A well-known Short Seller


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Excess Kurtosis






0.0685 0.0490

-0.0234

1.2203

0.0905

7.3804

1.3591 1.4204

-0.305 -0.371

-0.179 -0.225


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Synthetic Funds

Hedge Fund Indexation

Indexation is an investment approach for people that do not think active managers are worth their fees.

But as long as you invest in hedge funds the problem that indexation is meant to solve is still there.

We need hedge fund index returns but without investing in hedge funds.


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Synthetic Funds

Example: Edhec and HFRI Indices

Trading the following futures on CME and CBOT:

- 3M Libor

- 5Y note

- 10Y note

- S&P 500

- Russell 2000

- GSCI


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Note: Hedge Fund Indices Are Biased Upwards

Self-reporting bias : Only the more successful funds will report to a database.

Survivorship bias : Some index providers remove funds that close down from the index’s history.

Selection bias : Database and index providers may have strict criteria to decide which funds to include in the database and/or index.

Backfill bias : When a fund enters a database, typically its complete track record is included.

Deduct 2-3% to correct for these biases!


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Synthetic Funds

Edhec Hedge Fund Indices 1999 -2006

C A

M e a n S t D e v S k e w C o r r M e a n S t D e v S k e w C o r r

5 . 6 8 % 6 . 5 8 % - 0 . 0 2 0 . 2 2 5 . 0 4 % 6 . 5 7 % 0 . 1 0 0 . 2 4

D S

E M 1 2 . 6 0 % 1 3 . 3 5 % - 0 . 1 9 0 . 6 7 1 3 . 8 9 % 1 3 . 6 5 % 0 . 7 1 0 . 6 7

L S

E M N 4 . 4 6 %

F I 3 . 3 6 % 2 . 9 0 % - 0 . 1 7 0 . 2 6 3 . 8 0 % 3 . 0 7 % - 0 . 1 0 0 . 2 5

G M

M A

S S

C T A

F o F

4 . 7 8 % 4 . 0 8 % - 1 . 1 5 0 . 4 5 3 . 0 0 % 4 . 0 6 % - 0 . 1 7 0 . 4 4

- 3 . 5 8 % 2 1 . 5 7 % - 0 . 3 2 - 0 . 6 2 1 4 . 8 0 % 2 3 . 2 4 % 0 . 0 6 - 0 . 6 1


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HFRI Hedge Fund Indices 1999-2006

C A

D S

M A

M e a n S t D e v S k e w C o r r M e a n S t D e v S k e w C o r r

4 .9 8 % 5 .4 4 % -0 .0 4 0 .2 1 3 .8 9 % 5 .4 4 % -0 .0 3 0 .2 3

9 .4 8 % 7 .7 2 % 0 .2 3 0 .1 5 8 .5 6 % 7 .9 5 % 0 .2 8 0 .1 2

E M

L S

1 3 .6 9 % 1 6 .8 2 %

7 .4 7 % 1 0 .5 2 %

-0 .1 5 0 .6 8 1 7 .4 9 % 1 7 .4 0 %

0 .6 4 0 .5 8 9 .2 8 % 1 0 .9 4 %

0 .6 6 0 .6 8

0 .7 9 0 .5 9

E M N 2 .7 6 % 2 .7 7 % 0 .2 7 -0 .0 3 3 .5 8 % 2 .8 7 % 0 .0 4 -0 .0 7

F I 4 .2 9 % 3 .6 7 % -0 .1 4 0 .5 0 4 .1 7 % 3 .9 2 % 0 .0 9 0 .5 1

G M 5 .3 9 % 6 .5 1 % 0 .3 6 0 .3 1 6 .6 9 % 6 .6 0 % 0 .3 9 0 .3 1

4 .4 9 % 3 .8 6 % -0 .9 2 0 .3 7 3 .5 4 % 3 .7 2 % -0 .1 9 0 .3 6

-1 .9 9 % 2 3 .6 1 % -0 .5 2 -0 .5 5 1 7 .0 6 % 2 5 .6 1 % 0 .2 2 -0 .5 4 S S

F O F 4 .6 9 % 7 .1 4 % 0 .4 0 0 .5 1 7 .8 9 % 7 .1 9 % 1 .1 7 0 .4 9


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Synthetic Funds

Using FundCreator for Performance Evaluation

If it can be replicated, then it can’t be superior!

1. Create trading strategy generating returns with the same properties as found in a given fund’s track record.

2. Compare average return on the fund with that of the replicating strategy.


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Hedge Fund Evaluation

Volatility Replication of 875 Funds of Funds


39


Skewness Replication of 875 Funds of Funds


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Correlation Replication of 875 Funds of Funds


41


Evaluation of 875 Funds of Funds: 18.6% Efficient


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Volatility Replication of 2073 Individual Funds


43


Skewness Replication of 2073 Individual Funds


44


Correlation Replication of 2073 Individual Funds


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Evaluation of 2073 Individual Hedge Funds: 22.5%


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Evaluation over Two Equal Sub-Periods


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Some Conclusions I

Synthetic Funds

• Factor models only work well in cases where we don’t really need them to work.

• The properties of factor model based funds are unclear.

• FundCreator allows investors to design funds that optimally fit into an investor’s portfolio.

• FundCreator based funds have predefined statistical properties. You get what you ask for.

• Neither factor models nor FundCreator truly “replicate” or “clone” hedge fund returns.


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Some Conclusions II

Synthetic Funds

• Roughly 80% of hedge funds and funds of funds have not provided returns that could not have been generated mechanically trading a basket of liquid futures contracts.

• Hedge fund performance has deteriorated over time.

• Successful funds tend to become less successful over time.


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3/5/2007

For research papers visit the Alternative

Investment Research Centre website at: www.cass.city.ac.uk/airc

For further specifics on FundCreator visit: www.FundCreator.com


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The FundCreator Approach to Hedge Fund

The FundCreator Approach to Hedge Fund

Replication, Evaluation and New Fund Creation

Factor Models for Individual Funds

Factor Models for HFRI Indices

Factor Model for HFR EMN Indices

The Merrill Lynch Factor Index: It Works!

But Who Would Want the HFRI Composite?

Merrill Lynch Factor Index Portfolio

Conclusion Factor Models

The FundCreator Alternative

Example: Edhec and HFRI Indices

For research papers visit the Alternative

Investment Research Centre website at: www.cass.city.ac.uk/airc

For further specifics on FundCreator visit: www.FundCreator.com

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