Quantitative Methods in HFoF Construction ( December 2009 )

8/9/2019 Quantitative Methods in HFoF Construction ( December 2009 )

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Quantitative methods in HedgeFund of Fund construction

By Peter Urbani, CIOInfiniti-Capital


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Weaknesses of models used to analyse Hedge FundsWeaknesses of models used to analyse Hedge Funds

Models currently used to analyze hedge funds generally display a number of majorweaknesses:

The models do not pay sufficient attention to the asymmetry of hedge fund returns (hedgefunds returns are not normally distributed). VaR type models therefore do not measure riskaccurately.

The models do not correct for the presence of widespread auto-correlation causingsignificant understatement of volatility of hedge fund returns.

Benchmarks used are not often significant resulting in spurious comparisons.

The models do not consider the impact of asymmetry on dependence measures such ascorrelation.

The models do not consider the persistence of any alpha.

The models generally seek to condense all of the relevant detail into one single

standardized comparative number that is frequently meaningless.

The weaknesses in existing models mean that the unique characteristics of hedge funds andrisks are not captured.

Satyajit DasAuthor of Traders Guns and Money p28, Wilmott Magazine August 2007


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Some Unique Attributes of Hedge FundsSome Unique Attributes of Hedge Funds

Asymmetry

Autocorrelation

(i)Liquidity

Non-Linear dependence


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Hedge Funds v.s. Hedged FundsHedge Funds v.s. Hedged Funds

A Perfectly Hedged fund

Fund

Return

s

-ve Equity Returns +ve


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Hedge Funds v.s. Hedged FundsHedge Funds v.s. Hedged Funds

A Perfect Hedge fund

Fund

Return

s

-ve Equity Returns +ve

Has 0 or negative

downside correlationand Beta

Has positive alpha in

all market regimesHas positive upside

beta


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Avg HF vs. MSCI Daily TR Gross World Free USD, for 31-Jan-93 to 31-Mar-07

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

-16.0% -11.0% -6.0% -1.0% 4.0% 9.0%

BMKs 95%VaR

=-6.75%

BMKs 95%cVaR

=-9.87%

Funds 95%VaR

=-1.18%

Funds 95%cVaR

=-1.93%

-16.0% -13.4% -10.8% -8.2% -5.6% -3.0% -0.4% 2.2% 4.8% 7.4% 10.0%

0%- 5%

5%- 15%

15%- 25%

25%- 35%

35%- 45%

45%- 55%

55%- 65%

65%- 75%

75%- 85%

85%- 95%

95%- 100%

Theoretical Empiric

Prob[Fund>0.0%] = 80.44% 83.04

Prob[Fund>BMK] = 55.61% 54.39

Prob[Fund>MAX{0.0%& BMK}| BMK=x] = 45.30% 44.44

Fund BMK

Holding Period Return (HPR) 1104.93% 301.39

Compound Annual Growth Rate (CAGR) 19.08% 10.24

Mean (Ann.) 17.75% 10.67

Standard Deviation (Ann.) 5.72% 13.17

Skewness 0.683 -0.692

Excess Kurtosis 1.022 0.961

Maximum Drawdown -2.43% -46.31

95.0%Normal VaR -1.24% -5.36

95.0%Modified VaR -0.87% -6.01

Lowest Return -1.95% -13.32

95.0%Infiniti VaR -1.18% -6.75

95.0%Infiniti cVaR -1.93% -9.87

Down Up Overall

Beta 0.047 0.137 0.189

Alpha 0.61% 1.59% 1.31%

Correl 0.12 0.17 0.44

RSQ 1.5% 3.0% 18.9%

Piecewise RSQ= 22.2%

Note Asymmetric payoff


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Less than 12% of Hedge Funds Normally distributed

Gumbel (Min)

5%

Three ParameterLognormal

13%

Pearson I

1%

Skew-T

35%

Normal

11%

Gumbel (Max)

12%

Modified Normal

5%

Uniform

4%

Johnson (Lognormal)10%

Mixture of Normals

4%

Based on analysis of 5400 Hedge Fund distributions


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Impact of Autocorrelation on Volatility

What is it ?Stale pricing where priorestimates are revised orwhere valuation isinfrequent and Monthlyvalues are interpolated

Eg. Property Fund

Affects 30% of Hedge Funds

Fix using Blundell Wald orKalman filter

Average 28% increase inVolatility after filtering


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(i)Liquidity a Source of Alpha(i)Liquidity a Source of Alpha ??

Relationship between liquidty and Returns

Our research indicates that longer lock-ups are compensated for by additional alpha of 300 400bp per annum


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Infinitis Single Fund Analysis (SFA) ranking methodologyInfinitis Single Fund Analysis (SFA) ranking methodology

Funds cannot be

passed onto theQualified Funds / BuyList (QFL) without thesign-off of the 3Research

Department Heads

Qualitative

Quantitative

Forensic


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Infiniti SFA Risk score AmaranthInfiniti SFA Risk score Amaranth

Amaranth

-80.00%

-70.00%

-60.00%

-50.00%

-40.00%

-30.00%

-20.00%

-10.00%

0.00%

10.00%

20.00%

Se

p-0

Ja

n-0

May

-0

Se

p-0

Ja

n-0

May

-0

Se

p-0

Ja

n-0

May

-0

Se

p-0

Ja

n-0

May

-0

Se

p-0

Ja

n-0

May

-0

Se

p-0

Ja

n-0

May

-0

Se

p-0

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100

Amaranth

SFA Risk Score

Buy Threshold

Sell Below

First Warning signal

31 May 2005

Second Warning

signal 30 April 2006

Outright Sell signal

31 May 2006


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Amaranth VaR to 31 Mar 2006

-8.00%

-7.00%

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

F

eb-01

M

ay-01

A

ug-01

N

ov-01

F

eb-02

M

ay-02

A

ug-02

N

ov-02

F

eb-03

M

ay-03

A

ug-03

N

ov-03

F

eb-04

M

ay-04

A

ug-04

N

ov-04

F

eb-05

M

ay-05

A

ug-05

N

ov-05

F

eb-06

Normal VaR

Infiniti 'Best Fit' - VaR

Significant deviation as

distribution type changes

in April / May 2005

Infiniti Best Fit Value at Risk (VaR) AmaranthInfiniti Best Fit Value at Risk (VaR) Amaranth

l i f l i l i ( i h d ) d difi d l i (b


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Analysis of Classic Correlation (top Right Quadrant) and Modified Correlation (bottomLeft Quadrant) of sample Portfolio

Fund

1

Fund

2

Fund

3

Fund

4

Fund

5

Fund 1 1 0.629 0.651 0.357 0.633

Fund 2 1 0.537 0.486 0.428

Fund 3 1 0.548 0.313

Fund 4 1 0.238

Fund 5 1

0.589

0.601 0.470

0.387 0.476 0.553

0.695 0.522 0.306 0.249 0.486

0.428

0.548

0.313

0.238

0.589

0.601

0.470

0.387

0.476

0.553

0.695

0.306

0.249

Fund 1 vs Fund 2 0.629





Fund 2 vs Fund 4

Fund 2 vs Fund 5

Fund 3 vs Fund 4

Fund 3 vs Fund 5

Fund 4 vs Fund 5

0.357

0.522

Portfolios 95% Normal VaR = -0.77%

Portfolios 95% Modified VaR = -0.82%

i l i f l f liLi A l i f l P f li


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Linear Analysis of sample PortfolioLinear Analysis of sample Portfolio

0.486

0.428

0.548

0.313

0.238






Fund 2 vs Fund 4

Fund 2 vs Fund 5

Fund 3 vs Fund 4

Fund 3 vs Fund 5

Fund 4 vs Fund 5

0.357

Portfolios 95% Normal VaR = -0.77%

Pearson Correlation

Fund Name Mean StDev

Fund 1 0.84% 0.89%

Fund 2 0.80% 0.86%Fund 3 1.04% 1.78%

Fund 4 1.33% 2.26%

Fund 5 0.64% 1.01%

Sample Portfolio 0.93% 1.03%

VaR cVaR

-0.62% -0.99%

-0.62% -0.98%-1.89% -2.63%

-2.39% -3.34%

-1.03% -1.45%

-0.77% -1.21%

Normal/Gaussian

Descriptives and VaRs

Mean

ContributorStDev

Contributor

nVaR

Contributor

18.18% 13.15% -0.06%

17.17% 11.32% -0.03%

22.32% 28.56% -0.28%

28.60% 35.20% -0.33%

13.72% 11.78% -0.07%

100.00% 100.00% -0.77%

Fund Name

Fund 1

Fund 2

Fund 3

Fund 4

Fund 5

Sample Portfolio

Attribution of Portfolio Descriptives

Normal

Type

Diversifier

Diversifier

High Return

High Return

Diversifier

N Li A l i f l P f liN Li A l i f l P tf li


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Non-Linear Analysis of sample PortfolioNon-Linear Analysis of sample Portfolio

Fund 1 vs Fund 2

Fund 1 vs Fund 3

Fund 1 vs Fund 4

Fund 1 vs Fund 5

Fund 2 vs Fund 3

Fund 2 vs Fund 4

Fund 2 vs Fund 5

Fund 3 vs Fund 4

Fund 3 vs Fund 5

Fund 4 vs Fund 5

Portfolios 95% Modified VaR = -0.82%

Modified Correlation

0.589

0.601

0.470

0.387

0.476

0.553

0.695

0.306

0.249

0.522

Fund Name Mod SD Skew Kurtosis

Fund 1 0.84% 0.75% 0.458 6.619

Fund 2 0.80% 0.95% -0.685 0.634Fund 3 1.04% 1.68% 0.150 2.425

Fund 4 1.33% 2.00% 0.549 1.408

Fund 5 0.64% 1.26% -4.041 21.616

Sample Portfolio 0.93% 1.06% -0.254 1.160

VaR cVaR

Modified/Cornish Fisher

-0.38% -1.52%

-0.77% -1.27%-1.73% -3.05%

-1.96% -2.90%

-1.44% -2.75%

-0.82% -1.49%

Descriptives and VaRs

Mean

Attribution of Portfolio Descriptives

Mean

ContributorMod SD

Contributor

mVaR

Contributor

18.18% -0.06%

17.17% -0.06%

22.32% -0.27%

28.60% -0.32%

13.72% -0.11%

100.00% 100.00% -0.82%

Fund Name

Fund 1

Fund 2

Fund 3

Fund 4

Fund 5

Sample Portfolio

13.32%

12.54%

26.95%

33.48%

13.72%

Skew

Contributor

Kurt

Contributor

17.90% 15.59%

39.94% 9.56%

-10.79% 25.72%

-6.34% 33.45%

59.28% 15.67%

100.00% 100.00%

Diversifier

Diversifier

High Return

High Return

Diversifier

Normal

Type

Attempts to address the non-linear dependence of hedge funds by coming upwith an analogue or modified correlation matrix using the additional co-skewness and co-kurtosis matrices. This allows for a better understanding ofthe underlying risk factors within the portfolio

C i f N l d M difi d Di t ib tiC i f N l d M difi d Di t ib ti


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Normal and Cornish Fisher Probability Distribution Functions

-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00%

Modified

Normal

Comparison of Normal and Modified DistributionsComparison of Normal and Modified Distributions

Fatter Tails

NegativelySkewed

Normal Modified

95% VaR -0.77% -0.82%99% VaR -1.48% -1.93%

P i i ll h Th I fi i i C i l A l i S i (IAS)P tti it ll t th Th I fi iti C it l A l ti S it (IAS)


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Putting it all together The Infiniti Capital Analytics Suite (IAS)Putting it all together The Infiniti Capital Analytics Suite (IAS)

I t d t b f F dI t d t b f F d


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Import database of FundsImport database of Funds

F d D t bF d D t b


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Fund DatabaseFund Database

Filt b I fi iti Q lifi d (QFL) d I t d Li tFilt b I fi iti Q lifi d (QFL) d I t d Li t


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Filter by Infiniti Qualified (QFL) and Invested ListFilter by Infiniti Qualified (QFL) and Invested List


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Filter further by Fund AUM exclude funds with less than $20mFilter further by Fund AUM exclude funds with less than $20m


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Ensure all funds have up to date historyEnsure all funds have up to date history


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Ensure all funds have up to date historyEnsure all funds have up to date history

Load filtered list into Simulated Annealing OptimiserLoad filtered list into Simulated Annealing Optimiser


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Load filtered list into Simulated Annealing OptimiserLoad filtered list into Simulated Annealing Optimiser

Set weight constraintsSet weight constraints


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Set weight constraintsSet weight constraints


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Fee Information DefaultsFee Information - Defaults


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Fee Information - DefaultsFee Information - Defaults

Drag and Drop standard check-limits or build custom limitsDrag and Drop standard check-limits or build custom limits


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Drag and Drop standard check-limits or build custom limitsDrag and Drop standard check-limits or build custom limits

Default objective function is Infiniti SFA Total ScoreDefault objective function is Infiniti SFA Total Score


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Default objective function is Infiniti SFA Total ScoreDefault objective function is Infiniti SFA Total Score

What is SFA ScoreWhat is SFA Score ?? Ranking system for Risk Return and Ranking system for Risk Return and


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What is SFA ScoreWhat is SFA Score ?? Ranking system for Risk, Return and Ranking system for Risk, Return and

PersistencePersistence

Risk Return and Persistence scores made up of multiple factorsRisk Return and Persistence scores made up of multiple factors


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Risk, Return and Persistence scores made up of multiple factorsRisk, Return and Persistence scores made up of multiple factors

Can also use any other objective functionCan also use any other objective function


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Can also use any other objective functionCan also use any other objective function

Here objective function is maximise CAGR and minimise DrawdownsHere objective function is maximise CAGR and minimise Drawdowns


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Here objective function is maximise CAGR and minimise DrawdownsHere objective function is maximise CAGR and minimise Drawdowns

Run Portfolio improvement routine for 10,000 iterationsRun Portfolio improvement routine for 10,000 iterations


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Run Portfolio improvement routine for 10,000 iterationsRun Portfolio improvement routine for 10,000 iterations

Generates in-sample Returns of 12.65% with volatility of 2.22%Generates in-sample Returns of 12.65% with volatility of 2.22%


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Generates in sample Returns of 12.65% with volatility of 2.22%Generates in sample Returns of 12.65% with volatility of 2.22%

Change Benchmark to CSFB TremontChange Benchmark to CSFB Tremont


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Change Benchmark to CSFB TremontC a ge e c a o CS e o

Show Benchmark Returns and remove fees if investableShow Benchmark Returns and remove fees if investable


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S o e c a e u s a d e o e ees es ab e

Verify all Check-limit constraints satisfiedVerify all Check-limit constraints satisfied


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yy

Out of Sample performanceOut of Sample performance


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p pp p

Change Chart to SFA Total Score or any other statisticChange Chart to SFA Total Score or any other statistic


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g yg y

Verify SFA Score matches optimised valueVerify SFA Score matches optimised value


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y py p

Can be used to build portfolios with any shape distributionCan be used to build portfolios with any shape distribution


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p y p


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DISCLAIMER: This presentation is by Infiniti Capital AG, the Investment Manager of The Infiniti Capital Trust and its portfolios. Application for shares can only bemade on the basis of the current Prospectuses. The Funds are unregulated collective investment schemes in the UK and Switzerland and their promotion byauthorised persons in the UK is restricted by the Financial Services and Markets Act 2000. The price of shares and the income from them can go down as well asup and the value of an investment can fluctuate in response to changes in exchange rates.The following information is intended for institutional investors who are accredited investors and qualified purchasers under the securities laws.Investment in the Fund involves special considerations and risks. There can be no assurance that the Funds investment objectives will be achieved. Aninvestment in the Fund is only suitable for sophisticated investors who fully understand and are capable of assuming the risk of an investment in the Fund.

Multi Manager Multi StrategyFund of Funds

Quantitative Methods in HFoF Construction ( December 2009 )

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