Metodología avanzada enMetodología avanzada envaloración financiera (61416)

Style Analysis:Style Analysis:A review from Sharpe (1992)

Profesores: José Luis Sarto jlsarto@unizar.esLaura Andreu landreu@unizar.es

Bl htt // i t jl 13 14 bl t /Blog: http://asignaturajls13-14.blogspot.com/

The model

Sharpe, W. F. (1992), “Asset allocation: managementstyle and performance measurement”, Journal ofy pPortfolio Management, summer, 7-19.

ptktkptptppt eRRRR 2211Rpt is the return obtained by a portfolio p in month t.

R i th t f th b h k f th b i t t j

ptktkptptppt 1

Rjt is the return of the benchmark of the basic asset type jin month t; j=1,…, k.

pj is the sensitivity of a portfolio p to benchmark of the pj is the sensitivity of a portfolio p to benchmark of the basic asset type j.

ept is the residual return not explained by the model.

Requirements of this approach

Good specification of the model

Appropriate selection of benchmarks: Exhaustive Exclusive Independent

Ben Dor, A.; Jagannathan, R. and Meier, I. (2003), Ben Dor, A.; Jagannathan, R. and Meier, I. (2003),“Understanding mutual fund and hedge fund styles usingreturn-based style analysis”, Journal of Investment

Management 1(1) 94 134Management, 1(1), 94-134.

The restricted solution of the model

2

12211

1

2 )...(

T

tktpktptppt

T

tpt RRRRMineMin

subject to 10 11

pj

k

jpj

De Roon, F. A., Nijman, T. E. and Ter Horst, T. R. (2004),“Evaluating style analysis”, Journal of Empirical Finance,11(1) 29 5311(1), 29-53.

“Strong style analysis”

These authors provide evidence that this version works whenthe portfolios to be analysed fulfil these constraintsthe portfolios to be analysed fulfil these constraints

“ k” f h l l“Weak” version of the Style analysis

2

22112 )...(

T

ktpktptppt

T

pt RRRRMineMin

Fung, W. and Hsieh, D. A. (1997), “Empirical characteristics ofdynamic trading strategies: The case of hedge funds” Review

11 tt

dynamic trading strategies: The case of hedge funds”, Reviewof Financial Studies, 10, 275-302.

Ben Dor, A.; Jagannathan, R. and Meier, I. (2003),“Understanding mutual fund and hedge fund styles usingUnderstanding mutual fund and hedge fund styles usingreturn-based style analysis”, Journal of InvestmentManagement, 1(1), 94-134.

In the case of Hedge funds, the restricted version on Return-based analysis leads to biased estimations

A t i l tA controversial aspect

Betas reported in the return-based styleanalysis are not portfolio holdingsanalysis are not portfolio holdings

They represent the style allocated by the fund E g Fund with 90% in Spanish stocks E.g. Fund with 90% in Spanish stocks

If these stocks are defensive RV willb bl b l h 0 9probably be lower than 0,9But if they are aggressive RV > 90%

Does portfolio constraint make sense?Does portfolio constraint make sense?

Take a look at the model’s requirements

Exclusive benchmarksnot including any securities that already form part of anyg y y p yother benchmark considered

A common sense restriction with statistical sense

S ifi ti biSpecification bias

E.g. Ibex-35 and IGBM

It is not always an easy task!!! [Ibex-35 vs Euro Stoxx]

Take a look at the model’s requirements

Exhaustive benchmarks

As many strategic assets as possible should be includedAs many strategic assets as possible should be includedin the model to minimise the residuals

If relevant benchmarks are ommited, the model isnot specified on an appropriate basis.E g Not including Ibex-35 to model FI RVNE.g. Not including Ibex-35 to model FI RVN

So, it is an easy problem with an easy solution, isn´t it?

Let’s include in the model as many exclusive benchmarks as possible

Take a look at the model’s requirements

Exhaustive benchmarks

As many strategic assets as possible should be includedAs many strategic assets as possible should be includedin the model to minimise the residuals

If relevant benchmarks are ommited, the model isnot specified on an appropriate basis.E g Not including Ibex-35 to model FI RVNE.g. Not including Ibex-35 to model FI RVN

So, it is an easy problem with an easy solution, isn´t it?

Let’s include in the model as many exclusive benchmarks as possible

T k l k t th d l’ i tTake a look at the model’s requirements

Independent benchmarksThe correlation coefficients between the benchmarksshould be low in order to avoid linearity problems in theestimation of Sharpe’s betasE.g. Including MSCI EMU Stocks and MSCI UK StocksE.g. Including MSCI EMU Stocks and MSCI UK Stocks

If there are linearity (multicollinearity) problems, the beta parameters obtained may be biased.

So, this is an easy problem with an easy answer, isn´t it?

Let’s include in the model those exclusive benchmarks that are independent

T k l k t th d l’ i tTake a look at the model’s requirements

Independent benchmarksThe correlation coefficients between the benchmarksshould be low in order to avoid linearity problems in theestimation of Sharpe’s betasE.g. Including MSCI EMU Stocks and MSCI UK StocksE.g. Including MSCI EMU Stocks and MSCI UK Stocks

If there are linearity (multicollinearity) problems, the beta parameters obtained may be biased.

So, this is an easy problem with an easy answer, isn´t it?

Let’s include in the model those exclusive benchmarks that are independent

A diffi lt t kA difficult task

The literature provides that the accuracy of the return-based analysis is not necessarily improved by addingfurther exclusive benchmarks.further exclusive benchmarks.

MULTICOLLINEARITY PROBLEMLobosco A and DiBartolomeo D (1997) “Approximating theLobosco, A. and DiBartolomeo, D. (1997), Approximating theconfidence intervals for Sharpe style weights”, FinancialAnalysts Journal, 53 (4), 80-85.Buetow, G. W.; Johnson, R. and Runkle, D. (2000), “Theinconsistency of return based style analysis”, Journal ofPortfolio Management, spring, 61-77.Ferruz, L. y Vicente, L. (2004), “Effects of multicollinearity onthe definition of the mutual funds’ strategic style : the Spanishcase », Applied Economics Letters, 12(9), 553-556, pp , ( ),

A difficult election

So, we have to choose:

Exclusive, exhaustive, but not independentmodels Multicollinearity problems Multicollinearity problems Biased estimations Spurious return-based analysis Spurious return based analysis

Exclusive, independent, but not exhaustivemodelsmodels Missing benchmarks Increasing residuals Increasing residuals

A difficult election

So, we have to choose:

Exclusive, exhaustive, but not independentmodels Multicollinearity problems Multicollinearity problems Biased estimations Spurious return-based analysis Spurious return based analysis

Exclusive, independent, but not exhaustivemodelsmodels Missing benchmarks (but maybe not relevant) Increasing residuals (but maybe not very much) Increasing residuals (but maybe not very much)

Let’s work with the original restrictions

Let’s recapitulate:p

2

2

12211

1

2 )...(

T

tktpktptppt

T

tpt RRRRMineMin

101 j

k

j 10 11

pjj

pj

Let’s work with the original restrictions

Let’s recapitulate: Let s recapitulate:

2

12211

1

2 )...( T

tktpktptppt

T

tpt RRRRMineMin

11 tt

101 j

k

j

Does this portfolio constraint have any sense when we

10 11

pjj

pj

Does this portfolio constraint have any sense when weare working with non-exhaustive models?

Let’s work with the original restrictions

Let’s recapitulate: Let s recapitulate:

2

12211

1

2 )...( T

tktpktptppt

T

tpt RRRRMineMin

11 tt

101 k

We should test the increase of the residuals

10 11

pjj

pj

We know this is not an exhaustive model, and we are notmaking beta parameters to sum one, because theseparameters could be overestimatedparameters could be overestimated.

Our study (I)

“Return-Based Style Analysis: An Approach withoutPortfolio constraint” by Andreu, Sarto and VicenteWorking Paper draft 5th october 2007Working Paper, draft 5th october 2007

Data All Spanish personal pension plans (73 portfolios) thatinvest in Euro zone equities from May 2001 to December 2005q yMonthly net returns after fees and expenses

Methodology:f0 performance

ptktkptptppt eRRRR 22110

De Roon, F. A., Nijman, T. E. and Ter Horst, T. R. (2004),“Evaluating style analysis”, Journal of Empirical Finance, 11(1),29-5329-53.

O t d (II)Our study (II)

A h h b h k did An approach to the benchmark candidatesBenchmark Description

MSCI EMU Index Performance Return of the stock markets of the member States of the European Monetary UnionStates of the European Monetary Union.

MSCI USA Index Performance Return obtained by US stock market

MSCI USA Index Performance

MSCI JAPAN Index PerformanceReturn obtained by the Japanese stock market

MSCI UK Index Performance Return obtained by the UK stock market

3-year debtReturn of 3-year Spanish Government Debt.

5 year debt Return of 5 year Spanish Government Debt 5-year debt Return of 5-year Spanish Government Debt

10-year debtReturn of 10-year Spanish Government Debt

Cash Return of 1-year Spanish Treasury Bills for Cash1 day

Our study (III) C l ti ffi i tOur study (III) Correlation coefficients

MSCI EMU

MSCI USA

MSCI JAPAN MSCI UK

3-yeardebt

5-year debt

10-yeardebt Cash

MSCI EMU 1 .867(**) .436(**) .920(**) - 095 - 161 - 200 -.290(*)EMU 1 .867( ) .436( ) .920( ) .095 .161 .200 .290( )

MSCI USA1 .503(**) .860(**) -.071 -.149 -.196 -.187

MSCI JAPANJAPAN 1 .487(**) -.191 -.206 -.205 -.303(*)

MSCI UK1 -.165 -.230 -.273(*) -.302(*)

3-year3-yeardebt 1 .984(**) .944(**) .125

5-yeardebt 1 .986(**) .113

10-yeardebt 1 .117

Cash11

d ( )Our study (IV)

Model 1256 54321056

2 3

tttt yeardebtUKJAPANtUSAEMU

RMM

1 876

543210

1

2

105

t ttt

ttttpt

tpt

reposyeardebtyeardebty

RMineMin

1018 Strong version 10 1

1

i

ii

8

Semi-strong version 10 1 8

1

i

ii

Exclusive and exhaustive model, but not independent

d ( )Our study (V)

Model 2

256

3210

562 5 tttptpt reposyeardebtEMURMineMin

Strong version 1013

11 t

pt

Strong version 10 1 1

i

ii

Semi-strong version 10 1

3

1

i

ii

Exclusive and independent but non-exhaustive model

d ( )Our study (VI)

Model 3

256

210

562 ttptpt reposEMURMineMin

2

1

2101

t

ttptt

p p

Strong version 10 1 1

i

ii

Semi-strong version 10 1

2

1

i

ii

Exclusive and very independent model but this isthe less exhaustive

Our study (VII)Model 1 Model 2 Model 3

Strong V. Alternative V Strong V. Alternative V Strong V. Alternative V.

0-0,10%(0.0054)

-0,10%(0.0054)

-0,16%(0.0056)

-0,10%(0.0056)

-0,17%(0.0055)

-0,11%(0.0055)

EMU58,86%

(0.0550)**58,86%

(0.0550)**72,07%

(0.0266)**71,96%

(0.0265)**71,89%

(0.0264)**71,77%

(0.0263)**

USA5,36%

(0.0598)5,36%

(0.0598) - - - -

JAPAN8,84%

(0.0276)**8,84%

(0.0277)** - - - -

UK9,22%

(0.0939)9,23%

(0.0939) - - - -

3 0 00% 0 00%3-year debt

0,00%(0.2726)

0,00%(0.2726) - - - -

5-yeardebt

6,81%(1.2161)

6,81%(1.2235)

2,85%(0.0600)

2,89%(0.0599) - -

10-year 0,00% 0,00%10 yeardebt

0,00%(0.3084)

0,00%(0.3084) - - - -

Cash10,91%(0.0750)

10,91%(0.5954)

25,08%(0.0696)**

0,00%(0.6644)

28,11%(0.0264)**

0,00%(0.0000)

Total weights 100% 100% 100% 74,85% 100% 71,77%

Adj. R2 94,16% 94,16% 92,87% 92,88% 92,99% 92,99%