Sesión 8. análisis de estilos
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Transcript of Sesión 8. análisis de estilos
Metodología avanzada enMetodología avanzada envaloración financiera (61416)
Style Analysis:Style Analysis:A review from Sharpe (1992)
Profesores: José Luis Sarto [email protected] Andreu [email protected]
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%