1. Metodología avanzada en
valoración financiera (61416)
Style Analysis:
Style Analysis:
A review from Sharpe (1992)
Profesores:
José Luis Sarto jlsarto@unizar.es
Laura Andreu landreu@unizar.es
Blog:
Bl
http://asignaturajls13-14.blogspot.com/
htt // i
t
jl 13 14 bl
t
/

2. The model
 Sharpe, W. F. (1992), “Asset allocation: management
style and performance measurement”, Journal of
y
p
Portfolio Management, summer, 7-19.
R pt   p1 R1t   p 2 R2t     p k Rkt  e pt
Rpt is the return obtained by a portfolio p in month t.
Rjt i th return of th benchmark of the basic asset type j
is the t
f the b
h
k f th b i
tt
in
month t; j=1,…, k.
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.

3. 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),
“Understanding mutual fund and hedge fund styles using
return-based
style
analysis”,
Journal
of
Investment
Management, 1(1), 94-134.
Management 1(1) 94 134

4. The restricted solution of the model
T
T
t 1
t 1

Min e 2 pt  Min R pt  (  p1 R1t   p 2 R2t  ...   pk Rkt )
subject to
k
  pj  1
j 1


2
0   pj  1
De Roon, F. A., Nijman, T. E. and Ter Horst, T. R. (2004),
“Evaluating style analysis”, Journal of Empirical Finance,
11(1), 29-53.
11(1) 29 53
“Strong style analysis”

These authors provide evidence that this version works when
the portfolios to be analysed fulfil these constraints

5. “Weak” version of the Style analysis
“
k”
f h
l
l
T
T
t 1


2
t 1
Min e 2 pt  Min R pt  (  p1 R1t   p 2 R2t  ...   pk Rkt )

Fung, W. and Hsieh, D. A. (1997), “Empirical characteristics of
dynamic trading strategies: The case of hedge funds” Review
funds”,
of Financial Studies, 10, 275-302.
Ben Dor, A.; Jagannathan, R. and Meier, I. (2003),
Understanding
“Understanding mutual fund and hedge fund styles using
return-based
style
analysis”,
Journal
of
Investment
Management, 1(1), 94-134.

In the case of Hedge funds, the restricted version on Returnbased analysis leads to biased estimations


6. A controversial aspect
t
i l
t
 Betas reported in the return-based style
analysis are not portfolio holdings
 They represent the style allocated by the fund
 E g Fund with 90% in Spanish stocks
E.g.
If these stocks are defensive RV
probably b l
b bl be lower than 0 9
h
0,9
But if they are aggressive RV > 90%
Does portfolio constraint make sense?
will

7. Take a look at the model’s requirements
 Exclusive benchmarks
not including any securities that already form part of any
g
y
y
p
y
other benchmark considered
 A common sense restriction with statistical sense
Specification bias
S
ifi ti
bi
 E.g. Ibex-35 and IGBM
 It is not always an easy task!!! [Ibex-35 vs Euro Stoxx]

8. Take a look at the model’s requirements
 Exhaustive benchmarks
As many strategic assets as possible should be included
in the model to minimise the residuals
 If relevant benchmarks are ommited, the model is
not specified on an appropriate basis.
E.g.
E 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

9. Take a look at the model’s requirements
 Exhaustive benchmarks
As many strategic assets as possible should be included
in the model to minimise the residuals
 If relevant benchmarks are ommited, the model is
not specified on an appropriate basis.
E.g.
E 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

10. Take l k t the
T k a look at th model’s requirements
d l’
i
t
 Independent benchmarks
The correlation coefficients between the benchmarks
should be low in order to avoid linearity problems in the
estimation of Sharpe’s betas
E.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

11. Take l k t the
T k a look at th model’s requirements
d l’
i
t
 Independent benchmarks
The correlation coefficients between the benchmarks
should be low in order to avoid linearity problems in the
estimation of Sharpe’s betas
E.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

12. A diffi lt task
difficult t k
 The literature provides that the accuracy of the returnbased analysis is not necessarily improved by adding
further exclusive benchmarks.
MULTICOLLINEARITY PROBLEM
Lobosco, A.
Lobosco A and DiBartolomeo D (1997) “Approximating the
DiBartolomeo, D. (1997), Approximating
confidence intervals for Sharpe style weights”, Financial
Analysts Journal, 53 (4), 80-85.
Buetow, G. W.; Johnson, R. and Runkle, D. (2000), “The
inconsistency of return based style analysis”, Journal of
Portfolio Management, spring, 61-77.
Ferruz, L. y Vicente, L. (2004), “Effects of multicollinearity on
the definition of the mutual funds’ strategic style : the Spanish
case », Applied Economics Letters, 12(9), 553-556
, pp
,
( ),

13. A difficult election
So, we have to choose:
 Exclusive, exhaustive, but not independent
models
 Multicollinearity problems
 Biased estimations
 Spurious return-based analysis
return based
 Exclusive, independent, but not exhaustive
models
 Missing benchmarks
 Increasing residuals

14. A difficult election
So, we have to choose:
 Exclusive, exhaustive, but not independent
models
 Multicollinearity problems
 Biased estimations
 Spurious return-based analysis
return based
 Exclusive, independent, but not exhaustive
models
 Missing benchmarks (but maybe not relevant)
 Increasing residuals (but maybe not very much)

15. Let’s work with the original restrictions
 Let’s recapitulate:
p
T
T
t 1

t 1
Min e 2 pt  Min R pt  (  p1 R1t   p 2 R2t  ...   pk Rkt )
k
  pjj  1
j 1
0   pjj  1

2

16. Let’s work with the original restrictions
 Let’s recapitulate:
Let s
T
T
t 1


2
t 1
Min e 2 pt  Min R pt  (  p1 R1t   p 2 R2t  ...   pk Rkt )
k
  pjj  1
j 1
0   pjj  1
 Does this portfolio constraint have any sense when we
are working with non-exhaustive models?

17. Let’s work with the original restrictions
 Let’s recapitulate:
Let s
T
T
t 1


2
t 1
Min e 2 pt  Min R pt  (  p1 R1t   p 2 R2t  ...   pk Rkt )
k

j 1
pj
1
0   pj  1
 We should test the increase of the residuals
 We know this is not an exhaustive model, and we are not
making beta parameters to sum one, because these
parameters could be overestimated
overestimated.

18. Our study (I)

“Return-Based Style Analysis: An Approach without
Portfolio constraint” by Andreu, Sarto and Vicente
Working Paper draft 5th october 2007
Paper,

Data All Spanish personal pension plans (73 portfolios) that
invest in Euro zone equities from May 2001 to December 2005
q
y
Monthly net returns after fees and expenses

Methodology:
R pt   0   p1 R1t   p 2 R2t     p k Rkt  e pt
0 performance
f
De Roon, F. A., Nijman, T. E. and Ter Horst, T. R. (2004),
“Evaluating style analysis”, Journal of Empirical Finance, 11(1),
29-53.
29-53

19. Our t d
O study (II)

An
A approach to the b
h
h benchmark candidates
h
k
did
Benchmark
MSCI EMU Index Performance
MSCI USA Index Performance
Description
Return of the stock markets of the member
States of the European Monetary Union
Union.
Return obtained by US stock market
MSCI JAPAN Index Performance
Return obtained by the Japanese stock
market
MSCI UK Index Performance
Return obtained by the UK stock market
3-year debt
Return of 3-year Spanish Government
Debt.
5-year
5 year debt
Return of 5 year Spanish Government Debt
5-year
10-year debt
Return of 10-year Spanish Government
Debt
Cash
Return of 1-year Spanish Treasury Bills for
1 day

20. Our study (III)
Correlation coefficients
C
l ti
ffi i t

MSCI
EMU
MSCI
EMU
MSCI USA
MSCI
JAPAN
MSCI UK
3-year
debt
5-year
debt
10-year
debt
Cash
MSCI
USA
MSCI
JAPAN
MSCI UK
3-year
debt
5-year
debt
10-year
debt
Cash
1
.867( )
.867(**)
.436( )
.436(**)
.920( )
.920(**)
-.095
095
-.161
161
-.200
200
-.290(*)
.290( )
1
.503(**)
.860(**)
-.071
-.149
-.196
-.187
1
.487(**)
-.191
-.206
-.205
-.303(*)
1
-.165
-.230
-.273(*)
-.302(*)
1
.984(**)
.944(**)
.125
1
.986(**)
.113
1
.117
1

21. Our study ( )
d (IV)

Model 1
56
Min
M  e 2 pt
t 1
y

  0  1 EMU t   2USAt   3 JAPANt   4UK t   5 3 yeardebt t  

 M   R pt  
Min
  5 yeardebt   10 yeardebt   repos

t 1 
t
7
t
8
t
 6

56
8

Strong version
 i
1
i 1
8

Semi-strong version

i 1
i
1
0  i  1
0  i  1
Exclusive and exhaustive model, but not independent
2

22. Our study ( )
d (V)

Model 2

56
56
t 1

t 1
Min  e 2 pt  Min  R pt   0  1 EMU t   2 5 yeardebtt   3 repost 
p

Strong version
3

i 1

Semi-strong version
2
i
0  i  1
1
3

i 1
i
1
0  i  1
Exclusive and independent but non-exhaustive model

23. Our study ( )
d (VI)

Model 3

56
t 1

56
t 1
Strong version

i 1


Min  e 2 pt  Min  R pt   0  1 EMU t   2 repost 
p
p
2
Semi-strong version
i
1
2

i 1
2
i
1
0  i  1
0  i  1
Exclusive and very independent model but this is
the less exhaustive

24. 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)
EMU
58,86%
(0.0550)**
58,86%
(0.0550)**
72,07%
(0.0266)**
71,96%
(0.0265)**
71,89%
(0.0264)**
71,77%
(0.0263)**
USA
5,36%
(0.0598)
5,36%
(0.0598)
-
-
-
-
JAPAN
8,84%
(0.0276)**
8,84%
(0.0277)**
-
-
-
-
UK
9,22%
(0.0939)
9,23%
(0.0939)
-
-
-
-
3-year
3
debt
0,00%
0 00%
(0.2726)
0,00%
0 00%
(0.2726)
-
-
-
-
5-year
debt
6,81%
(1.2161)
6,81%
(1.2235)
2,85%
(0.0600)
2,89%
(0.0599)
-
-
10 year
10-year
debt
0,00%
(0.3084)
0,00%
(0.3084)
-
-
-
-
Cash
10,91%
(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%