346 Performance Measurement in Finance

return to market timing is very negative. Although UK equity managers are

comparatively good at selecting equities – only 16% of the sample beat peer

group average. Thomas and Tonks (2001) using the same dataset as the one

in this chapter ﬁnd that average pension fund performance is insigniﬁcantly

different from zero using a two factor benchmark.

13.3 MEASURING FUND PERFORMANCE

Jensen’s technique is to regress the excess returns on the individual fund

above the risk-free rate R

pt

− R

ft

against the excess return on the market

R

mt

− R

ft

. In the case of a single factor, this is equivalent to specifying the

CAPM as the benchmark. We also specify a three factor model, where the

additional two factors are the returns on a size factor and a default risk factor,

which includes the single factor CAPM as a special case when γ

p

= λ

p

= 0.

We estimate

R

pt

−r

ft

= α

p

+ β

p

(R

mt

−r

ft

) + γ

p

(R

mt

−R

HGt

) + λ

p

(R

dt

− r

ft

) + ε

pt

(13.1)

for each fund p over the t data periods, and save the coefﬁcients α

p

, β

p

, γ

p

and λ

p

. This three factor model is a version of the Fama and French (1993)

three factor model, where their SML factor is replaced with the difference

between the returns on the market minus the returns on the Hoare–Govett

Small Firm Index. The book-to-market HML factor is replaced with a default

risk premia deﬁned as the quarterly return on UK long-term corporate bonds

(from DataStream) minus the risk-free rate. Fama and French (1996) suggest

that their HML factor is related to the default risk in the economy. Carhart

(1997) suggests that a fourth factor representing momentum should also be

included in tests of portfolio performance, but such a factor is not readily

available for UK data.

Under the null hypothesis of no-abnormal performance the α

p

coefﬁcient

should be equal to zero. For each fund we may test the signiﬁcance of α

p

as a measure of that fund’s abnormal performance. We may test for overall

fund performance, by testing the signiﬁcance of the mean α when there are

N funds in the sample

¯α =

1

N

N

p=1

α

p

(13.2)

The appropriate t-statistic is

t =

1

√

N

N

p=1

α

p

SE (α

p

)

(13.3)

Measurement of pension fund performance in the UK 347

The original Jensen technique made no allowance for market timing abilities

of fund managers when fund managers take an aggressive position in a bull

market, but a defensive position in a bear market. When portfolio managers

expect the market portfolio to rise in value, they may switch from bonds into

equities and/or they may invest in more high beta stocks. When they expect

the market to fall they will undertake the reverse strategy: sell high beta stocks

and move into ‘defensive’ stocks.

If managers successfully engage in market timing then returns to the fund

will be high when the market is high, and also relatively high when the market

is low. More generally fund managers may time with respect to any factor. If

managers successfully market time, then a quadratic plot will produce better

ﬁt (Treynor–Mazuy test). For the single factor model

R

pt

− r

f

= α

p

+ β

p

(R

mt

− r

f

) + δ

p

(R

mt

− r

f

)

2

+ε

pt

(13.4)

The signiﬁcance of market timing is measured by δ

p

. An alternative test of

market timing for the single factor model suggested by Merton–Henriksson is

R

pt

− r

f

= α

p

+ β

p

(R

mt

− r

f

) + δ

p

(R

mt

− r

f

)

+

+ η

pt

(13.5)

where (R

mt

− r

f

)

+

= max(0,R

mt

− r

f

).

Recently Ferson and Schadt (1996) advocate allowing for the benchmark

parameters to be conditioned on economic conditions – called conditional

performance evaluation – on the basis that some market timing skills may be

incorrectly credited to fund managers, when in fact they are using publicly

available information to determine future market movements. In which case

Ferson and Schadt argue that the predictable component of market move-

ments should be removed in order to assess fund managers’ private market

timing skills. Under a conditional version of the CAPM, the Jensen regression

becomes

R

it

−r

ft

= α

i

+ β

i

(Z

t−1

)(R

mt

− r

ft

) + ε

it

(13.6)

where Z

t−1

is a vector of instruments for the information available at time

t (and is therefore speciﬁed as t −1) and β

i

(Z

t

) are time conditional betas,

and their functional form is speciﬁed as linear

β

i

(Z

t

) = b

0

+B

z

t−1

(13.7)

where z

t−1

= Z

t−1

− E(Z) is a vector of deviations of the Zs from their

unconditional means. Implementing this approach involves creating interac-

tion terms between the market returns and the instruments. Instruments used

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