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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