Measurement of pension fund performance in the UK 363
Table 13.8 Performance evaluation with conditional estimation for CAPM with market timing
No.
funds
Average
α
αt-stat Average
β
βt-stat Average
δ
δt-stat R
2
Treynor all (n>12) 1714 0.0018 19.38 1.041 811.7 −0.405 −21.39 0.967
Teynor all (n>20) 1299 0.0020 19.85 1.025 847.0 −0.2583 −20.697 0.964
Teynor small funds
(n>20)
486 0.0016 8.4993 1.019 430.03 −0.1507 −7.874 0.961
Treynor large funds
(n>20)
256 0.0021 11.443 1.0176 499.9 −0.2903 −14.638 0.974
Merton–Henriksson
(n>20)
1299 0.0016 16.466 1.003 517.3 0.1593 2.003 0.970
For each fund we regress the conditional single factor model augmented by a market
timing term, where each of the time series regressions is restricted to those funds having a
minimum of 20 quarters, since the parameters in the amended Merton–Henriksson regressions
require 11 degrees of freedom. The Treynor–Mazuy test in (13.8) is R
pt
− r
f
= α
p
+ b
p
(R
mt
−
r
f
) + B
z
t−1
(R
mt
− r
f
) + δ
p
(R
mt
− r
f
)
2
+ ε
pt
where the sensitivity of the manager’s beta to
the private market timing signal is measured by δ
p
. The amended Merton–Henriksson test
is R
pt
− r
f
= α
p
+ b
d
(R
mt
− r
f
) + B
d
z
t−1
(R
mt
− r
f
) + δ
c
(R
mt
− r
f
)
+
+
z
t−1
(R
mt
− r
f
)
+
+
η
pt
where (R
mt
− r
f
)
+
= (R
mt
− r
f
)
∗
max[0,R
mt
− r
f
− E(R
mt
− r
f
|Z
t−1
)]; and δ
c
= b
up
− b
d
;
= B
up
− B
d
. The signifiance of market timing is represented by the significance of δ
c
.The
reported coefficients are the mean parameter values of the time series estimates from the individual
fund regressions. The relevant overall t-statistic for the average value of each parameter is computed
as in equation (13.3) in the case of the α’s, and similarly for the other parameters.
therefore bound to be small. We also investigated the sensitivity of the fund
returns to the addition of a size premium, which we found to be significant,
and important for the smaller funds in our sample.
Over the whole period and across all funds the outperformance was insignif-
icant when measured by a single factor benchmark. However, when we
applied a three factor benchmark we were able to detect slight but signif-
icant average outperformance. However, during the subperiods there was
significant average underperformance during the strong bull market of the
mid-1980s, but significant outperformance since 1987. In particular in the
period 1987–1992 the average outperformance across pension funds was a
percentage point per year.
Decomposing this abnormal performance we found that most of it could
be explained by the ability of both large and small funds to time the size
premium. On the whole there were negative returns to both selectivity and to
market timing.
ACKNOWLEDGEMENTS
The data used in this study was provided by CAPS Ltd, and we are grateful for
the assistance of Alan Wilcock and Ian Ibbotson. This chapter has benefited
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