Fund liquidation, self-selection and look-ahead bias in the hedge ...

If w 2,it
implies look-ahead bias if w 1,it
≠1and this is the case analyzed
liquidation
Baquero, ter Horst and Verbeek (2005). In this paper, we disentangle
by
two sources of bias by identifying both sets of weights and applying
the
with one weight or their product. The correction for self-selection
corrections
application of the above
The
weights allows us to determine to what extent we get different
correction
if we only correct for selection bias due to liquidation, assuming
results
is random.
self-selection
identify the weights (and to derive (8)) we need to assume that the
To
do not depend upon future, potentially unobserved returns.
probabilities
we assume that self-selection and fund liquidation are mutually
Further,
events, and both describe “absorbing states”. That is, once a fund
exclusive
Then the denominator of w 1,it
P {Y 1,it =1|Ω t ,z it } = (10)
similarly for w 2,it . The right hand side probabilities are described by
and
probit model in (3) provided the appropriate functional form (and con-
the
variables) are chosen in x it . Consequently, consistent estimation
ditioning
the binary choice models for liquidation and self-selection allows us to
of
consistent estimators for the two sets of weights, which enables us
obtain
correct for look-ahead bias due to these two processes and separate their
to
Statistically, equation (9) also holds with the role of Y1,it and Y2,it reversed, so that
8
correction for liquidation bias would be conditional upon the fund not stopping re-
the
Given that existing literature (Baquero, ter Horst and Verbeek, 2005) assumes
porting.
is exogenous (w2,it =1), the most natural ordering is employed here.
self-selection
(8) as
{Y it
=1|Ω t
}
P
{Y it =1|Ω t ,z it } = (9)
P
w it
=
{Y 2,it
=1|Ω t
,Y 1,it
=1}
P
{Y 2,it
=1|Ω t
,z it
,Y 1,it
=1} × P {Y 1,it
=1|Ω t
}
P
=
P {Y 1,it
=1|Ω t
,z it
}
= w 2,it w 1,it .
1for all i, t, then self-selection is exogenous and does not lead
=
look-ahead bias in measures for performance (persistence). In this case,
to
is conditional upon the fund not liquidating. 8
stops reporting to TASS, it will not return in the database at a later stage.
can be determined from the binary choice
model as
P {L i,t+1
=1|r it
,r i,t−1, ..., x i,t+1}...P {L i,t+s+1
=1|r i,t+s,r i,t+s−1,...,x i,t+s+1}
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