Extreme Events – Specimen Question
A.5.2(b) – Answer/Hints
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Q. Suppose that she is just
about to adjust her portfolio mix so that it includes no holding in A3 and with
the amounts that were invested in A3 in the above table redistributed equally
between the remaining four asset categories. What return assumptions might she
be adopting when choosing her new portfolio mix? Can you specify mathematically
all possible sets of return assumptions she could have adopted and still
reached this answer?
A similar approach as used in Question
A.5.2(a) can be used here, but with 
rather
than 
and with
one further important difference. This is that it is impossible to identify
precisely the magnitude of the implied alpha for the first asset class relative
to the others – we merely know that it is worse than a certain value, since the
no short-selling constraint (
applies
to it.
To solve this question we therefore need to select a very
negative return for 
and find
implied alphas for 
as if we
only had a 4 asset problem. We would then carry out optimisation exercises
using these values for 
but
selectively increasing until 
just
starts to become positive for the chosen value of 
.
This has introduced a further parameter in the specification of possible asset
mixes, but one that is constrained to fall below a given value.
N.B. Conceptually the same sort of approach can be used if
we have more than one inequality biting although the trial and error approach
used above would soon become relatively impractical.
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