Extreme Events – Specimen Question
A.3.1(a) – Answer/Hints
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Q. Explain the advantages and
disadvantages of attempting to back-fill data for Index C for the first seven
periods from data applicable to either Index A or Index B when creating a model
that jointly describes the behaviour of all three indices.
In general, the advantage of back-filling data in the
proposed manner is so that we do not throw away information available on the
(joint) behaviour of A and B merely because we do not have information
available on C for the relevant period. If we have many assets with varying
history lengths then not doing so can result in only a small number of
overlapping periods, resulting in us throwing away most of the available data.
The disadvantages of back-filling data in this manner are:
The linkage between C, had it existed, and A and B during the time that
data was not available for C may not bear much relationship to its linkage when
there was overlapping data, i.e. we are implicitly making an assumption about
time stationarity that may not be reasonable.
Back-filling data merely using either A or B (or a combination)
implicitly eliminates the idiosyncratic risk that C might have had during the
period being back-filled. If the period being backfilled is large compared to
the overall data set then this may result in the overall idiosyncratic
characteristics of C being understated. Thus there is a risk that we fool
ourselves into believing that C is more like A or B (or a combination) than it
really is, merely because for convenience we have ‘assumed’ that it is for some
of the data set.
Point (b) could have important implications for the fine structure of
asset allocations deemed optimal, since selection of C versus A or B (or a
combination) depends heavily on the assumed characteristics of idiosyncratic risk
expressed by each asset class.
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