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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:

 

         i.            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.

 

       ii.            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.

 

      iii.            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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