Risk Attribution

2. Implied Alphas

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2.1          An individual security’s marginal contribution to risk is closely allied to its implied alpha, , i.e. the expected outperformance (or underperformance) you need to expect from the instrument if the portfolio is to be ‘efficient’ in the sense of optimally trading off risk against return. For the portfolio to be efficient we need to have, for some portfolio risk aversion parameter, , all of the following  equations simultaneously to be true (in a mean-variance world):

2.2          Here  is an arbitrary constant that might be chosen so that the weighted average implied alpha of the benchmark is zero, since the implied alpha of a given portfolio or instrument is then more directly related to the expected excess alpha that such a portfolio might deliver versus the benchmark.

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