Derivatives performance attribution

This paper shows how to decompose the dollar profit earned from an option i nto two basic components: i) mispricing of the option relative to the asset at the time of purchase; and profit from subsequent fortuitous changes or mispricing of the underlying asset. This separation hinges on measuring the "true relative value" of the option from its realized payoff. The payoff f rom any one option has a huge standard error about this value that can be r educed by averaging the payoff from several independent option positions. S imulations indicate that 95% reductions in standard errors can be further a chieved by using the payoff of a dynamic replicating portfolio as a Monte C arlo control variate, In addition, the paper shows that these low standard errors are robust to discrete rather than continuous dynamic replication an d to the likely degree of misspecification of the benchmark formula used to implement the replication. Option mispricing profit can be further decomposed into profit due to super ior estimation of the volatility (volatility profit) and profit from using a superior option valuation formula (formula profit), To make this decompos ition reliably, the benchmark formula used for the attribution needs to be similar to the formula implicitly used by the market to price options. If s o, then simulation indicates that this further decomposition can be achieve d with low standard errors. Basic component ii) can be further decomposed i nto profit from a forward contract on the underlying asset (asset profit) a nd what I term pure option profit. The asset profit indicates whether the i nvestor was skillful by buying or selling options on mispriced underlying a ssets. However, asset profit could also simply be just compensation for bea ring risk-a distinction beyond the scope of this paper. Although simulation indicates that the attribution procedure gives an unbiased allocation of t he option profit to this source, its standard error is large-a feature comm on with others' attempts to measure performance of assets.