Endogeneity of Return Parameters and Portfolio Selection: An Analysis on Implied Covariances

The paper presents a method to measure forward-looking covariance risk for any two assets even when the explicit market for barter trades does not exist. We argue that the terms of trade in any barter exchanges also follow a martingale process with no arbitrage. We then compute various bivariate martingale probabilities for different assets to value all possible pseudo exchange options. This makes it possible for one to compute implied covariances embedded in the value of any exchange options as in Margrabe (1978). The paper also discusses how these recoverable implied return distribution parameters can impact portfolio choice.