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 the condition of no arbitrage. We look at multiple assets with different strike prices. Using a programming approach, we then compute various bivariate risk neutral probabilities for different assets to value all possible pseudo exchange options. This now makes it possible for one to compute implied covariances embedded in the value of any exchange options as in Margrabe [21] even in the absence of the actual exchange option prices. The paper also discusses how these 'recoverable' implied return distribution parameters can impact portfolio choice.
Key words: Endogeneity of return parameters; Option implied covariance; Option implied volatility; Forward looking volatility; Forward looking covariance; Forward looking portfolios; Risk neutral probability; Portfolio selection; Capital Asset Pricing Model; Quadratic programming
JEL: G11 and G12