Working papers

Projection Pricing (To appear in the Journal of Optimization Theory and Application, April 2001). When the Capital Asset Pricing Model (CAPM) prices an asset that is outside the span of marketed assets, it assigns a price equal to the price of the closest marketed payoff, where "closest" is defined in term of mean-square error. Thus the CAPM prices an asset by first projecting its payoff onto the space of marketed assets and then using the market price of that projection. The usual "beta" formula, however, is sometimes singular even though the problem itself is not. This paper gives alternative formulas for the projection price that avoid the singularity and are in some cases more convenient than the standard CAPM.

A Correlation Pricing Formula (To appear in the Journal of Economic Dynamics and Control). A classic method of pricing is the capital asset pricing model (CAPM) which expresses price in terms of a payoff's correlation with the market portfolio. Project characteristics, however, are not always easily related to market performance and this makes application of the CAPM difficult. This paper shows that the CAPM price can be expressed, alternatively, in terms of the payoff's correlation with a portfolio that is most highly correlated with the payoff. This is a rigorous version of the standard method of using closely related ("comparable") assets to judge the value of a new venture.

Arbitrage and Universal Pricing (To appear in the Journal of Economic Dynamics and Control). One way to determine the price of a project or new venture is to imagine that it is introduced into the market at a certain price. Some price assignments may cause arbitrage opportunities. Such prices are deemed unacceptable. This paper gives conditions for a price to be arbitrage free, and shows that in many cases there is a unique price that every risk-averse investor will find exactly marginal, in the sense that neither a long or a short position in that asset is beneficial.