Senior Affiliate Professor of Finance
Incomplete Markets; Martingale Approach; Nontraded Assets; Optimal Portfolio Choice; Valuation; JEL Classification: G11
This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price.The author first derives the private valuation, which the investor assigns to the nontraded asset in order to determine his optimal investment in the traded assets. She thereby shows that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. The author also studies the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to remove the trading restriction.All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.