What is an Acceptable Rate of Return for an Undiversified Investor?

Abstract

The valuation of illiquid or non-marketable assets is complicated by the fact that the discount rate cannot be computed by using the risk attributes of the asset along with market parameters. Rather, individual attitudes toward risk affect the discount rate. Some recent research has avoided this difficulty by adopting an "opportunity cost approach", arguing that an undiversified holder of a risky asset will require at least the return that they could have earned by leveraging the market portfolio to achieve the same level of risk. We evaluate this claim in a model with an explicit utility function. It turns out not to be true that the opportunity cost necessarily understates the required rate of return unless we also restrict the holder of an illiquid asset to invest all her liquid wealth in the market portfolio. When the holder can also invest in a riskless asset, the opportunity cost method actually overstates the required rate of return for investors with sufficiently low risk-aversion. In general, however, the opportunity cost approach provides a reasonable approximation to the exact required rate of return over a wide range of risk-aversion levels provided the investor can also borrow and lend.

Keywords: Illiquid Asset, Marketability Discount, Diversification

JEL Classification: G0, G1