Why Investors Want Risk

We imagine investors taking shares in an exogenous lognormal cash payoff with known parameters. Using a power utility (constant relative risk aversion (CRRA)) replica of Lintner’s static payoffs-based constant absolute risk aversion-normal capital asset pricing model, we examine how an investor’s expected utility is affected by the payoff parameters and surrounding market conditions. The market clearing asset price falls as a proportion of wealth when market wealth is higher, implying that CRRA investors hold a lower (rather than fixed) proportion of wealth in the risky asset when they are wealthier. Investors prefer conditions where they can obtain more risk, either because the risky payoff is exogenously riskier or competing investors want less. The equilibrium asset price is “disproportionately” lower when the asset is riskier, or when there are fewer willing buyers, leaving a better opportunity with higher expected utility.