Risk taking and optimal contracts for money managers

Recent empirical work suggests a strong connection between the incentives money managers are offered and their risk-taking behaviour. We develop a general model of delegated portfolio management, with the feature that the agent can control the riskiness of the portfolio. This represents a departure from the existing literature on agency theory in that moral hazard is not only effort exertion but also risk-taking behaviour. The moral hazard problem with risk taking involves an incentive-compatibility constraint on risk, which we characterize. We distinguish between one period and several periods. In the former case, under mild conditions, there exists a first-best contract, which takes the form of a bonus contract. In the latter, we show that there exists no first-best contract and we use a numerical approximation to study the properties of the second-best contract.