Portfolio Choice and Benchmarking: The Case of the Unemployment Insurance Fund in Chile

A new Unemployment Insurance System based on individual accounts was launched in Chile on October 2002. One of the most interesting features of the system is given by the compensation scheme of the fund manager, which contains a performance based incentive benchmarked to one of the default portfolios of the pension system (pension funds Type E, with a 100% investment in fixed-income securities). This paper studies the portfolio choice problem of a fund manager which is subject to a similar performance-based compensation scheme. We model the portfolio choice problem of a risk averse portfolio manager that must finance an exogenous sequence of benefits, and whose terminal payoff depends upon the terminal value of the portfolio under management, relative to an exogenous benchmark portfolio. Our interest is on the consequences of the incentive scheme over the portfolio that is selected by the portfolio manager. For the Black and Scholes [1973] economy we are able to determine the investment policy in closed form. We show that the riskiness of the portfolio depends on the composition of the benchmark, and that the fund manager is motivated to imitate the investment policy of the benchmark in some random scenarios.