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

Abstract

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 performancebased 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.JEL Classification: D81; G11; G18; and H55.

Evaluating the Financial Performance of Pension Funds

“…The resulting expression corresponds to a weighted sum (as ∈ [0, 1] and ) of portfolio policies that are themselves optimal for different scenarios that can occur at time T. The quantities attached to each weighting factor involve two components: the equilibrium portfolio policy that finances the equilibrium terminal wealth that is optimal in the corresponding scenario (see equation 5), and the marginal change in its conditional probability of occurrence, . For instance, in the case of the term attached to the first weight the term on the left-hand side stands for the optimal investment rule in the scenario in which neither of the two portfolio managers is restricted by the MRG constraint at time T, whereas the term on the right-hand side corresponds to the marginal change at time t in the conditional probability that the respective scenario turns out to be optimal at time T. The term on the right-hand side is also present in cases of incentive schemes rendering local convexities in preferences (for example, Castañeda 2006;Basak, Pavlova, andShapiro 2007, 2008). The statement in Corollary 2 also applies in this case because g (1,1) = 1, and hence the term on the left-hand side reduces to the myopic portfolio.…”

Portfolio Choice, Minimum Return Guarantees, and Competition in DC Pension Systems

“…the term on the LHS stands for the optimal investment rule in the scenario where neither of the two portfolio managers is restricted by the MRG constraint at time T , while the term on the RHS corresponds to the marginal change at time t in the conditional probability that the respective scenario turns out to be optimal at time T . The term on the RHS is also present in cases of incentive schemes rendering local convexities in preferences (e.g., Basak et al (2007, Castañeda (2006)). The statement in Corollary 2.2 also applies in this case, as (1; 1) = 1 and hence the term on the LHS boils down to the myopic portfolio.…”