Estimating Risk and Return Combinations for New Derivatives Funds

Abstract

Active funds are typically managed by placing bets against a well defined passive bench-mark. In this context, when examining the launching of a new actively managed fund with a target expected excess rate of return relative to the benchmark equal to µ, asset managers face the problem of estimating the risk σ of excess rates of return. This estimate is critical to examine whether the product is commercially feasible and to define risk limits for the manager, if the product is launched. This paper proceeds to examine the solution to this problem assuming an especial form of the binomial model, in the context of the market timing structure advanced by Merton (1981). The paper shows that two variables are relevant for the solution of the proposed problem. The first, and the most relevant, is the skill level of the manager. A ore skilled manager is able to operate a less risky product with the same target excess rate of return µ. The second relevant variable is the trade-off between risk and return determined by existing investment opportunities in the market. The smaller the increases in risk exposure required to obtain an increase in excess returns, the less risky the product will be After solving the problem under specific assumptions, the paper proceeds to test empirically their validity using a representative sample of hedge funds in the Brazilian market. The empirical results strongly support the validity of the required assumptions.