An analytic derivation of the efficient frontier in biobjective cash management and its implications for policies

Abstract

Cash managers who optimize returns and risk rely on biobjective optimization models to select the best policies according to their risk preferences. In the related portfolio selection problem, Merton (J Financ Quant Anal 7(4):1851–1872, 1972) provided the first analytical derivation of the efficient frontier with all non-dominated return and risk combinations. This first proposal was later extended to account for three or more criteria by other authors. However, the cash management literature needs an analytical derivation of the efficient frontier to help cash managers evaluate the implications of selecting policies and risk measures. In this paper, we provide three analytic derivations of the efficient frontier determining a closed-form solution for the expected returns and risk relationship using three different risk measures. We study its main properties and its theoretical implications for policies. Using the variance of returns as a risk measure imposes limitations due to invertibility reasons.