Optimal Portfolios with End-of-Period Target

We study the estimation of optimal portfolios for a Reserve Fund with an end-of-period target and when the returns of the assets that constitute the Reserve Fund portfolio follow two specifications. In the first one, assets are split into short memory (bonds) and long memory (equity), and the optimality of the portfolio is based on maximizing the Sharpe ratio. In the second, returns follow a conditional heteroskedasticity autoregressive nonlinear model, and we study when the distribution of the innovation vector is heavy-tailed stable. For this specification, we consider appropriate estimation methods, which include bootstrap and empirical likelihood. 1. Introduction The Government Pension Investment Fund (GPIF) of Japan was established in April 1st 2006 as an independent administrative institution with the mission of managing and investing the Reserve Fund of the employees’ pension insurance and the national pension (http://www.gpif.go.jp/ for more information) [1]. It is the world’s largest pension fund ($1.4 trillions in assets under management as of December 2009), and it has a mission of managing and investing the Reserve Funds in safe and efficient investment with a long-term perspective. Business management targets to be achieved by GPIF are set by the Minister of Health, Labour, and Welfare based on the law on the general rules of independent administrative agencies. In the actuarial science, “required Reserve Fund” for pension insurance has been investigated for a long time. The traditional approach focuses on the expected value of future obligations and interest rate. Then, the investment strategy is determined for exceeding the expected value of interest rate. Recently, solvency for the insurer is defined in terms of random values of future obligations (e.g., Olivieri and Pitacco [2]). In this paper, we assume that the Reserve Fund is defined in terms of the random interest rate and the expected future obligations. Then, we propose optimal portfolios by optimizing the randomized Reserve Fund. The GPIF invests in a portfolio of domestic and international stocks and bonds. In this paper, we consider the optimal portfolio problem of the Reserve Fund under two econometric specifications for the asset’s returns. First, we select the optimal portfolio weights based on the maximization of the Sharpe ratio under three different functional forms for the portfolio mean and variance, two of them depending on the Reserve Fund at the end-of-period target (about 100 years). Following the asset structure of the GPIF, we split the assets into cash and