A Liability Tracking Approach to Long Term Management of Pension Funds

Abstract

<p align="justify"> <span style="font-family:Verdana;">We propose a long term portfolio management method which takes into account a liability. Our approach is based on the LQG (Linear, Quadratic cost, Gaussian) control problem framework and then the optimal portfolio strategy hedges the liability by directly tracking a benchmark process which represents the liability. Two numerical results using em</span><span style="font-family:Verdana;">pirical data published by Japanese organizations are served: simulations tracking an artificial liability and an estimated liability of Japanese organization. The latter one demonstrates that our optimal portfolio strategy can hedge his or her liability.</span> </p> <p> <span></span> </p

A Liability Tracking Portfolio for Pension Fund Management

“…We observe that the mean wealth indicated by the blue line tracks the liability indicated by the red line well. The mean hedging error E t described in the lower panel of Figure 3 is approximately 4.5 % of the liability and it is the equivalent level without the no-short-selling constraint studied in [1]. Hence we find that the liability tracking ability of our optimal portfolio strategy does not drop if we restrict the short selling.…”

“…In this section, we serve numerical simulations base on our method using the empirical data provided by the Japanese organizations. The usage of data is the same as in the literature [1]. Let C t and B t be the estimated income and expense of the pension fund which are determined by the data published by the Japanese Ministry of Health, Labour and Welfare [4].…”

“…The first remarkable one is that the liability tracking ability of our optimal portfolio strategy does not drop if we restrict the short selling. The mean hedging error is approximately 4.5% of the liability and it is the equivalent level without the no-short-selling constraint studied in [1]. The hedge is realized by borrowing the money a lot and investing the lowrisk assets.…”

“…We define the performance criterion J π t based on the downward side of the mean square error between the liability and our wealth which improve the negative point in the previous study [1] mentioned in the introductory section:…”

“…The literature [1] studies the long term pension fund management taking into account the liability employing the LQG (Linear, Quadratic cost, Gaussian) control problem which is a class of stochastic control problem. Since the analytical solution of the LQG control problem is available, the optimal portfolio strategy is obtained in realistic time.…”