背景风险下DC型养老基金的最优投资策略——基于Legendre转换对偶解法

An Application of Legendre Transform-dual Solutions for DC Pension Funds Optimal Investment Strategy under Background Risk

假设养老基金为确定缴费型,其所面临的背景风险为通货膨胀风险和工资波动风险,养老基金计划中的员工工资为一个随机过程并受到背景风险的影响;研究了养老基金如何对股票和银行存款进行最优投资,并利用Legendre转化对偶方法给出了此优化问题的解析解。将背景风险下养老基金的最优资产配置问题与Legendre转化对偶方法相结合,并得到了此优化问题的解析解,是本文与以往文献的显著不同和主要创新。

The pension funds management is becoming an important issue because China＇s population is aging rapidly. The investment of a pension fund lasts for 20 to 30 years. Thus, the fund manager must cope not only with financial risks （asset price） , but also with ＂background risks＂ （ i. e. all the risks other than the financial market-like inflation risk and salary volatility risk）. This paper assumes that the background risks that DC pension funds face include inflation risk and salary volatility risk. These background risks influence the salary in the pension plan that is a stochastic process. We research a DC pension fund on how to optimally allocate its wealth among the following securities： a stock and a bank account. Using Legendre transform-dual solution, we derive a closed-form solution to this optimal problem. The most novel feature of our research is the application of these background risks. The method of combining Legendre transformation with the dual theory has not been reported in the existing literature. The pension fund＇s optimal investment strategy is an increasing function of stock risk premium. In another word, a pension fund manager purchases more stocks when the stock risk premium is greater. Greater stock risk premium increases stock return. Thus, a pension fund can hold more stocks. Optimal investment strategy is a decreasing function of stock volatility. That is, the pension fund manager can hold less stock when stock volatility is greater. Since greater stock volatility increases stock risk, pension fund will reduce stock holding. Optimal investment strategy is an increasing function of the contribution rate. That is, the pension fund manager purchases more stocks when the contribution rate is higher. The simulation study shows that pension fund＇s optimal investment strategy is an increasing function of wage volatility related to stock. That is, a pension fund manager purchases more stocks when the wage volatility related to stocks is greater. Greater wage volatility related to stocks means that stocks have more influence on wage. Thus, pension funds will increase the investment of stocks in order to hedge wages volatility. The optimal investment strategy is a decreasing function of wage volatility related to inflation. Pension fund will take greater inflation risk when the wage volatility related to inflation is greater. However, the inflation risk is background risk, which cannot be hedged through the financial markets. So the pension fund manager is more likely to adopt conservative investment strategies, and reduce the investment of risk assets. This tells us that the existence of background risks will lead pension fund managers to reduce the holding of risk assets-the stock. The optimal investment strategy is an increasing function of the time to maturity. The fund manager allocates more when he/she has longer investment horizon. The investment trend is consistent with the portfolio manager＇s experience and conventional wisdom. During the beginning of the investment horizon, the fund manager realizes a more aggressive investment policy in order to boost the fund. As the time approaches the deadline, fund managers will shift their wealth from investment in risky assets to certified deposit in banks.