Langsiktig sparing til pensjon - En analyse av optimale porteføljevalg for pensjonssparing løst ved dynamisk programmering

Abstract

In this thesis, we try to find optimal behaviour when saving for retirement. We compare different savings options and find which portfolio combinations that will become the best for the different investors. The various options are to save on a tax- deferred pension account with no withdrawals prior to retirement or on a taxable account. The investment universe is confined to one risky and one risk-free asset. The model is solved by using stochastic dynamic programming where the value functions are approximated by the sum of concave functions with coefficients calculated with least squares method based on Hermite data. We find that it is rational to hold a higher percentage of bonds on the retirement account over the retirement period in order to minimize the risk towards the pay-out period, and at the same time have the opportunity to take advantage of the tax benefit by not paying tax on the gain in the savings period. It will also be rational for the investor to save a high percentage of the salary in the beginning and towards the end of the working period, in order to smooth the consumption through both the working period and the retirement period. We also find that the investor don`t want to save a high percentage of the salary on the retirement account early in the working period, because of the no withdrawals prior to retirement on the account. The results indicate that expected developments on wage of the three different occupational groups will affect the investor’s behavior, and we find that higher wages will result in both higher consumption and a higher risk taking. We also find that the optimal behavior is sensitive to different levels of risk aversion for the different occupational groups. A higher degree of risk aversion among the investors, leads to lower equity share in the portfolio, the consumption approximates the same, and the saving pattern will be different.