Stochastic Pension Modelling: A Study of Risk Sensitivity and Demand for Savings

Abstract

This paper examines the increasing significance of risk assessment for individuals saving for retirement. The need for such assessment has shown persistent growth in recent years as the amount deposited to market-rate pension products has risen from 10% of total deposits in 2003 to over 60% in 2015. This change in the environment has shifted the investment risk from the pension provider to the individual and thus has brought increased responsibilities to both parties to track and be informed of the risks involved. This thesis provides an alternative to the deterministic frame used in pension advice today with an introduction of a stochastic model for asset prices. The short rate is modelled with the 1-factor Vasicek Model. The stock fund and bond fund is modelled as Geometric Brownian Motions with constant parameters for volatility and risk premiums over the short rate. The stochastic model is combined with numerous parameters and a limited number of personal preferences. The model output provides an overview of the needed savings as a percent of the income and the risks associated with different weight-paths for the short rate, stock fund and bond fund respectively. Furthermore, the model functions as a tool to easily solve the maximum risk and minimum savings rate before fulfilling a pre-specified minimum income from pensions measured as a 10% Value-at-Risk and the desired income when retired. The modelling shows that the pension varies substantially with the individual’s attitude towards risk and that the savings rate needed to reach the desired pension differs substantially with the percentage of pension constituted by the stable amount of income from the Danish public pension. The model and the sensitivity analysis stresses this point as wealthy individuals are especially exposed to changes in the investment environment. I finally conclude that the payout phase must be included for the pension advice to be reliable and reflect the risk in the pension payments. A focus on wealth lacks inclusion of the exposure towards longevity, the short rate and the importance of the proportion of the pension constituted by the public pension.