استراتژی های سرمایه گذاری مطلوب و تدابیر ریسکی در تعریف برنامه های سهم بازنشستگی

In this paper, we derive a formula for the optimal investment allocation (derived from a dynamic programming approach) in a defined contribution (DC) pension scheme whose fund is invested in n assets.We then analyse the particular case of n = 2 (where we consider the presence in the market of a high-risk and a low-risk asset whose returns are correlated) and study the investment allocation and the downside risk faced by the retiring member of the DC scheme, where optimal investment strategies have been adopted. The behaviour of the optimal investment strategy is analysed when changing the disutility function and the correlation between the assets. Three different risk measures are considered in analysing the final net replacement ratios achieved by the member: the probability of failing the target, the mean shortfall and a value at risk (VaR) measure. The replacement ratios encompass the financial and annuitisation risks faced by the retiree.We consider the relationship between the risk aversion of the member and these different risk measures in order to understand better the choices confronting different categories of scheme member. We also consider the sensitivity of the results to the level of the correlation coefficient.

In this paper we first derive and analyse the optimal investment strategy for a defined contribution (DC) pension scheme whose fund is invested in n assets, and then consider the special case of two assets and study the optimal investment strategy behaviour and the downside risk (in terms of the net replacement ratio achieved at retirement) faced by the member of the scheme, thereby extending the model introduced in Vigna and Haberman (2001). The extensions introduced are three-fold: 1. we consider n assets instead of two; 2. we now consider assets which are correlated with each other; 3. we generalise the disutility function in such a way that deviations of the fund above the target are not penalised to the same degree as deviations below and the risk profile of the individual is taken into consideration. For the case of the n = 2, the downside risk has been studied by examining three risk measures: the probability of failing the target, the mean shortfall and the value at risk (VaR) measure at three different confidence levels (1, 5 and 10%). The annuity risk faced by the member has been analysed through these risk measures by comparing the results relative to the net replacement ratio both in the case of a fixed conversion factor and in the case of a random conversion factor, which depends on the prevailing yield on the low-risk asset.

In our paper we have derived a formula for the optimal investment allocation (using a dynamic programming approach as in Vigna and Haberman (2001)) in a DC pension scheme whose fund is invested in n assets. Then, considering the particular case of a two-asset portfolio, we have investigated the financial risks of a DC scheme, considering the investment risk borne by the member during the accumulation period up to retirement and the annuity risk arising when the fund is converted into an annuity at retirement. We have analysed numerically the investment allocation and the downside risk faced by the retiring member, where approximately optimal investment strategies have been adopted (or “sub-optimal” investment strategies, due to the fact that we have added the constraint that short selling is not allowed). The behaviour of the optimal investment strategy has been analysed allowing for changes in the disutility function (via the parameter α). Three different risk measures have been considered in analysing the final net replacement ratios achieved by the member: the probability of failing the target, the mean shortfall and a VaR measure. We have considered the relationship between the risk aversion of the member and these different risk measures in order to understand better the choices confronting different categories of scheme member. We have also considered the sensitivity of the results to the level of the correlation coefficient ρ between the two asset returns. The main results of our investigation are the following: • The optimal investment strategy to be adopted by a risk averse member of a DC pension scheme is the so-called lifestyle strategy, which consists in investing the whole fund in high-risk assets at the beginning of the membership, and then switching into low-risk assets some years prior to retirement. The point in time when the switch occurs depends on both the risk aversion of the individual (the more risk averse, the sooner the switch) and the time to retirement (the longer the accumulation period, the later the switch). • The optimal investment strategy for a risk neutral member of a DC pension scheme is to invest the whole fund in high-risk assets for the whole period of membership, and never switch into low-risk assets. • The different risk measures of the downside risk faced by the member of a DC pension scheme give different and contradictory indications. • Looking at the results for the probability of failing the target, the conclusion seems to be that increasing the risk aversion of the individual or (which is the same) adopting more cautious strategies leads to a greater number of failures relative to a target, chosen a priori. • Looking at the results for the mean shortfall, the conclusion seems to be that increasing the risk aversion of the individual or (which is the same) adopting more cautious strategies leads to slightly lower mean shortfall, which means more limited reductions in pensioner income when a failure occurs. • Looking at the VaR results, we note that the VaR at 1, 5 and 10% level does not change very much when changing the risk aversion of the individual. • The effect of changing the correlation factor ρ between the assets is very small both on the optimal investment strategy and on the downside risk borne by the member of the scheme. • The annuity risk borne by the member is underlined both by the behaviour of the VaR (with VaR values of bN being always higher than VaR values of ˜bN), which shows that poor outcomes are more adverse when a variable conversion factor is used to buy the annuity, and by the observed distributions of bN and ˜bN (for example, the mode of the distribution being higher in the bN case than in the ˜bN case). We suggest that the risk profile of the individual and the trade-off between different risk measures of the downside risk borne by the member (for example, the number of failures and size of failures in respect of a certain target), are important factors to be taken into consideration when determining the choice of investment strategies in DC pension schemes.