Long-Run Savings and Investment Strategy Optimization

Abstract

We focus on automatic strategies to optimize life cycle savings and investment. Classical optimal savings theory establishes that, given the level of risk aversion, a saver would keep the same relative amount invested in risky assets at any given time. We show that, when optimizing lifecycle investment, performance and risk assessment have to take into account the investor's risk aversion and the maximum amount the investor could lose, simultaneously. When risk aversion and maximum possible loss are considered jointly, an optimal savings strategy is obtained, which follows from constant rather than relative absolute risk aversion. This result is fundamental to prove that if risk aversion and the maximum possible loss are both high, then holding a constant amount invested in the risky asset is optimal for a standard lifetime saving/pension process and outperforms some other simple strategies. Performance comparisons are based on downside risk-adjusted equivalence that is used in our illustration.

An Optimal Turkish Private Pension Plan with a Guarantee Feature

“…For this purpose, we will introduce a pension fund allocation problem where the multiplier is selected optimally. We consider the portfolio problem in which the aim is to maximize the participant's utility obtained from the cushion at maturity T referring to [19,25,26].…”

“…PM aims to compare the strategies with different risk profiles. In PM, the risk equivalent benchmark strategy of the corresponding strategy is searched for, and then the internal returns of these two strategies are compared [19,35]. For this purpose, we follow the procedure as follows:…”

“…For example, Haberman and Sung [2] try to minimize the 'solvency' and 'contribution rate' risks in order to stabilize the pension fund, and Cairns et al try to optimize the terminal utility gained from the pension fund with a stochastic interest rate [3]. Some other examples of the studies that deal with the optimal asset allocations for pension funds can be found in [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. On the other hand, there are limited numbers of studies that consider a target or a guaranteed wealth concept.…”

“…Di-Giacinto et al solve a portfolio selection problem with a minimum guarantee for a defined contribution pension fund [24]. Moreover, Gerrard et al [19] study the problem of maximizing the expected utility of the difference between the terminal wealth and the fixed guarantee. In the relevant study, they assume a Black-Scholes market and consider a pension fund in which the premiums and withdrawals are constant.…”

“…This can be effective to develop some new products in the sector. Additionally, the plan is an extended version of the study of Gerrard et al [19], in which a linear function of wealth is modeled by a geometric Brownian motion, and the optimal multiplier is obtained accordingly (see also [25,26]). …”