Investing for Retirement: How Loss Aversion Risk Preferences Naturally Leads to Greater Retirement Income Certainty
47 Pages Posted: 30 Jul 2019
William Lim
Catherine Donnelly
Gaurav Khemka
Date Written: July 26, 2019
Abstract
We analyze the ability of different investment strategies to give pre-retirees more certainty about their income in retirement, while allowing them to benefit from taking investment risk. Specifically, we look at the optimal strategies that maximize the expected values of a loss aversion utility function and a constant relative risk aversion (CRRA) utility function. We also include a typical lifestyle strategy.
We find that the loss aversion utility function gives a high degree of certainty about its reference point, the latter chosen to give the desired replacement ratio. Adding in constraints on the income purchased at retirement does not improve the certainty of achieving the desired replacement ratio enough to counter-balance the increased chance of obtaining an income far below it. A CRRA utility function fails to get adequate certainty on the retirement income, and becomes too risk-averse when constraints are added. The lifestyle strategy performs well but is overall out-performed by the loss aversion-derived strategy.
We include inflation in our model, and allow for inflation-indexed bonds in our investment universe. Our results are analyzed in both a Brownian motion-driven financial market model and using UK historical data.
Keywords: finance, retirement planning, optimal asset allocation, stochastic optimal control, constrained optimization
We analyze the ability of different investment strategies to give pre-retirees more certainty about their income in retirement, while allowing them to benefit from taking investment risk. Specifically, we look at the optimal strategies that maximize the expected values of a loss aversion utility function and a constant relative risk aversion (CRRA) utility function. We also include a typical lifestyle strategy.
We find that the loss aversion utility function gives a high degree of certainty about its reference point, the latter chosen to give the desired replacement ratio. Adding in constraints on the income purchased at retirement does not improve the certainty of achieving the desired replacement ratio enough to counter-balance the increased chance of obtaining an income far below it. A CRRA utility function fails to get adequate certainty on the retirement income, and becomes too risk-averse when constraints are added. The lifestyle strategy performs well but is overall out-performed by the loss aversion-derived strategy.
We include inflation in our model, and allow for inflation-indexed bonds in our investment universe. Our results are analyzed in both a Brownian motion-driven financial market model and using UK historical data.
We find that the loss aversion utility function gives a high degree of certainty about its reference point, the latter chosen to give the desired replacement ratio. Adding in constraints on the income purchased at retirement does not improve the certainty of achieving the desired replacement ratio enough to counter-balance the increased chance of obtaining an income far below it. A CRRA utility function fails to get adequate certainty on the retirement income, and becomes too risk-averse when constraints are added. The lifestyle strategy performs well but is overall out-performed by the loss aversion-derived strategy.
We include inflation in our model, and allow for inflation-indexed bonds in our investment universe. Our results are analyzed in both a Brownian motion-driven financial market model and using UK historical data.
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