At, in, or near retirement, investors need to make specific decisions about how they are going to use their savings to generate income during retirement. These decisions include deciding how much to invest in annuities, how to invest non-annuitized assets, and how much to withdraw from the non-annuitized assets each year. Retired investors face the risk of running out of assets while they still need the income. Since the income needs usually remain until death, this risk is often called “longevity risk.” Furthermore, many investors wish to leave some portion of their retirement accounts as part of their estates.
Retirement income management is choosing a combination of annuity, withdrawal, and investment strategies such that it is unlikely that the investor will run out of money before death while achieving the investor’s financial goals. In making these decisions, the investor must manage both market risk and longevity risk.
In this paper, we explore retirement income solutions in a simple setting to illustrate the trade-offs that retired investors face regarding how much income they can generate, how much short-term risk they are exposed to, how large an estate they can expect to leave, and how likely they are to not run out of assets before dying (the “success” probability). We assume that at the beginning of the retirement period, the investor chooses how much annual income to generate (in real dollars), how much to invest in single premium immediate annuities, and what asset mix to use to manage non-annuitized assets.
We use a Monte Carlo simulation approach to solve the model for the probability of not running out of money before death with various combinations of real income, annuitization, and asset allocation. Our approach differs from many other simulation models in the way that we treat the level of income to generate. The usual approach is to fix the income level and solve for the probability of running out of money. In our approach, rather than picking an income level rate a priori, we find the trade-off curve between the income level and success probability. We then compare the trade-off curves across different combinations of annuitization and asset mixes to see how the choice of income level affects the highest achievable success probability and the combination of annuitization and asset mix needed to achieve that success probability.
The type of annuity that we explore pays a fixed nominal amount of money each year to the owner until death; so inflation causes the real value of the annuity payout to change over time. Hence, we need to include a model of inflation in our analysis. We construct three different inflation models, all with the same expected inflation rate, and find the relationship between the real income goal and the highest achievable success probability under each model. Our analysis shows that how we choose to model the inflation process can have a substantial impact on this relationship and on optimal investment and annuitization decisions.
Success probability may not be the only criterion for selecting a withdrawal and investment strategy. Potential future wealth, which becomes the estate value at death, may also be a criterion. So for a given income level, we also calculate median estate values as well as the success probability for various combinations of annuitization and asset mixes to find the trade-off between success probability and potential estate size under one of our inflation models.
The remainder of this paper is organized as follows: Section 2 reviews the basic withdrawal model that is commonly used to address the issues of retirement income management with simulation in which the income level is a given. This provides the background for the literature review in Section 3. Section 4 presents our basic model without annuities in which we find the trade-off curves between the income level and the probability of not running out of money before death. Section 5 presents the three inflation models. Section 6 introduces annuities into our model and shows the impact of annuitization on the trade-off between income and success probability under each of the inflation models. It also shows the trade-off between success probability and potential estate size for a given income level under one of the inflation models. Section 7 discusses extensions to the model. Section 8 summarizes our approach and findings.
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