The Tradeoff Between Income And Capital In Retirement Withdrawals

July 19, 2016

by John Walton

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In my prior articles (here and here), I evaluated a series of methods for obtaining retirement income from savings, leading to two strategies that perform best over a broad range of market conditions and “tilts[1].” The first strategy is a constant-rate method with “tilt” from slightly negative to strongly positive. The second strategy, the mortgage method, takes advantage of finite lifetime to increase income and was found to outperform mortality based methods that appear to be similar but are not. This article examines how the best performing strategies can be combined with annuities, pensions, Social Security and different tilts to allow clients to best choose between capital preservation and income stability.

My simulation assumptions were identical to the prior companion article except as noted: returns consistent with Vanguard 10-year predictions, an asset allocation of 80% world stock, 20% bonds was assumed (annual real return 5.3%, standard deviation 0.11) and an annuity payout for a 65-year-old female of 4.5% (Income Solutions Quote, CPI adjusted). Social Security is assumed to provide $25,000 of income.

The graphs are shown with 0%, 25%, 50% and 75% of the initial capital converted to a single-premium immediate annuity (SPIA) at the start of retirement (female age 65). Those correspond approximately to 38%, 55%, 70% and 85% (respectively) of the anticipated income coming from the guaranteed income portion (Social Security + pension + SPIA).

I used a constant relative risk aversion (CRRA) utility function with a risk-aversion factor of four and simulated over two million person-years (for each dot/triangle marker in the graphs that follow). The utility function results were dominated by periods when either capital or income became low for an extended period (Figure 1). Two functions were calculated: one for the annual income and one for the capital balance. The income for the utility function was adjusted at a rate of 2%/year to reflect the observed pattern of lower spending with age. The arrow shows how to align the four markers in each line with the fraction of initial capital placed into the SPIA. All the selected methods perform well and have regions where they are superior. By selecting method, tilt and degree of annuity, the client can be placed anywhere along the top surface of the figure (i.e., the efficient frontier). Relatively high tilts along with zero tilts were simulated to illustrate the range available with intermediate tilts. The graphs steepen at higher levels of annuitization, suggesting that the amount of annuities should range from 25-50% of initial capital (guaranteed income 50-75%) in order to balance income and capital risk. High positive tilts should be applied with a greater fraction of annuitization.

Figure 1. CRRA utility function measures risk of low capital or low income during any time period of any realization.

Retirement Withdrawals, Income Tradeoff, Capital Tradeoff

Retirement Withdrawals

For example, in the above graph, the horizontal axis represents the utility function score for annual income and the vertical axis represents the utility function score for annual capital balance. The dark blue line represents a constant-rate strategy with +1 tilt. The blue dots from left to right along this line represent 0%, 25%, 50% and 75% of initial capital placed into the SPIA. As the proportion of SPIA increases, the capital utility decreases (i.e., less capital remains) while income utility increases (i.e., SPIA stabilizes the income). Moving from left to right on the figure, each additional aliquot of SPIA results in a greater loss in capital utility with a correspondingly smaller increase in income utility.

Median/anticipated results (Figure 2) illustrate the tradeoff between final capital at death (bequest) and anticipated income. Death occurs at any age past 65 based on mortality tables (single female). All methods work well. Depending on the method chosen, annuities either increase or decrease the income, but the range is small. The tilted options produce higher incomes. Under the same conditions, the 4% rule would have provided $65,000 income.

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