It always fun for us to review budget calculations done by others. In this post we will review example calculations done for Hank and Marie in Michael Kitces’ and Derek Tharp’s January 6 post, Why 50% Probability Of Success Is Actually A Viable Monte Carlo Retirement Projection. We briefly discuss Hank and Marie’s data below, the assumptions we made and compare results using our Actuarial Budget Calculator (ABC) with results from the Kitces’ Monte Carlo model to gauge how conservative their model results are. In summary, their model is less conservative (more aggressive) than the ABC with default assumptions, in that it produces higher initial total spending budgets.
Background
As we have noted many times, the general retirement spending axiom is, “you can spend it now or you (or your heirs) can spend it later.” A corollary to this general axiom is, “if you spend more now, you (or your heirs) will have less to spend later, all things being equal.” The key, of course, is to avoid spending too much or too little initially so that you don’t end up with too little or too much at the end. Unfortunately, since none of us can predict the future (even with very complicated stochastic models), we must make our best assumptions about the future and make necessary adjustments as we go along.
Data and Assumptions
Hank is a 66-year-old male retiree and Marie is a 64-year-old female retiree. Their Social Security benefits total $42,000 per annum and they have accumulated savings of $1,000,000. For this post, we have assumed that Hank’s annual Social Security benefit is $25,000 and Marie’s is $17,000, and Marie’s benefit will increase to $25,000 (in real dollars) upon Hank’s assumed demise. They want to leave $200,000 in today’s dollars to their children upon the last death within the couple.
For this post, we have assumed Hank and Marie have the following current recurring expenses and they assume that these expenses will increase in the future by the following rates of annual increase:
Type of Expense | Annual Amount | Annual rate of future increase |
Essential non-health related | $39,750 | 2% |
Essential health related | $12,000 | 3% |
Discretionary | $20,000 | 1% |
Total | $71,750 |
Not coincidentally, funding these assumed projected essential expenses with low-risk investments using our default assumptions will involve all of Hank and Marie’s Social Security benefits and about 38% of their accumulated savings, leaving about 62% of their accumulated savings that may be invested in risky assets (equities) to fund their future discretionary expenses and bequest motive. We have made these assumptions to be approximately consistent with the Kitces’ investment mix of 60% equities and 40% fixed income for Hank and Marie’s invested assets. If Hank and Marie had a different mix of essential and discretionary expenses, they may require a different investment mix to fund their expenses.
Actuarial Budget Calculator Results
The screen shot below shows the Input & Results tab for Hank and Marie based on their data and the default assumptions. We have also assumed that Marie will be ok with a 33% drop in spending upon Hank’s expected demise.
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This tab shows an annual recurring spending budget of $71,060, which would be expected to increase with inflation each year if all default assumptions are realized in the future. Under the default assumptions, the “cost of retirement lifetime retirement income benefits” for Hank and Marie for each dollar of annual real-dollar retirement income is approximately $27.45 (as shown in cell N(18)). This cost is the theoretical cost of purchasing an annuity from an insurance company providing the same joint and 2/3rds last survivor real dollar annuity benefits. By comparison, the BlackRock Cost of Retirement Income (CORI) as of today for a single 66 year-old was $24.0 and Hank’s cost for a single life annuity under the default assumptions would be $23.85, so we believe the default assumptions are quite consistent with the current CORI calculations. We refer to the actuarial spending budget calculated using the theoretical cost of purchasing an annuity as the Actuarial Budget Benchmark (ABB).
Note that to be consistent with the Kitces’ calculations, we have assumed no other future non-recurring expenses, such as long-term care, or other expected or unexpected expenses. On its face, this strikes us as unrealistic and probably very aggressive, but perhaps these expenses are funded separately in Hank and Marie’s plan.
The screen shot below shows the Asset Reserves by Expense Type tab for Hank and Marie based on their estimated current recurring expenses as summarized above. This tab shows that under the expenses and expense increase assumptions inputted by Hank and Marie, they have a little bit more than $600,000 that they can invest in equities to fund their future discretionary expenses.
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Comparison of Kitces’ Model and Actuarial Budget Benchmark
Here are the initial annual real dollar spending budget results from the Kitces’ model as compared with the spending budget of $71,060 using the ABC and default assumptions. To facilitate the comparison, we have also backed into the implied real rates of investment return used in the Kitces model (instead of the 1% risk-adjusted real rate used in the ABC as a default assumption) and the implied cost of retirement income per $1 (instead of the $27.45 amount used in the ABC with default assumptions).
Probability of Success | Calculated Spending Budget | Approximate implied real rate of investment return assumption on invested assets | Approximate implied cost of retirement Income per $1 |
95% | $81,228 | 2.6% | $22.19 |
70% | $94,777 | 4.5% | $17.72 |
50% | $101,547 | 5.5% | $15.92 |
This comparison shows that the assumptions used in the Kitces’ model are more aggressive (less conservative) than the current default assumptions used in the ABC. Investment return assumptions based on historical experience and longevity assumptions made by Kitces are both somewhat more optimistic.
Spending budgets determined under either the Kitces’ model or the Actuarial Approach are self-correcting as actual future experience emerges. Therefore, as noted in the Background section above, if spending under the Actuarial Approach is lower initially than spending under the Kitces’ model, it will catch up in time and eventually exceed the Kitces’ spending budget if assets are invested similarly, (which we have assumed).
Modifications to the Actuarial Approach to make it less conservative
There are many ways that we have previously discussed to front-load spending under the Actuarial Approach. Some of these include:
- Using more aggressive assumptions for investment return, inflation and longevity planning periods either for all expenses or only for discretionary expenses funded by risky assets (as discussed in our post November 12, 2019),
- Assuming some future expenses, such as bequest motives will be funded from future investment return gains, and
- Separately budgeting expected non-recurring expenses (like travel costs and remaining mortgage payments) over shorter planning periods.
For example, Hank and Marie’s initial actuarial spending budget could be increased by $5,281 by assuming their bequest motive will be funded by future excess investment returns, and their initial spending budget could be further increased by about $6,170 using the approximation approach described in the post of November 12, 2019. How aggressive you want to be with your spending is your choice.
Kitces’ Monte Carlo Modeling takeaways
For budgeting purposes, we are not terribly impressed with the Kitces’ Monte Carlo model outlined in this article, which Mr. Tharp describes “as the most commonly used method of conducting retirement projections for clients.”. He correctly notes that despite involving sophisticated projection processes and many simulations,
- it is not a set-and-forget approach,
- it does not accurately predict the future
- and it should be revisited periodically to update for actual experience, just like the Actuarial Approach.
As discussed in our post of May 19, 2020, current Monte Carlo modeling generally by financial advisors falls short of the Actuarial Approach in many functional areas. The fact that many financial advisors may use more aggressive real investment return assumptions (arguably without adequately reflecting increased risk) to inflate initial spending rates does not, in our opinion, make this approach superior. We believe that when returns are properly risk-adjusted, spending budgets that anticipate higher returns on risky assets will converge to the Actuarial Budget Benchmark.
Summary
Insurance companies sell annuity products that guarantee payments for life. In today’s low-interest rate environment, these annuity products aren’t cheap. For Hank and Marie that cost is around $27 for each dollar of real lifetime income. Insurance companies don’t invest the proceeds of premiums they receive for these annuity products in equities, even though insurance company executives expect (just like you do) to earn higher returns on equities than fixed income. Investment in equities is risky.
Unlike insurance companies, however, financial advisors don’t make guarantees. They charge you for advice and their expertise. They tell you that if future returns follow historical returns on risky investments, you will have a 95% probability of funding spending of $X per year if you invest Y% of your assets in equities. But, financial advisors won’t make you whole if your spending subsequently falls below $X. Therefore, you have to decide how much risk you are willing to take to fund your future expenses. And the more risk you are willing to take, the more you need to be willing to reduce future expenses when necessary.
As actuaries, we want to take steps to mitigate our risks, and we prefer to err on the conservative side. Given a choice, we prefer to have future favorable experience that increases our future budgets rather than future unfavorable experience that decreases our future budgets. Therefore, we recommend you consider conservative e low-risk investments and making more conservative (close to insurance company costing) assumptions with respect to funding of your essential expenses, with more risky assets and possibly more aggressive assumptions with respect to funding of your discretionary expenses.
Whether you use a budget prepared by your financial advisor, you use one of our workbooks or you use some other approach, we suggest that you compare your final spending budget with the Actuarial Budget Benchmark determined with default assumptions so that you can gauge how conservative or how aggressive your budget may be and how much risk you (and not your financial advisor) are assuming with your spending plan.
