Monte Carlo Retirement Planners have become an increasingly popular way for investors to test the probable success rates of different retirement plans. But most of these planners either use highly questionable assumptions, or force the user to make very speculative guesses about future inflation, equity returns, and volatility. Moreover, most planners are highly ambiguous about the kind of inputs they are seeking, and most fail to give the user any guidance on making educated guesses about these inputs.
1. Why not just forecast real return rates instead of inflation and nominal return rates?
Most Monte Carlo Retirement Planners ask you to guess both what inflation and nominal returns will be for the duration of your retirement. Because inflation and nominal returns have historically been extremely volatile, these are difficult — and highly speculative — inputs to guess. These tools provide you with little guidance on how to guess long-term inflation and nominal return rates. Moreover, the results of such simulations are highly sensitive to your speculative inputs.
It is easier to make an educated guess about future real rates of return than it is to speculate about future inflation and nominal return rates. Historically, real Treasury Inflation Protected Securities (TIPS) return rates have rarely strayed outside a narrow range of between about 1% and 3% per year. Also, current real rates of return on long terms TIPS, as long as 20 years in duration, are available on numerous websites. This readily-available information gives users a sound (and not so speculative) basis for entering an expected real rate of return.
Why then, do most Monte Carlo Retirement Planners require users to enter harder-to-guess-at long-term expected inflation and nominal return rates?
2. Why not encourage the user to think in terms of the expected “Equity Risk Premium”?
A dangerous flaw of most Monte Carlo Retirement Planners is that they assume that future stock returns will be just as attractive as past returns. By simulating an extraordinarily prosperous and rapidly growing period of history, they promote unreasonable expectations. Furthermore, most Monte Carlo Retirement Planners assume that future nominal stock returns will mimic past nominal stock returns, regardless of future inflation rates. There is simply no rational basis for this assumption.
When thinking about equity returns, economists have long focused on the so-called “equity risk premium.” And you should too. The “equity risk premium” (ERP) is the difference between the expected total return on an equity index and the return on a risk-free asset. To put it another way, the ERP refers to the additional expected return for stocks — to compensate for the risk — over the so-called “risk-free” rate.
The ERP is the most important variable in financial economics. It is a central input of the “Capital Asset Pricing Model.”
Thinking in terms of the ERP led to the development of the so-called “Dividend Discount Model” (DDM) for projecting future equity returns. The DDM theorizes that the stock market is worth the discounted sum of its future dividend payments. The DDM, in turn, leads to the following formula for expressing the long-term expected real return on a Total Market portfolio:
R = D + G – L – E
where
R = expected real return for the Total Market portfolio;
D = percentage dividend yield for the Total Market portfolio;
G = expected future real per capita economic growth;
L = expected annual percentage dilution of real per capita economic growth growth as it flows through to real dividends; and
E = trading & fund expenses, negative tracking error, and advisory fees
For example, if the expected immediate dividend yield on a broad stock market index is 3% (D = 3%), real per capita GDP is expected to grow 2% per year (G = 2%), the broad stock market is expected to capture all but 1% of that growth (i.e., L = 1%), and trading expenses are about 0.2% (as might occur with the use of low cost index funds), then the expected real return R on the Total Market Portfolio is 3.8% (i.e., 3% + 2% – 1% – 0.2% = 3.8%). If the applicable real risk-free rate (after expenses) is 2%, then the broad stock market provides an expected “risk premium” of 1.8% (i.e., 3.8% – 2% = 1.8%).
The Dividend Discount Model provides a far sounder, and more fundamental, basis for projecting future equity returns than a speculative guess or a hopeful assumption that historical returns will persist.
3. Why Not Use Annualized — Rather Than Arithmetic Average — Expected Rates of Return?
Many Monte Carlo Retirement Planners allow you to enter a custom expected return rate and volatility. But these tools rarely specify whether they are expecting you to enter an expected arithmetic average rate of return or an expected annualized rate of return. (Experimentation suggests that most expect you to enter the expected arithmetic average rate of return).
It is important to understand the distinction between an annualized and an arithmetic average rate of return. If the stock market goes up 25%/year five out of ten years, and goes down 10%/year the other five years, the arithmetic average return is (5 * .25 + 5 * (-.10)) / 10 = 7.5%/year. But the annualized rate of return is (1.25^5 * .9^5)^(1/10) – 1 = 6.1%/year. Incidentally, the annualized rate of return is always less than or equal to the arithmetic average return.
This distinction between annualized and arithmetic average returns makes a dramatic difference in predicted outcomes. See Prof. Peter Ponzo, “Average vs. Annualized Gains.” A person using the ERP formula (R = D + G – L – E) discussed above would be forecasting an expected annualized risk premium. But most Monte Carlo Retirement Planners won’t let you enter an expected annualized rate of return. If you want to do so, these simulators require you to convert your expected annualized return rate into an expected arithmetic average return rate all by yourself — and without providing you with any guidance on how to do so. Good luck with that