Abstract
We study inflation adjusted sustainable withdrawal rates from a retirement portfolio. We make use of a Monte-Carlo simulator driven by historical stock market and mortality data. Adjusting the simulation for stock market returns in the future being expected to be lower than in the past significantly lowers the sustainable withdrawal rate compared to prior studies. Most of these loses can however be made up for by having a portfolio partially made up of inflation protected securities. An optimal portfolio comprised 70% inflation protected securities and 30% stocks and provided a 98% likelihood of providing a lifetime income stream at an initial inflation adjusted withdrawal rate of 4.4%.1. Introduction
A key question for an investor approaching retirement is how large a retirement portfolio they are going to need to sustain a given inflation adjusted withdrawal amount over their lifetime. Or equivalently, what is the inflation adjusted sustainable withdrawal rate a portfolio can support. Throughout this paper we assume all amounts withdrawn are adjusted annually to keep pace with inflation.One of the first to study the sustainable withdrawal rate problem was Bengen (1994), who recommended a retirement portfolio of 50-75% stocks and the remainder in intermediate-term bonds. Cooley et al. (1999) also studied the problem and likewise recommended a portfolio of at least 75% stocks. Meanwhile an apparently conflicting study by Charnes et al. (2005) recommend 0% large cap. stocks, 33% small cap. stocks, and 67% bonds. More recently Stout and Mitchell (2006) studied the problem using 65% stocks and 35% intermediate-term bonds basing this asset allocation on the experience of prior researchers.
This paper is concerned less with untangling the asset allocation details of prior research, and more with an orthogonal question: What role might inflation indexed bonds play in a retirement portfolio? Prior studies have looked at portfolios made up of a mixture of intermediate-term or long-term bonds and stock, but none has explored the use of inflation indexed bonds. Inflation indexed bonds might be expected to be useful in a retirement portfolio, because like regular bonds they provide for diversification by offering a return that is largely orthogonal to that of stocks. Additionally inflation indexed bonds should be immune to increased inflation eating away at the real value of the regular bonds.
Treasury Inflation Protected Securities, or TIPS, are a form of inflation indexed bond first issued by the U.S. Treasury in 1997. TIPS provide a fixed coupon rate applied to an inflation indexed principal amount, thus protecting the holder from the risk of inflation. TIPS represent an increasingly significant share of Treasury securities, $400b out of the $4.9t Treasury securities outstanding, or 8.2% of the total as of 2007 Q2 (author's own calculations based on TIPS auction statistics and Flow of Funds data).
We consider tax free savings because most retirement savings will likely be held in either a Roth IRA, or a Traditional IRA, and the results presented here can readily generalized to the returns needed from a Traditional IRA. Fees and costs of investing are also not considered.
2. Initial validation of the model
Table 2.1 shows the probability of successfully withdrawing from a 100% stock portfolio for the indicated number of years at the indicated initial withdrawal rate adjusted for inflation as reported by Cooley et al..
| initial inflation adjusted withdrawal rate | ||||||||||
| 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% | |
| 20 years | 100% | 100% | 91% | 77% | 66% | 57% | 42% | 32% | 28% | 19% |
| 25 years | 100% | 100% | 85% | 69% | 56% | 42% | 33% | 29% | 25% | 15% |
| 30 years | 100% | 98% | 81% | 65% | 56% | 44% | 33% | 33% | 19% | 7% |
The data in Cooley et al. are based on monthly total return data from Ibbotson Associates for overlapping intervals in the range 1926-1997. The results produced by our Monte-Carlo simulator for a 100% stock portfolio using overlapping annual non-wrapping intervals for the same period are in approximate agreement as shown in Table 2.2.
| initial inflation adjusted withdrawal rate | ||||||||||
| 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% | |
| 20 years | 100% | 100% | 89% | 74% | 64% | 55% | 46% | 35% | 27% | 19% |
| 25 years | 100% | 98% | 75% | 65% | 55% | 44% | 30% | 30% | 26% | 19% |
| 30 years | 100% | 95% | 79% | 69% | 56% | 42% | 33% | 29% | 21% | 14% |
3. Comparing TIPS
Cooley et al. report the monthly success rates for a 100% long term corporate bond portfolio shown in Table 3.1, and once again based on data from Ibbotson:
| initial inflation adjusted withdrawal rate | ||||||||||
| 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% | |
| 20 years | 100% | 96% | 57% | 23% | 15% | 13% | 9% | 0% | 0% | 0% |
| 25 years | 100% | 52% | 19% | 15% | 10% | 0% | 0% | 0% | 0% | 0% |
| 30 years | 79% | 19% | 16% | 12% | 0% | 0% | 0% | 0% | 0% | 0% |
TIPS offer a very different profile. We conservatively assume a fixed return on TIPS of 2.0% above inflation. TIPS have offered returns of 2.7% +/- 0.9% since they have been offered, and returns of 2.1 +/- 0.4% over the past 5 years. The probability of successfully withdrawing from a 100% TIPS portfolio is shown in Table 3.2.
| initial inflation adjusted withdrawal rate | ||||||||||
| 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% | |
| 20 years | 100% | 100% | 100% | 100% | 0% | 0% | 0% | 0% | 0% | 0% |
| 25 years | 100% | 100% | 100% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
| 30 years | 100% | 100% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% |
As might be expected, since the return on TIPS is determinate, portfolio success is an all or nothing thing. What might be surprising is that if you want to avoid depleting a portfolio with 98% certainty, a 100% TIPS portfolio is superior to a 100% stock portfolio or a 100% bond portfolio for the 20, 25, and 30 year periods studied by Cooley et al.. Even at 95% certainty TIPS were found to be superior to stock, although the full details needed to verify this are not apparent from the above tables.
TIPS then are expected to provide a strong boost in performance, needed to offset what turn out to be overly optimistic age estimates, and a forecast decline in returns to equity.
4. Longevity
Cooley et al. use intervals of 20, 25, and 30 years for estimating the success of a retirement portfolio. While this is reasonable for estimating the average additional lifespan of an individual aged 65, it is inadequate for retirement planning. This is because the concern is with providing 95 or 98% certainty to the forecasts, and so we are not concerned with the average additional lifespan, but with the 95th and 98th percentile of the additional lifespan distribution. For someone aged 65, the 95th and 98th percentile of additional lifespan are 33 and 36 years respectively according to Arias (2006) (revised).Further, retirees are typically couples, and it is important that the portfolio outlive the longest living partner. Assuming a couple both aged 65, at lower percentiles this can add as much as 10 additional years of income onto what is required, but at the 95th and 98th percentiles, this only adds 2 years. This is displayed in Figure 4.1, with detail for the 90th-100th percentiles provided by Figure 4.2.
Like earlier studies, one factor which we considered, but which we decided not to model was increases in life span due to either changes in behavior or advances in medical technology. Over the past 30 years the median lifespan has increased by 6 years, and there is no reason to expect this trend won't continue. However, increases in the 95th and 98th percentile haven't increased nearly as much. Based on the limited data available, they appear to be increasing at about half the rate of the median lifespan over the last 5 years. Thus by using historical data our simulated results understate the 95th and 98th percentiles of longevity by about 3 years.
Another factor which we fail to capture is the difference between male and female lifespans. The difference between the average lifespan, which we model, and the female lifespan is only 1-1.5 years when measured at the 95-98th percentile of the lifespan distribution. Similarly differences based on race only have a small effect.
5. Declining returns for equity
It is widely agreed that the historical returns on stocks are unlikely to be repeated in the future. There are three reasons for thinking this.First part of the gain in stock prices from 1926-2006, 0.6% per year, has been the result of increasing P/E ratios. These increasing P/E ratios seem unlikely to continue indefinitely.
Second high P/E ratios mean that the sustainable total payout, dividends plus net share repurchases, is on the low side. Right now it is true that the total payout as a result of share repurchases is high, but this total payout level isn't sustainable. Liang and Sharp (1999) report a sustainable rate of total payout to be in the range 50-60% of earnings. This matters because this is the dividends term in the Gordon formula dividends + growth in dividends for estimating the total return on an investment. A back of the envelope calculation can give a rough handle on the implications of this. Computing the payout ratio times the difference between the inverse of the historical and current as reported P/E: 55% x (1/14 - 1/18) = 0.9% gives a decline in returns according to the Gordon formula.
Thirdly, according to the Social Security OASDI Trustees, GDP is projected to grow at 1.0% less in the long term future due to a decline in the employment growth rate as a result of the Baby Boomers retiring. GDP matters, because ultimately shares represent an ownership interest in something real, the overall economy.
Combining these three factors gives a 2.5% reduction from the historical real rate of return of 7.2% for 1926-2006 according to Morningstar, Inc.. Thus in the future real returns in the 4-5% range seem more reasonable. This decline in equity returns is in line with the 4.6% median predicted real return for equity of a survey of experts performed by Whitehouse (2005) for the Wall Street Journal.
6. The model
We use a Monte-Carlo simulator to simulate portfolio success for inflation adjusted withdrawals for a couple age 65 through to simulated death. When one member of the couple has died, we assume withdrawals at 70% of the level needed by the couple. The portfolio is rebalanced annually to its original asset distribution. Returns for TIPS are assumed to be a fixed 2.0% per year.We assume returns for equity based on the historical record of 1926-2006 as reported by Morningstar, Inc., but geometrically scaled back to give mean returns of 4.0, 4.5 or 5.0%. Unlike Cooley et al. we assume the years wrap, with 2006 being followed by 1926. This isn't ideal, but nor is the alternative of having intervals only within 1926 and 2006. This later option would have meant that when simulating say a 35 year lifespan only the years 1960-1971 had maximal probability of inclusion, and all other years, especially the first and last years, having minimal probability of inclusion in the data set.
7. Impact of increased longevity and declining equity returns
Utilizing our model to incorporate increased longevity and with returns to equity reduced to 4.5% provides the picture of portfolio success for a portfolio made up of stocks and long term corporate bonds for the period 1926-2006 shown in Table 7.1.
| initial inflation adjusted withdrawal rate | ||||||||||
| % stocks | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% |
| 0% | 96% | 81% | 66% | 55% | 46% | 38% | 27% | 19% | 13% | 10% |
| 20% | 100% | 90% | 74% | 62% | 52% | 41% | 30% | 21% | 14% | 10% |
| 40% | 100% | 94% | 82% | 68% | 56% | 44% | 33% | 23% | 16% | 11% |
| 60% | 100% | 94% | 84% | 74% | 60% | 47% | 35% | 25% | 17% | 12% |
| 80% | 100% | 94% | 83% | 72% | 61% | 51% | 38% | 28% | 19% | 13% |
| 100% | 99% | 90% | 79% | 70% | 60% | 51% | 40% | 30% | 22% | 16% |
The optimal portfolio is about 60% stock and 40% bonds, and only supports a 3.5% withdrawal rate with 98% certainty.
8. Results of the model with TIPS
Results of the model with TIPS in place on long term corporate bonds are shown in Table 8.1 for 4.5% mean returns, with the percentage of stock indicated. The reminder of the portfolio being made up of TIPS.
| initial inflation adjusted withdrawal rate | ||||||||||
| % stocks | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% |
| 0% | 100% | 99% | 78% | 49% | 28% | 18% | 12% | 9% | 6% | 5% |
| 20% | 100% | 100% | 91% | 63% | 39% | 24% | 15% | 11% | 8% | 5% |
| 40% | 100% | 100% | 91% | 74% | 51% | 32% | 21% | 14% | 10% | 7% |
| 60% | 100% | 98% | 88% | 75% | 59% | 42% | 28% | 19% | 13% | 9% |
| 80% | 100% | 96% | 84% | 73% | 61% | 49% | 35% | 24% | 17% | 12% |
| 100% | 99% | 90% | 79% | 70% | 60% | 51% | 40% | 30% | 22% | 16% |
As can be seen by comparing tables 7.1 and 8.1 TIPS offer superior performance relative to long term corporate bonds. What is perhaps surprising is the large fraction of TIPS held by the optimal retirement portfolio, which is seen to be about 30% stock and 70% TIPS. This is in comparison to models that looked at stocks versus regular bonds and reported almost the opposite holding being optimal. An explanation for this is that TIPS are far more stable than bonds with respect to being able to produce inflation adjusted returns.
9. International diversification
We simulated international stock returns as a strategy to reduce the variability in stock returns, and boost stock holdings, but found little to no gain from doing so. The reason for this is simple over the last 5-10 years the correlation between US and international stock returns has become very high. R-squared which measures the correlation is probably somewhere around 80%. Consequently even with a 50/50 portfolio split, the fraction of the portfolio that is truly independent is only around 10%. This is insufficient to have a significant diversifying effect. These results are in line with the results of Cooley et al. (2003) who found a modest 1-3% increase in portfolio success for international diversification at higher withdrawal rates based upon a lower R-squared value.10. Conclusion
The maximum sustainable withdrawal rates for different stock market rates of return and different probabilities of success are shown in Table 10.1.
| 4.0% return | 4.5% return | 5.0% return | |||||||||||||
| probability of success | probability of success | probability of success | |||||||||||||
| % stocks | 100% | 98% | 95% | 90% | 100% | 98% | 95% | 90% | 100% | 98% | 95% | 90% | |||
| 0% | 3.7% | 4.1% | 4.3% | 4.6% | 3.7% | 4.1% | 4.3% | 4.6% | 3.7% | 4.1% | 4.3% | 4.6% | |||
| 20% | 3.8% | 4.4% | 4.6% | 4.9% | 3.9% | 4.4% | 4.7% | 5.0% | 3.9% | 4.5% | 4.8% | 5.1% | |||
| 40% | 3.7% | 4.2% | 4.5% | 4.9% | 3.7% | 4.3% | 4.6% | 5.0% | 3.8% | 4.4% | 4.8% | 5.2% | |||
| 60% | 3.3% | 3.9% | 4.2% | 4.7% | 3.3% | 4.0% | 4.4% | 4.9% | 3.6% | 4.2% | 4.6% | 5.0% | |||
| 80% | 2.9% | 3.5% | 3.8% | 4.3% | 3.1% | 3.7% | 4.0% | 4.4% | 3.2% | 3.8% | 4.2% | 4.6% | |||
| 100% | 2.5% | 3.0% | 3.3% | 3.8% | 2.6% | 3.2% | 3.5% | 4.0% | 2.8% | 3.4% | 3.7% | 4.2% | |||
An optimal portfolio is comprised of about 30% stocks and 70% TIPS and provides a withdrawal rate of 4.4% with 98% confidence. These withdrawal rates are not very dependent on the precise stock market rate of return. This is almost a full percentage point higher than the optimal withdrawal rate for a portfolio made up of stocks and long term corporate bonds.
References
Arias, E. (2006; revised 2007) "United States Life Tables, 2003" in National Vital Statistics Reports 54:14.Bengen, W.P. (1994) "Determining Withdrawal Rates Using Historical Date" in FPA Journal October 1994.
Charnes, J.M., Robinson, T.R., and Marmorstein, H. (2005) "Sustainable Retirement Withdrawals: Live Well, Die Broke" in Proceedings of the 2005 Crystal Ball User Conference.
Cooley, P.L., Hubbard, C.M., and Walz, D.T. (1999) "Sustainable Withdrawal Rates From Your Retirement Portfolio" in Financial Counseling and Planning 10 (1).
Cooley, P.L., Hubbard, C.M., and Walz, D.T. (2003) "Does International Diversification Increase the Sustainable Withdrawal Rates from Retirement Portfolios?" in Journal of Financial Planning January 2003.
Liang, J.N. and Sharp, S.A. (1999) "Share Repurchases and Employee Stock Options and their Implications for S&P 500 Share Retirements and Expected Returns" Finance and Economics Discussion Series, Federal Reserve Board, 1999-59.
Morningstar, Inc. (2007) Stocks, Bonds, Bills, and Inflation: 2007 Yearbook Classic Edition
OASDI Trustees (2007) 2007 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds, U.S. Government Printing Office.
Stout, R.G., and Mitchell, J.B. (2006) "Dynamic retirement withdrawal planning" in Financial Services Review 15.
Mark, W. (2005) "Social Security Overhaul Plan Leans on a Bullish Market" in The Wall Street Journal February 28th: C1.
Have any questions or comments? thanks!
To gordoni's page.