The whole point of having an investment portfolio is that it can be spent sometime. The real question, though, is how to spend it to meet investors’ needs while sustaining the portfolio value so that the money will never run out within the spending horizon. The purpose of this article is to study feasible retirement withdrawal rates by looking at historical return data. The data source I used is the same as this article. I ran my analysis on both the NYU dataset (1928 – 2010) and the Robert Shiller dataset(1871-2010). The portfolios are a mix of stocks and fixed-income securities where the stock portion is based on S&P 500 returns and the fixed-income portion consists of returns derived from 50% T-Bills and 50% T-Bonds. For example, if the stock percentage is 60%, it means the portfolio is 60% S&P 500, 20% T-Bills and 20% T-Bonds. The results presented here are based on the Shiller data set which yields more conservative conclusions. You can check out at all the details and the residual values year by year by looking into this spreadsheet.

The sustainable withdrawal rates vary depending on investors’ age and life expectancy. For investors who are near the traditional retirement age (>62), they are probably most concerned about if money will run out after 30 years or so. For younger investors, since the life expectancy is less predictable, they probably want their portfolio to last forever while making modest withdrawal each year. This article covers both scenarios and aims to provide readers with insights on feasible retirement withdrawal rates.

Table 1 shows the probabilities that the portfolio will totally run out within 30 years with specified withdrawal rates and stock allocation. The withdrawal amount is set at the beginning of the investment horizon based on the specified withdrawal rate and increases with inflation (based on CPI). For example, if your starting portfolio is $1M and the withdrawal rate is 4%. You will withdraw $40K initially and the amount will increase each year by inflation. As you can see, the failure rate is pretty low as long as the withdrawal rate is low (<=4%). Owning more stocks does help reduce the failure rate when the withdrawal rate is higher. With that said, any withdrawal rate higher than 4% is at a non-trivial risk of portfolio running out within 30 years.

Furthermore, investors probably don’t want to see the money actually run out at the end of their time. Table 2 shows the probabilities that the probabilities that the portfolio will preserve at least 50% of original value (inflation adjusted) after 30 years with varying withdrawal rates and stock allocations. It shows that the max withdrawal rate decreases to around 3.5% with at least 40% of stock allocations in order to preserve the 50% value.

Table 1: Portfolio failure rates (probabilities that the portfolio would go to zero within 30 years.)

Stock Percentage 0.50% withdrawal

1.00% 1.50% 2.00% 2.50% 0% 0.0% 0.0% 0.0% 0.0% 2.7% 5% 0.0% 0.0% 0.0% 0.0% 0.0% 10% 0.0% 0.0% 0.0% 0.0% 0.0% 15% 0.0% 0.0% 0.0% 0.0% 0.0% 20% 0.0% 0.0% 0.0% 0.0% 0.0% 25% 0.0% 0.0% 0.0% 0.0% 0.0% 30% 0.0% 0.0% 0.0% 0.0% 0.0% 35% 0.0% 0.0% 0.0% 0.0% 0.0% 40% 0.0% 0.0% 0.0% 0.0% 0.0% 45% 0.0% 0.0% 0.0% 0.0% 0.0% 50% 0.0% 0.0% 0.0% 0.0% 0.0% 55% 0.0% 0.0% 0.0% 0.0% 0.0% 60% 0.0% 0.0% 0.0% 0.0% 0.0% 65% 0.0% 0.0% 0.0% 0.0% 0.0% 70% 0.0% 0.0% 0.0% 0.0% 0.0% 75% 0.0% 0.0% 0.0% 0.0% 0.0% 80% 0.0% 0.0% 0.0% 0.0% 0.0% 85% 0.0% 0.0% 0.0% 0.0% 0.0% 90% 0.0% 0.0% 0.0% 0.0% 0.0% 95% 0.0% 0.0% 0.0% 0.0% 0.0% 100% 0.0% 0.0% 0.0% 0.0% 0.0% Stock Percentage 3.00% withdrawal

3.50% 4.00% 4.50% 5.00% 0% 12.6% 15.3% 48.6% 63.1% 68.5% 5% 8.1% 12.6% 36.0% 62.2% 66.7% 10% 2.7% 12.6% 25.2% 59.5% 64.9% 15% 0.0% 6.3% 17.1% 50.5% 63.1% 20% 0.0% 3.6% 12.6% 42.3% 61.3% 25% 0.0% 0.0% 9.0% 36.9% 55.9% 30% 0.0% 0.0% 6.3% 24.3% 52.3% 35% 0.0% 0.0% 1.8% 20.7% 43.2% 40% 0.0% 0.0% 1.8% 14.4% 36.9% 45% 0.0% 0.0% 0.9% 9.0% 34.2% 50% 0.0% 0.0% 0.9% 9.0% 28.8% 55% 0.0% 0.0% 0.9% 8.1% 26.1% 60% 0.0% 0.0% 0.9% 8.1% 23.4% 65% 0.0% 0.0% 0.9% 7.2% 21.6% 70% 0.0% 0.0% 0.9% 7.2% 20.7% 75% 0.0% 0.0% 0.9% 6.3% 18.9% 80% 0.0% 0.0% 0.9% 7.2% 19.8% 85% 0.0% 0.0% 0.9% 7.2% 18.9% 90% 0.0% 0.0% 0.9% 7.2% 18.9% 95% 0.0% 0.0% 0.9% 7.2% 18.0% 100% 0.0% 0.0% 1.8% 8.1% 18.9%

Table 2: Probabilities that at least 50% original inflation adjusted value remains after 30 years.



Stock Percentage 0.50% withdrawal

1.00% 1.50% 2.00% 2.50% 0% 100.0% 97.3% 86.5% 81.1% 70.3% 5% 100.0% 100.0% 91.9% 86.5% 76.6% 10% 100.0% 100.0% 98.2% 89.2% 84.7% 15% 100.0% 100.0% 100.0% 96.4% 88.3% 20% 100.0% 100.0% 100.0% 100.0% 93.7% 25% 100.0% 100.0% 100.0% 100.0% 98.2% 30% 100.0% 100.0% 100.0% 100.0% 100.0% 35% 100.0% 100.0% 100.0% 100.0% 100.0% 40% 100.0% 100.0% 100.0% 100.0% 100.0% 45% 100.0% 100.0% 100.0% 100.0% 100.0% 50% 100.0% 100.0% 100.0% 100.0% 100.0% 55% 100.0% 100.0% 100.0% 100.0% 100.0% 60% 100.0% 100.0% 100.0% 100.0% 100.0% 65% 100.0% 100.0% 100.0% 100.0% 100.0% 70% 100.0% 100.0% 100.0% 100.0% 100.0% 75% 100.0% 100.0% 100.0% 100.0% 100.0% 80% 100.0% 100.0% 100.0% 100.0% 100.0% 85% 100.0% 100.0% 100.0% 100.0% 100.0% 90% 100.0% 100.0% 100.0% 100.0% 100.0% 95% 100.0% 100.0% 100.0% 100.0% 100.0% 100% 100.0% 100.0% 100.0% 100.0% 100.0% Stock Percentage 3.00% withdrawal

3.50% 4.00% 4.50% 5.00% 0% 46.8% 28.8% 23.4% 20.7% 15.3% 5% 54.1% 35.1% 27.0% 22.5% 18.0% 10% 64.0% 39.6% 31.5% 23.4% 18.0% 15% 76.6% 45.9% 34.2% 28.8% 21.6% 20% 86.5% 51.4% 35.1% 30.6% 25.2% 25% 91.9% 70.3% 38.7% 32.4% 28.8% 30% 95.5% 81.1% 48.6% 34.2% 31.5% 35% 99.1% 89.2% 61.3% 39.6% 33.3% 40% 100.0% 95.5% 68.5% 46.8% 35.1% 45% 100.0% 97.3% 77.5% 52.3% 43.2% 50% 100.0% 98.2% 85.6% 61.3% 46.8% 55% 100.0% 98.2% 88.3% 66.7% 48.6% 60% 100.0% 98.2% 89.2% 71.2% 56.8% 65% 100.0% 98.2% 89.2% 73.9% 63.1% 70% 100.0% 98.2% 91.0% 77.5% 66.7% 75% 100.0% 98.2% 91.9% 79.3% 68.5% 80% 100.0% 98.2% 92.8% 78.4% 68.5% 85% 100.0% 98.2% 91.9% 79.3% 69.4% 90% 100.0% 99.1% 92.8% 81.1% 70.3% 95% 100.0% 99.1% 93.7% 81.1% 71.2% 100% 100.0% 99.1% 93.7% 81.1% 72.1%

For young investors/retirees, they probably want the portfolio to last forever. In other words, they want the portfolio to preserve 100% value after adjusted for inflation. Table 3 shows the probabilities of successfully sustaining the portfolio value after withdrawing from the portfolio for 30 years. The max feasible withdrawal rate is about 2.5% with stock allocations > 50%. If investors want additional growth, they can further decrease the withdrawal rate to 1.5% where they will have a very high chance (90+%) of doubling their money with significant stock allocations (>60%).

Table 3: Probabilities that at least 100% original inflation adjusted value remains after 30 years.



Stock Percentage

0.50% withdrawl

1.00% 1.50% 2.00% 2.50% 0% 78.4% 69.4% 60.4% 40.5% 26.1% 5% 83.8% 76.6% 67.6% 45.9% 30.6% 10% 90.1% 83.8% 73.0% 61.3% 39.6% 15% 99.1% 91.9% 82.9% 67.6% 47.7% 20% 100.0% 98.2% 91.0% 79.3% 52.3% 25% 100.0% 100.0% 95.5% 90.1% 61.3% 30% 100.0% 100.0% 100.0% 94.6% 82.9% 35% 100.0% 100.0% 100.0% 99.1% 91.0% 40% 100.0% 100.0% 100.0% 100.0% 96.4% 45% 100.0% 100.0% 100.0% 100.0% 99.1% 50% 100.0% 100.0% 100.0% 100.0% 100.0% 55% 100.0% 100.0% 100.0% 100.0% 100.0% 60% 100.0% 100.0% 100.0% 100.0% 100.0% 65% 100.0% 100.0% 100.0% 100.0% 100.0% 70% 100.0% 100.0% 100.0% 100.0% 100.0% 75% 100.0% 100.0% 100.0% 100.0% 100.0% 80% 100.0% 100.0% 100.0% 100.0% 100.0% 85% 100.0% 100.0% 100.0% 100.0% 100.0% 90% 100.0% 100.0% 100.0% 100.0% 100.0% 95% 100.0% 100.0% 100.0% 100.0% 100.0% 100% 100.0% 100.0% 100.0% 100.0% 100.0% Stock Percentage

3.00% withdrawal

3.50% 4.00% 4.50% 5.00% 0% 21.6% 18.0% 14.4% 13.5% 10.8% 5% 25.2% 19.8% 17.1% 13.5% 11.7% 10% 26.1% 22.5% 18.0% 15.3% 13.5% 15% 32.4% 25.2% 19.8% 17.1% 14.4% 20% 35.1% 29.7% 22.5% 18.9% 16.2% 25% 40.5% 32.4% 28.8% 20.7% 17.1% 30% 48.6% 32.4% 30.6% 24.3% 20.7% 35% 64.0% 37.8% 31.5% 27.9% 22.5% 40% 75.7% 47.7% 35.1% 29.7% 25.2% 45% 85.6% 56.8% 40.5% 32.4% 27.0% 50% 92.8% 67.6% 46.8% 37.8% 32.4% 55% 97.3% 78.4% 54.1% 42.3% 36.9% 60% 98.2% 79.3% 60.4% 49.5% 40.5% 65% 98.2% 82.0% 69.4% 51.4% 43.2% 70% 98.2% 87.4% 71.2% 59.5% 45.9% 75% 98.2% 88.3% 74.8% 63.1% 47.7% 80% 98.2% 90.1% 74.8% 64.0% 53.2% 85% 98.2% 91.0% 76.6% 65.8% 55.9% 90% 98.2% 90.1% 78.4% 67.6% 58.6% 95% 98.2% 90.1% 79.3% 68.5% 61.3% 100% 98.2% 90.1% 81.1% 70.3% 63.1%

Table 4: Probabilities that at least 200% original inflation adjusted value remains after 30 years.



Stock Percentage

0.50% withdrawal

1.00% 1.50% 2.00% 2.50% 0% 28.8% 20.7% 16.2% 15.3% 12.6% 5% 34.2% 22.5% 18.9% 15.3% 14.4% 10% 38.7% 30.6% 21.6% 17.1% 15.3% 15% 41.4% 34.2% 24.3% 20.7% 16.2% 20% 54.1% 41.4% 28.8% 22.5% 19.8% 25% 61.3% 47.7% 37.8% 26.1% 21.6% 30% 73.9% 52.3% 42.3% 31.5% 24.3% 35% 83.8% 64.9% 48.6% 37.8% 28.8% 40% 91.0% 79.3% 61.3% 42.3% 31.5% 45% 96.4% 88.3% 68.5% 51.4% 36.9% 50% 97.3% 93.7% 80.2% 61.3% 47.7% 55% 97.3% 97.3% 86.5% 73.0% 52.3% 60% 100.0% 97.3% 92.8% 79.3% 62.2% 65% 100.0% 97.3% 95.5% 82.0% 68.5% 70% 100.0% 97.3% 95.5% 85.6% 73.9% 75% 100.0% 99.1% 95.5% 86.5% 76.6% 80% 100.0% 100.0% 96.4% 91.0% 79.3% 85% 100.0% 100.0% 96.4% 92.8% 82.0% 90% 100.0% 100.0% 96.4% 92.8% 82.0% 95% 100.0% 100.0% 98.2% 92.8% 84.7% 100% 100.0% 100.0% 98.2% 92.8% 85.6% Stock Percentage

3.00% withdrawal

3.50% 4.00% 4.50% 5.00% 0% 10.8% 7.2% 6.3% 5.4% 4.5% 5% 11.7% 8.1% 6.3% 6.3% 4.5% 10% 12.6% 9.9% 6.3% 6.3% 6.3% 15% 14.4% 11.7% 9.0% 6.3% 6.3% 20% 15.3% 13.5% 9.9% 6.3% 6.3% 25% 18.0% 14.4% 11.7% 8.1% 6.3% 30% 19.8% 18.0% 13.5% 9.9% 7.2% 35% 23.4% 18.9% 14.4% 12.6% 8.1% 40% 27.0% 23.4% 18.0% 13.5% 9.9% 45% 30.6% 27.0% 21.6% 16.2% 12.6% 50% 36.0% 28.8% 24.3% 18.9% 13.5% 55% 39.6% 35.1% 30.6% 22.5% 16.2% 60% 46.8% 37.8% 35.1% 27.9% 20.7% 65% 55.0% 43.2% 36.9% 33.3% 26.1% 70% 58.6% 48.6% 40.5% 36.9% 30.6% 75% 65.8% 52.3% 44.1% 40.5% 33.3% 80% 67.6% 58.6% 49.5% 43.2% 38.7% 85% 70.3% 62.2% 51.4% 45.0% 42.3% 90% 72.1% 63.1% 54.1% 47.7% 44.1% 95% 73.0% 64.9% 55.0% 48.6% 45.9% 100% 73.9% 66.7% 56.8% 50.5% 47.7%

The withdrawal rates presented here are all pre-tax and pre-fees. Assuming investors will withdraw principal first and then the gains, I am not too worried about the tax for older retirees with their limited time horizon . For younger retirees, they shall count the tax as part of their expense because after a long period of time, the amount they withdraw from the portfolio will probably be fully taxed.

The real thing I am worried about is the fees. If you work with an asset management company that charges 1% a year plus transaction and mutual fund expenses, you will have to dramatically reduce your withdrawal rate. This largely means decreases the max withdrawal rate from 2.5% to 1.5% for young retirees and from 4% to 3% for older retirees. A low cost adviser (typically in the 20 basis point range) is thus recommended unless a high cost adviser can prove that he or she can generate superior return over a long period of time.

Finally, a lot of people would argue that the limited historical data might not predict the future 100%. I don’t disagree with that. However, I believe most people are resilient. Investors’ expense doesn’t have to go up with inflation. They can start their withdrawal rate at 2% and adjust it down in difficult times. (Please don’t adjust it up in good times.) This article serves as a guide to drive decisions on withdrawal rates. Investors can make adjustment along the way, which further reduces the failure rate.

Appendix: