The Trinity study is a famous study that looked at how much one could draw from savings in retirement while invested in stocks and bonds, without completely depleting the portfolio over a period of time. The safe withdrawal rate, as it was called, is the percentage of the invested savings that could be withdrawn in the first year of retirement. Each year thereafter, for the duration of retirement, the amount withdrawn would be adjusted up or down by the rate of inflation.
To give an example, let’s say our hypothetical new retiree used a 6% withdrawal rate and had $1 million initially invested in 90% stocks and 10% bonds at the start of retirement. He or she would withdraw $60,000 from the portfolio at the beginning of the year for living expenses (6%), leaving the remaining $940,000 invested. Now let’s say the market return for the year was -5% for stocks and 3% for bonds, and inflation was 2%. At the end of the year, the retiree’s investments would be $900,520 due to the change in the stock and bond market. At the beginning of the next year, the retiree would take out $61,200 ($60k adjusted upwards for inflation by 2%), for living expenses in the new year, leaving a portfolio of $839,320 to be invested. This process would continue each year of retirement until the portfolio is completely depleted or the retirement otherwise ends. The reason the amount withdrawn is adjusted upwards each year is so that the retiree can maintain constant purchasing power / standard of living in retirement.
The Trinity study found that a portfolio invested in 75% stocks and 25% bonds with a 4% safe withdrawal rate was 98% successful for a 30 year retirement over the time period studied (1926 – 1995). This finding has been generally used as a rule of thumb for what you will need in retirement to retire relatively safely. This study has been quite useful and discussed quite often within the retirement and investment communities.
It has also faced a number of criticisms:
- The time period of 1926 – 1995 is somewhat short. Particularly for long retirements of 30 years or more, there are few observations within this time period. For example, if one uses a 30 year retirement length, the last observation year with a full 30 years of observation would be 1966. This misses some of the worst years for retirement, namely 1967, 1968, and 1969.
- The bond portion of the portfolio was composed of corporate bonds. It is posited by some that risk should be taken on the equity side of the portfolio, and the bond side should be low risk / certain income. In that case, US treasury bonds would be a better choice.
- In the majority of cases, if a retiree picks a safe withdrawal rate of 4%, very often at the end of their life, the retiree will have much more than they started with at the beginning of retirement. This means they could have raised their standard of living or retired earlier with less savings had they known they could take a higher safe withdrawal rate.
- Retirees can adjust their safe withdrawal rate based on market conditions. Conditions in 1966, the absolute worst year for retirement in US history, saw a coming decade with stagflation and followed by lingering high inflation after that. Stagflation is a particularly bad combination for retirement of high inflation and poor economic performance for the US (and as a result, poor performance in the market). In such situations, a retiree could decide to adjust their safe withdrawal rate lower and subsist on a lower standard of living if such a situation descended.
I thought it would be useful to update the Trinity study somewhat, by building a retirement simulator of my own. In this update, I will address the shortcomings of the Trinity study in the first 2 points above (the latter 2 points I will address in a future post). I will simulate safe withdrawal rates with 10 year treasury bonds, which are generally safer and less volatile than corporate bonds, and I will use the data from Robert Shiller to study the time period from 1871 – 2024, encompassing many more situations than the original study.
The Shiller data includes 10 year US Treasury bond yield data only. The problem with this is that a real bond return does not just include the interest paid each year. If you hold the bond for 1 year, it is no longer a 10 year bond, it now has a duration of 9 years. Further, if the yield falls a lot, the bond will increase in price a lot, and if the yield increases, the price of the bond will fall. This represents a capital gain or loss that is not accounted for if you look at only the interest paid on the bond. Therefore, I needed to reconstruct a total return index for the 10 year US treasury bond based on the available yield data. I will be rebalancing the portfolio yearly, so the total bond return will be calculated based on the price of a zero coupon treasury bond of the given yield at the time of purchasing with a 10 year duration and the price of the same bond with a 9 year duration at the beginning of the next year with the resulting change in yield. The price of the zero coupon bond can be calculated with this formula (assuming the price of the bond grows to $100 at maturity):
$100 / (1 + GS10)n
where GS10 is the annual yield on the 10 year treasury bond expressed as decimal fraction and n is the number of years left in the bond. This includes both capital gains, duration changes, and yields in the bond return. In the same fashion, we can construct a total return index for the S&P500 using both price change in the index as well as dividends paid. Finally, for inflation, we can use the historical data for the CPI (consumer price index) to calculate the rate of inflation each year. We will use this to essentially rebalance each year between stocks and bonds, and set aside a given amount for expenses for the year.
Armed with these key pieces of information, we can calculate the maximum safe withdrawal rate for all years from 1871 – 2024. We can do this for different retirement lengths (10, 20, 30, 40, 50 years), and for different portfolio compositions (100% stocks, 80/20 stocks/bonds, 60/40, 40/60, 20/80, and 100% bonds). Figure 1 shows the maximum safe withdrawal rate for each starting year for an 80% stocks / 20% bonds portfolio rebalanced annually for different lengths of retirement. We chose this because it is a common allocation to stocks and bonds, and as you will see in a moment, within the most desirable range of allocations. As shown in Figure 1, the maximum safe withdrawal rate decreases for longer retirements, but decreases most going from 10 to 20 years, and not as much going from 20 to 40 years or more. Furthermore, the shape of the curve is very similar across the different lengths of retirements. This suggests that the earlier years are more important in determining the maximum safe withdrawal rate than later years.
Figure 2 shows the maximum safe withdrawal rate for each starting year for different portfolio compositions for a 30 year retirement. As you can see, it is generally better for a portfolio to contain more stocks than bonds. This is not just the situation for young investors, it can even be true for retirees, particularly those with longer retirements. While bonds offer lower volatility in most years, they are still subject to volatile years, and the fixed bond payments are more prone to destruction of value from inflation while the components of the stock market have some pricing power to combat inflation. 1929 and 1930 were the only years where a portfolio of 100% bonds outperformed a high stock portfolio, and still did not outperform an intermediate stocks / bonds mix. It would appear that a portfolio with somewhere between 80 – 100% stocks and 20 – 0% bonds is best. There are a few stretches of years where it is better to be 80% stocks rather than 100% stocks. In those cases, it appears that rebalancing annually between stocks and bonds helps to smooth volatility and mitigate a bit against sequence of return risk. However, it is certainly the case, particularly for long retirements, that 100% stocks is also a good choice. For very short retirements with large safe withdrawal rates, volatility can really affect the maximum safe withdrawal rate, so some bonds are advised.
The absolute lowest maximum safe withdrawal rate observed over the period of 1871 – 2014 was 1.3% for a 50 year retirement and a portfolio of 100% bonds in 1941. From Figure 2 with a 30 year retirement, the lowest maximum safe withdrawal rate was 2.4% and was also in 1941 with a portfolio of 100% bonds. The period 1933 – 1968 was the worst for a high bond portfolio. During that time, bonds reached a generational low in 1940/1941 and began a long climb to the highs in the 1980’s. The absolute worst year for a high stocks portfolio was 1966 with 1965 a close second. The lowest maximum safe withdrawal rate in 1966 for a portfolio of 80% stocks / 20% bonds was 3.3% for a 50 year retirement, or 3.7% for a 30 year retirement. For a 30 year retirement, and an 80% stocks / 20% bond portfolio, the maximum safe withdrawal rate only dipped below 4% in 4 years: 1965, 1966, 1968, and 1969. These years all fell just before entering a period of low economic growth as well as high inflation – a particularly nasty combination for retirees to experience in the early years of retirement. For a 30 year retirement, there are 125 observable years from 1871 – 1995, so this represents a 97% success rate for the 4% safe withdrawal rate. This compares to a 98% success rate for the Trinity study (1926 – 1995) which misses some of the worst years in the mid-late 60’s because there are not yet enough observation years for the 30 year retirement. This also misses some periods where corporate bonds (which were utilized in the Trinity study) had high default rates (like the early 1990’s, early 2000’s and early 2010’s).
From this new study, we could probably say that at no point should a prediction for maximum safe withdrawal rate ever fall much below 1.3% for a high bonds portfolio and a long retirement, or much below 3.3% for a high stocks portfolio with a long retirement. Of course, it would be great if we could further refine this to understand when we should dial back our safe withdrawal rate, and when we can increase it. To do this, we will need to understand how to predict real returns with decent accuracy, since real (inflation adjusted) returns will determine the maximum safe withdrawal rates. This is exactly what we have been building towards in the previous posts looking at modelling real and nominal returns in the market using equity allocation of investors and 10 year treasury bond “P/E” (1 divided by the bond yield, 1 / GS10). In the next post, I will look at some scenarios for predicting the maximum safe withdrawal rate based on equity allocation of investors and 10 year US Treasury bond data.
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