An Introduction to Design Using SWR Tools

Research on Safe Withdrawal Rates

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JWR1945
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An Introduction to Design Using SWR Tools

Post by JWR1945 »

An Introduction to Design Using SWR Tools

There are many issues surrounding retirement finances. Not only is there a choice of an initial take-out number, but there is the task of monitoring performance. There are a variety of ways to adapt the numbers from our calculators to suit one's own needs. There are many worthwhile lessons and insights to learn from using our calculators. I consider it folly to rely on a single take out number or to restrict your own actions to those that have been modeled. I refer to this expanded view, far beyond the direct capability of our calculators, as SWR based design.

I have already presented a couple of approaches to design.

One was the result of examining what has supported portfolio survival in the past. The answer: dividends. Dividends provide a floor below which it is never necessary to sell any shares of stock. As long as dividend amounts continue to increase in real terms, one can maintain his buying power into the indefinite future. Dividends have done so in the past although dividend increases have been erratic. Notice that we are no longer dependent upon the numbers produced by our calculators. We rely only upon the reasoning, the cause and effect relationship.

Another approach has been to use the floor provided by TIPS and/or ibonds to set a minimal withdrawal rate. For example, if the timeframe is 30 years and if the ending balance is allowed to go to zero, there is never a need to accept an income level that is less than 3.33% of the initial balance in real terms. If TIPS and/or ibonds have a positive interest rate, we can withdraw more. Again, we depend upon the rationale. In this case we take notice of our need to sell securities. There is the possibility of capital loss and it is not part of the calculation. Once again, we know what to look for. We know cause and effect.

Now we extend our outlook beyond the direct capabilities of our calculators.

Final Balances Other Than Zero

Let us write Gummy's equation differently.

The balance after N years / the initial balance = (total return0) * (1 - w/WFAIL) where total return0 is the total return without any withdrawals, w is the withdrawal rate and WFAIL is the withdrawal rate which causes the balance to be zero after N years. The total return0 and WFAIL both depend upon the actual returns in the first N years.

Total return0 refers to the ratio of the final balance to the initial balance. The Nth root of this ratio is the annualized gain multiplier. Subtract 1 and then multiply by 100% to get the annualized return.

WFAIL is 1 divided by Gummy's Magic Sum. Its equation is 1/WFAIL = [1/g1] + [1/(g1*g2)] + [1/(g1*g2*g3)] + ... + [1/(g1*g2*g3*...*gN)] where g1 is the gain multiplier for the first year, g2 is the gain multiplier for the second year, g3 is the gain multiplier for the third year and so on up to gN, which is the gain multiplier for the Nth year. A gain multiplier for a year is 1 plus the return (expressed as a decimal, not as a percentage) for that year. For example, if the return for a year is 8%, the gain multiplier for that year is 1.08.

Notice that it is entirely unnecessary to limit our thinking to a final balance of zero. Once you are able to determine WFAIL, which is what our calculators help us estimate, your estimate of the final balance after N years of withdrawals at any other rate is as good as your estimate of the total return0.

If you think that you have a credible estimate of a portfolio's total return over the next decade or two, you can calculate your portfolio's balance at any withdrawal rate.

Breaking the Timeframe into Segments

There is no need for us to restrict our analysis to a single timeframe. We can join a 10-year timeframe with a 20-year timeframe to come up with a 30-year timeframe. We can focus on the transition point. We can focus on this transition to monitor our portfolio's performance more precisely.

There are many ways to estimate return0. They often include upper and lower bounds of the return or the timeframe or both. We can add information about WFAIL from our calculators (along with its confidence limits). This allows us to catch errors more rapidly.

The result is not the same as looking at a 30-year timeframe directly. It has greater uncertainty. The difference is the result of the return-to-the-mean behavior (when the term return-to-the-mean is precisely and properly defined). That is, if performance has been way beyond historical norms for a decade, it is unreasonable to expect that the next twenty years of performance would be entirely unaffected.

Focus on Earnings Yield

Until recently, there were three related factors that I have examined. One has been Historical Database Rates (or WFAIL at various timeframes). Dividends have been another. Valuation, as measured most successfully by P/E10, has been the third.

As a result of extensive email discussions with Rob Bennett, I have discovered that dividends do not have to be included separately. Their effects are captured adequately by using earnings yield (from the inverse of P/E10). Dividends come from earnings and dividend yields ultimately come from earnings yield (as measured by 1/[P/ E10] or E10/P). In fact, earnings yield is better than initial dividend yield. The E10/P earnings yield already includes information about the quality of earnings and the safety of dividends.

Dividend yields should still be considered since they provide an income floor.

I have found that straight-line plots of Historical Database Rates (including the WFAIL values) versus earnings yield E10/P provides an excellent fit to the data. I find that it is advantageous to eliminate a couple of points at extremely high earnings yields (and low valuations). The behavior of the statistics is not especially good. The scatter increases as the earnings yield increases (and as the valuations become more favorable, at smaller values of P/E10). Interestingly, plots of Historical Database Rates versus P/E10 produce a poor curve fit but good statistics. (The amount of scatter does not change much as a function of P/E10.)

[Excel can provide you with trendlines and their equations along with R squared. You have to check the appropriate boxes on the other tab after you have selected the type of curve.]

In the full set of data 1871-1980, the amount of uncertainty at 10 years is very high, with R squared values of 0.21 and 0.30, for portfolios with 50% stock and 80% stock, respectively. If you restrict yourself to the years 1925-1980, R squared increases to 0.29 and 0.40. The 10-year WFAIL80 values are between 8% and 10% at high valuations (with E10/P = 4% and P/E10 = 25, but lower than today's valuations). It ranges between 10% and 17% when E10/P = 7%, which is close to historical norms.

The uncertainty with 20-year values is lower. For the 80% stock portfolio, R squared values are 0.52 for the years 1871-1980 and 0.59 for the years 1925-1980.

[R squared tells you how much of the variance in the scatter plot is captured by the curve. The remaining fraction is explained by unknown, random and/or other causes.]

Remaining Details

We are at a very early stage of our investigations.

At the moment, it seems best to think in terms of two segments, each with the same withdrawal rate (based on the initial balance). That simplifies matters since the starting balance and the final balance are already specified ahead of time. Introducing an additional segment allows for more than one solution (in theory).

I have posted tables of 10-year and 20-year WFAIL values. An alternative approach is to set the withdrawal rate w to a specified value and then to determine the number of years N at which failure occurs. Those data are easier to collect. The problem is that I end up wanting to know all of the WFAIL and return0 numbers up to the year that fails. I suspect that there are benefits in collecting data that way. Right now, I do not know what they are.

Have fun.

John R.
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JWR1945
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Post by JWR1945 »

Here are tables listing earnings yield percentages (100%/[P/E10]).

Have fun.

John R.

Earnings Yield

Code: Select all

Year   P/E10   E10/P %
1871   13.3     7.5
1872   14.5     6.9
1873   15.3     6.5
1874   13.9     7.2
1875   13.6     7.4
1876   13.3     7.5
1877   10.6     9.4
1878    9.7    10.3
1879   10.7     9.3
1880   15.3     6.5
1881   18.5     5.4
1882   15.7     6.4
1883   15.3     6.5
1884   14.4     6.9
1885   13.1     7.6
1886   16.7     6.0
1887   17.5     5.7
1888   15.4     6.5
1889   15.8     6.3
1890   17.2     5.8
1891   15.4     6.5
1892   19.0     5.3
1893   17.7     5.6
1894   15.7     6.4
1895   16.5     6.1
1896   16.6     6.0
1897   17.0     5.9
1898   19.2     5.2
1899   22.9     4.4
1900   18.7     5.3

Code: Select all

Year   P/E10   E10/P %
1901   21.0     4.8
1902   22.3     4.5
1903   20.3     4.9
1904   15.9     6.3
1905   18.5     5.4
1906   20.1     5.0
1907   17.2     5.8
1908   11.9     8.4
1909   14.8     6.8
1910   14.5     6.9
1911   14.0     7.1
1912   13.8     7.2
1913   13.1     7.6
1914   11.6     8.6
1915   10.4     9.6
1916   12.5     8.0
1917   11.0     9.1
1918    6.6    15.2
1919    6.1    16.4
1920    6.0    16.7
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Post by JWR1945 »

Earnings Yield (continued)

Code: Select all

Year   P/E10   E10/P %
1921    5.1    19.6
1922    6.3    15.9
1923    8.2    12.2
1924    8.1    12.3
1925    9.7    10.3
1926   11.3     8.8
1927   13.2     7.6
1928   18.8     5.3
1929   27.1     3.7
1930   22.3     4.5
1931   16.7     6.0
1932    9.3    10.8
1933    8.7    11.5
1934   13.0     7.7
1935   11.5     8.7
1936   17.1     5.8
1937   21.6     4.6
1938   13.5     7.4
1939   15.6     6.4
1940   16.4     6.1
1941   13.9     7.2
1942   10.1     9.9
1943   10.2     9.8
1944   11.1     9.0
1945   12.0     8.3
1946   15.6     6.4
1947   11.5     8.7
1948   10.4     9.6
1949   10.2     9.8
1950   10.7     9.3

Code: Select all

Year   P/E10   E10/P %
1951   11.9     8.4
1952   12.5     8.0
1953   13.0     7.7
1954   12.0     8.3
1955   16.0     6.3
1956   18.3     5.5
1957   16.7     6.0
1958   13.8     7.2
1959   18.0     5.6
1960   18.3     5.5
1961   18.5     5.4
1962   21.2     4.7
1963   19.3     5.2
1964   21.6     4.6
1965   23.3     4.3
1966   24.1     4.1
1967   20.4     4.9
1968   21.5     4.7
1969   21.2     4.7
1970   17.1     5.8
1971   16.5     6.1
1972   17.3     5.8
1973   18.7     5.3
1974   13.5     7.4
1975    8.9    11.2
1976   11.2     8.9
1977   11.4     8.8
1978    9.2    10.9
1979    9.3    10.8
1980    8.9    11.2
Have fun.

John R.
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