A New Tool: Overview

Research on Safe Withdrawal Rates

Moderator: hocus2004

Post Reply
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

A New Tool: Overview

Post by JWR1945 »

While examining a more general problem, I have discovered a strong relationship between a portfolio's annualized total return when there are no withdrawals, which I call return0, and its 30-Year Historical Database Rate. This relationship is strongest at 14 years.

Straight-line curve fits are sufficient. At 14 years, R squared is just over 0.90. That is, the straight-line relationship explains over 90% of the variance (or scatter). Random, unexplained and unknown sources combined make up slightly less than 10% of the remaining uncertainty (i.e., variance).

The relationship is weak when the number of years is very low or very large. R squared remains above 0.80 at years 11 through 18 or 19.

The scatter tells us about the importance of the order of returns. The annualized return depends only on the initial and final balances of a portfolio. A Historical Database Rate depends upon both the order of investment returns and their magnitudes.

The earliest years are most important for determining Historical Database Rates. But the randomness in return0 (the annualized return when there are no withdrawals) is greatest when the number of years is smallest. As the number of years increases, the randomness in return0 decreases. But the relative influence of the earliest years decreases. The sweet spot is 14 years.

I have applied this tool to calculate something closely related to a Safe Withdrawal Rate for the years 1929, 1937, 1965 and 1966 with portfolio allocations of 50% stock and 80% stock. I have done this by assuming that I was able to calculate the annualized total return (return0) at year 14 exactly. I have compared the resulting estimates, which I have called conditional Safe Withdrawal Rates, with the actual Historical Database Rates. In all cases except one, the conditional Safe Withdrawal Rate was smaller than the Historical Database Rate. This tells us that the actual historical sequences were lucky sequences.

Here are some comparisons with HDBR50 (50% stocks).
1) For 1929, the conditional Safe Withdrawal Rate with 50% stocks was 4.48%. The value of HDBR50 turned out to be 4.5%.
2) For 1937, the conditional Safe Withdrawal Rate with 50% stocks was 3.79%. The value of HDBR50 turned out to be 3.9%.
3) For 1965, the conditional Safe Withdrawal Rate with 50% stocks was 3.94%. The value of HDBR50 turned out to be 4.2%.
4) For 1966, the conditional Safe Withdrawal Rate with 50% stocks was 3.73%. The value of HDBR50 turned out to be 4.1%.

The standard deviation at 14 years and 50% stocks is 0.39%. The 90% confidence limits are plus and minus 0.62% (i.e., plus and minus 1.6 times the standard deviation).

Here are some comparisons with HDBR80 (80% stocks).
1) For 1929, the conditional Safe Withdrawal Rate with 80% stocks was 4.16%. The value of HDBR80 turned out to be 4.4%.
2) For 1937, the conditional Safe Withdrawal Rate with 80% stocks was 4.64%. The value of HDBR80 turned out to be 4.5%.
3) For 1965, the conditional Safe Withdrawal Rate with 80% stocks was 3.49%. The value of HDBR80 turned out to be 4.0%.
4) For 1966, the conditional Safe Withdrawal Rate with 80% stocks was 3.24%. The value of HDBR80 turned out to be 3.9%.

The standard deviation at 14 years and 80% stocks is 0.67%. The 90% confidence limits are plus and minus 1.07% (i.e., plus and minus 1.6 times the standard deviation).

All of the historical data are used in the process of estimating conditional Safe Withdrawal Rates. The effective number of degrees of freedom is high. In contrast, the actual Historical Database Rates are discrete values and their effective number of degrees of freedom is much lower. (Both are affected by data overlap. The influence of overlap on conditional SWRs is much less than on HDBRs.)

It is important to remember that this tool calculates a Safe Withdrawal Rate only if its input (the annualized total return of the portfolio at a specified number of years) is a mathematical calculation based on information up to a specific date but not later. It can translate other annualized total return inputs into projections closely related to Safe Withdrawal Rates. Such projections are not Safe Withdrawal Rates. This tool can also be used in sensitivity studies.

Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

This tells us that the actual historical sequences were lucky sequences.
I believe that raddr was the first to discover this. My research confirms his earlier finding while using a different methodology. The fact that two different approaches come up with the same conclusion increases our confidence in the result.

Have fun.

John R.
Mike
*** Veteran
Posts: 278
Joined: Sun Jul 06, 2003 4:00 am

Post by Mike »

This tells us that the actual historical sequences were lucky sequences.
Since we have no way of knowing whether the next 10 years will contain a lucky or unlucky sequence, this provides another reason for caution. Combined with the historically high P/E ratios, the S&P looks even less appealing.
Post Reply