Effect of Altering the Sequence of Yearly Returns Upon the Portfolio Safe Withdrawal Rate

 

I wondered  awhile back how sensitive the portfolio SWR ("safe" withdrawal rate) is to the sequence of returns from year to year. I played around with Shiller's market data since 1871 and found that merely switching two years in the sequence could make a huge difference. In other words if you take the 130 years since 1871, randomly switch two, and leave the other 128 alone you can significantly change the SWR in many cases. Each time I started out with the historical data anew before switching 2 years.

I  ran the simulation 1000 times exactly as was done for the historical data except I randomly switched 2 years of historical data for each run. Details:

-75:25 stocks:commercial paper - real inflation adjusted (CPI) returns
-30 year simulated retirement for each year from 1871 to 1971 (100 overlapping periods)
-0.2% annual expenses
-returns for two random years switched for each run


Here's what happens:

 


As you can see just above the blue "simulation mean" line there is a dense green line of dots at about 3.85%, just above the simulation mean. This is same as the historical 30-year SWR as determined by the real historical data. Note that this is where most of the dots are congregated which means that switching 2 years in the return sequence made no difference in the SWR. However, approximately 25% of the dots fall below this grouping meaning that the SWR would've been lower if only 2 years in the sequence had been different. In a few cases the SWR would have been below 3%! Of course, in some cases the switch would have raised the SWR but not by much (less than 0.5%). Not only that but only 13% of the time did the SWR go up - roughly half of the number of times it went down.

Just to show how little the change was in the returns sequence here is a representative sample of 9 switched-data return histories (red lines) plotted against the actual historical data (blue line):

 



A fair criticism could be made that taking returns out of sequence is an artificial situation and I wouldn't disagree. However, I left 128 out of 130 exactly the same. And history won't repeat exactly the same way which is why you have to take a historical studies with a large grain of salt. After all,  who can predict when an event like 9-11 will happen and throw the markets out of whack for a year or two.

 

Last edited: 06/28/2004
 

 

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