*You cannot ignore rate of return volatility if you are projecting over long periods. I recently saw a piece that put forward the idea that volatility costs yield if there are withdrawals during the period. *

It seems reasonable that over the long haul, volatility could not possibly help you if you were taking money out of your account. Sort of negative dollar cost averaging. So a test.

I have not tested all possible time scales, nor have I looked at all possible markets. The period I tested was very long. From 1 January 1924 to 31 December 1993. The market is the Toronto Stock exchange as represented by the total return index. The average rate of return, (geometric average) is a little over 10.20% and the standard deviation of annual returns is more than 18.88%. A volatile market.

I chose an opening balance of $10,000 and made constant $500 withdrawals each year. Over 70 years, the ending balance, with the volatility, is $3.6 million. With a constant rate of return equal to the average, it is $4.1 million. Volatility, therefore, cost half a million dollars.

Interesting, but not terribly useful.

What I want to know is the answer to this question, “What is the equivalent constant yield that provides the same ending amount as the volatile yields.”

Answer: Roughly 10.02% 18 basis points less but with standard deviation of 0%.

There are two important truths. 1) You can only calculate this adjustment after the fact. In the beginning, you merely need to be aware of it. 2) Be reluctant to count on average rates of return if the withdrawals are a high percentage of the original capital. In this case, if the withdrawal was level and equal to the average yield, exposed to volatile markets, the portfolio would crash in the 22^{nd} year

Using bond returns instead, we find the following. Average yield 5.7+% with a standard deviation of 8.5+%. Much less volatile. However, the end balance will be negative by the end of 1973 with the same $500 withdrawal. If instead of $500, I draw the average return each year, it will last until 1961, 37 years. Notice. That period is longer than equities because the volatility is less.

At a constant rate of return and $500 out, I will need to reduce the average yield by 104 basis points to get the same result as I do with volatility. Almost a six times bigger adjustment than for equities.

The take away, is that the average yields for a given dollar amount withdrawal are more misleading when you use bonds as your underlying investment than when you use equities. Probably balanced portfolios are somewhere in between.

For different periods, different withdrawal rates and different market choices you will get materially different answers. When building a model of your future finances, the key element is the mix of your expected rate of return and your withdrawals. You can use the average over long periods and expect to survive, if you draw money at less than half the expected average rate of return. If you draw more than that, you should adjust the yield expectation downwards, possibly by a lot or shorten the period that you can do it.

Contact: [email protected] | Follow Twitter @DonShaughnessy

*Don Shaughnessy is a retired partner in an international public accounting firm and is presently with The Protectors Group, a large personal insurance, employee benefits and investment agency in Peterborough Ontario.*