Recognizing The Effect Of Volatility

Monte Carlo simulation and today’s powerful spreadsheet applications give us far more insight into the problem, and point out some additional solutions that would not have been possible with historical back testing.

Simply put, Monte Carlo Simulation utilizes random draws of numbers from pools constructed with specified rates of return and volatility (risk). Much like a lottery, we build a pool of numbers and pull them out at random to construct a single test. Then we repeat the process 1000 or 10,000 times and summarize the results. The summary provides a quantitative estimate of the range and distribution of the possible returns. By varying the construction of the pools of numbers we can examine different strategies to see which ones give a higher probability of success.

For instance, we could construct pools of numbers that have an average return of 10% and a standard deviation of 10%. Then starting with a $1 million dollar portfolio, we can test the survival rates of a 4%, 5%, 6% and 7% withdrawal amounts 1000 times each. Our findings will generally confirm the Cooley, Hubbard, Walz study.

For instance, we run the tests again using a pool of numbers with a 10% rate of return  but a standard deviation of 10%, 15%, and 20%, and a withdrawal rate of 6% per year. At 30 years only 1% of trials fail at 10%, but 23% fail at a standard deviation of 20%. Failure rates soar with the higher volatility! All ten percent returns are not equal. (See Illustration at left.)

The simulation reveals a clear link between volatility and survival of the portfolio at any given time horizon. So that anything we can do to reduce portfolio volatility (given the same rate of return and withdrawal rates) will significantly enhance the chance that a retiree’s nest egg will survive.

Totally skewed

In the traditional analysis referred to above, you might think that half of all trials would result in greater than expected returns, and half less. But, it’s worse than that. The only case where each trial yields the average result occurs where there is no portfolio volatility. In that special case, every trial survives and gets the identical result.

With volatility, outcomes become skewed. Even though we obtain the expected rate of return across the sample, the median return is less than the average. The higher the volatility, the greater the sample becomes skewed at any time horizon. So, while we get the average return we expect, the average result is less than what we expect. As the number of failures goes up, the number of extraordinary results also goes up. A small number of players obtain much higher than expected results, while a large number of players’ portfolios either fail or obtain lower than expected results.

For example, suppose we expect a terminal value of $100,000 for a particular withdrawal rate, rate of return and time horizon. If one result yields $1,000,000, and nine results yield $0 at some particular risk level, we have achieved our average return. But, nine of ten retirees are broke!

Summary

It’s hard to overestimate the importance of selecting a realistic withdrawal rate.

• If capital is insufficient, the retiree may be tempted to increase the withdrawal rate.
• A high withdrawal rate increases his chance of going broke
• Reaching for higher investment returns increases volatility which in turn increases the chance of going broke

Next: Frank talks about constructing an investment strategy.

Copyright ã 2000 Francis C. Armstrong

Frank Armstrong, CFP, is the author of Investment Strategies for the 21st Century, published here, President of Managed Account Services, Inc., a fee-only Registered Investment Advisor, and Chief Investment Strategist of DirectAdvice.com.