# Dollar Cost Averaging: Effects of Volatility

### By: Frank Armstrong

By: Frank Armstrong, CFP

A simple exercise turns conventional wisdom on its head.

Conventional wisdom held that Dollar Cost Averaging works best with funds or stocks that have sharp ups and downs, since that gives you more opportunities to purchase shares less expensively. It was generally agreed that during the accumulation phase, high risk investments were preferable, and that long time horizon would equal out the fluctuations.

Not so! In fact, volatility turns out to be the enemy of an accumulation program. Swinging for the fences may be just exactly the wrong strategy.

To illustrate why, lets assume four different investments. We will invest $1000 a year for fifty years. Each investment has an average return of 10%. But, they each have different risks with standard deviations of 0%, 10%, 20% and 30% per year.

To model out a random future return probabilities we will put each investment into a random number generator (Monte Carlo Simulator) and run 1000 trials to see how the distribution of returns compares. Each trial run is one possible future scenario. Any one is equally likely to occur if we assume random market returns going forward. The distributions of returns will give us an idea of the likelihood of success with various scenarios. This type of exercise is a useful tool when forced to make decisions in an atmosphere of uncertainty.

Before we get into the results, let’s think for a second about two simple statistical concepts.

- Average return is the sum of all the individual returns divided by the number of trials.
- Median return is the return in the middle of the sample. In this case, 500 trials will have higher returns, and 500 will have lower returns.
- The median return
**is not**the average return.

The reason I point this out, is that the average return or better will not be enjoyed by half of the trials except in the special case where there is no volatility. In that case only, each and every trial will enjoy the average return.

Whenever there is volatility, the average return will still be what we expect, but the median trial will experience lower returns than average. The results are skewed by a few trials that experience extreme positive returns. The higher the volatility, the worse the skewing of returns becomes!

To put it into terms that are easier to understand, the average trial gets less than the average return. But a few trials win the jackpot! Perhaps more correctly we should say that given random returns over time, terminal values will not be evenly distributed.

In our example, the future value of $1000 a year for 50 years at 10% where there is no volatility is $1,281,301. We will assume that a successful trial means that it achieved that return or better. Let’s look at how this might work in practice.

Without volatility, each trial gets the same result, $1,281,301. Each trial is successful.

As volatility increases from zero, we begin to see the skewing of returns. With a 10% S.D, only about 42% of the trials are successful.

At 20% S.D. only 31% achieve the expected or average return. The skewing becomes pronounced.

Finally, with a 30% S.D., only about 22% of the trials result in success. However, the best trial out of 1000 random throws produced a whopping $38 million return! The number of trials producing far lower than average is distressingly high. Half returned less than $413,106, and the worst result was $9691! This is a far cry from what the investor might have expected upon beginning the program. Few investors could have imagined the worst outcome where terminal value was less than 20% of the total contributions. And the fact that another potential outcome might have been $38 million will be little consolation to the vast majority (78%) of losers that failed to achieve their “expected” results.

The implications of this simple test are profound for any investor in a long term accumulation mode.

- Assumed straight line returns (zero volatility) are inappropriate for financial models.
- Investors must carefully consider both risk and return when designing their accumulation plans.
- Given equal return expectations, higher volatility leads to lower median returns, or increased failure to achieve “expected” returns.
- Employ standard techniques including broad diversification across borders, size and style to control risk. Avoid concentrated portfolios either within an individual asset class or between asset classes.
- Investors should construct efficient portfolios, or those with the highest return per unit of risk available.
- When choosing between efficient portfolios, the optimum strategy the one that produces the highest probability of meeting the investor’s objectives.

Conventional wisdom during the accumulation phase ignored the problem of risk while focusing entirely on returns. By targeting the highest possible returns, investors actually decreased their chances of meeting their goals. A more sophisticated approach that accounts for the impact of variable returns over time will yield a far higher probability of success.