Standard deviation measures investment risk in terms of the volatility of returns and it is the standard measure of investment risk. It is a measure of the total risk of individual assets and portfolios of assets.

In the Mean & Standard Deviation subsection, I introduced the standard deviation as the standard measure of the total risk of individual assets and portfolios of assets. I also gave you some rules of thumb that should help you assess risk on a relative basis using standard deviations. Now we'll delve a little deeper into the evaluation of investment risk.

Individual large-cap stocks have a standard deviation of about 35%, on average, but many are well in excess of 35%. Large-cap stocks in aggregate have had a standard deviation of about 20% in recent years, which would be the non diversifiable market risk for the universe comprised of large-cap stocks. As individual stocks from various industries are added to a portfolio, the standard deviation of the portfolio will diminish until all of the specific risk has been wrung out of the portfolio. Large-cap mutual funds, being diversified portfolios, tend to have standard deviations close to the market's standard deviation, with any difference, plus or minus, being attributable to the funds' investing styles, i.e., whether their styles are aggressive or conservative.

You need to condition yourself to look at your portfolio's overall performance and variation of returns rather than focusing on individual assets. Remember, the fluctuation of your portfolio's value is smoothed by diversification because some assets will be doing well when other are not doing so well. There will be some short periods when everything is going up and some when everything is going down, but those times are the exception rather than the rule. Over the long haul some will be up while others are down and that is what you should expect. So learn to take the good with the bad and have faith in the power of diversification to limit your investment risk.

Now, I know what you're thinking and you need to get that thought out of your mind. "Why not hold the assets that are doing best and swap them for others when conditions change?" The answer is simple: Because timing doesn't work and it will increase your investment risk. Whatever you do, don't try to time the markets. There have been innumerable empirical studies which have all concluded that market timing is a sure way to lose money. Yes, there are some market timing newsletters that have done well off and on, but in the long run they're all losers. You'll hear about so and so who predicted a couple of major market moves, but with so many people trying to do it, there's bound to be a couple who get it right occasionally, but nobody does it consistently. On the other hand, there is a wealth of empirical evidence that shows that diversification works and that asset allocation accounts for over 90% of investing success. The only way to time the market is passively with dollar-cost-averaging and disciplined rebalancing. Dollar-cost-averaging will ensure that you buy more shares when prices are low and less shares when prices are high, and religious rebalancing will ensure that you consistently sell high and buy low. Maintaining the diversity of your portfolio by rebalancing will ensure that you limit your investment risk.

As I stated above, standard deviation is used to measure the total risk of individual assets, which includes specific risk. This is fine for comparing similar assets but it won't, by itself, tell you the probable effect an asset will have on your portfolio. Remember, the standard deviation is the absolute value of the average deviation from the mean, as such, it is a measure of the variability of a variable with respect to its own mean.

When comparing two assets, it's sometimes helpful to use the coefficient of variation (CV), which is the standard deviation divided by the mean, thus normalizing the standard deviation and facilitating the comparison of assets on a risk-to-return basis. This works well period-by-period but, because actual returns include the risk-free rate, which varies over time; it is not appropriate for period-to-period comparisons.

The Coefficient of Variation (CV)

_{i}÷ r

_{i}

_{i}= the standard deviation of asset i

r

_{i}=the mean return of asset i

Using
the data from our 10-year example, the CV of the S&P 500 is
17.3/9.6 = 1.8 and the large-cap growth fund is 23.9/13.4 = 1.8. This
tells us that on a risk adjusted basis, the growth fund has the same
risk per unit of return as the S&P 500 based on that 10 year
period.

Another useful means of comparing assets on an equal basis is the risk-adjusted return. A security's risk-adjusted return is determined by adjusting its return in proportion to its investment risk relative to the risk of an appropriate benchmark. For example, if you wanted to compare the return on the large-cap growth fund to that of the S&P 500, you would divide the fund's return by its standard deviation then multiply it by the standard deviation of the S&P 500:

[r_{fund}
÷ s_{fund}]
s_{market}
=[13.4% ÷
23.9%] 17.3% = 9.7%

9.7%
vs 9.6% for the market index

So,
on a risk-adjusted basis, the the S&P 500 beat the fund by 0.1
percentage points, which is a virtual dead heat, is consistent with
what the CV told us and is consistent with the notion that investors
are rational and factor risk into the prices they are willing to pay
for securities.

You'll find more detailed discussions on the use of key statistics for comparing mutual funds in the section devoted to Comparing Mutual Funds.

Standard deviation also measures the total variation of returns of a portfolio. But given the assumption that all investors are rational and therefore hold fully diversified portfolios, the total investment risk is the market risk, as 100% of the specific risk has been diversified away. This is a subtle but important difference.

You should also remember the rules of thumb presented in the statistics subsection: the mean plus or minus one standard deviation covers 68% of the total probability; plus or minus two standard deviations covers 95.4% of the total probability; and plus or minus three standard deviations covers 99.7% of the total probability. And, of course, the plus and minus are each half of those probabilities.

So, using that information, you know that a Wilshire 5000 index fund with a long-term average annual return of 10% and a standard deviation of returns of 17%, delivered annual returns of 10% +/- 17% 68% of the time and 10% +/- 34% 95% of the time. If you make a leap of faith and use that information to project future performance, you can see that you're looking at some pretty broad ranges. For instance, there would be a 68% probability that your returns on a Wilshire 5000 index fund would be between -9% and +27% in any given year. And that represents the total U.S. stock market, which presumably would be free of any specific risk, thus limiting your investment risk to systematic risk. (For the same 10 year period as the four-asset example, the Wilshire 5000 had a mean annual return of 9.5% with a standard deviation of 15.7%.)

Obviously, even a broad market fund will give you a pretty wild ride. If that was just one of the funds in your well-diversified portfolio, you'd undoubtedly be glad to have complementary assets to damp the gyrations of the portfolio. Even our simple example of computing the standard deviation of a four-asset equally-weighted portfolio was a lot smoother and delivered a higher return: 12.4% return with a standard deviation of 9.3%. Like I said earlier, look at the whole portfolio when deciding how much risk you can tolerate. In the four-asset example (of real funds) there was a 68% probability of realizing an annual return between +3 and +22%, which is still fairly broad but not as broad as the single-asset example above.

I encourage you to get the names of some mutual funds, go to Yahoo! Finance, type their names or ticker symbols into the white box next to the "Get Quotes" button, click the button, select "Risk" from the menu on the left and take a look at some real 3, 5 and 10-year returns and standard deviations to get a feel for what you'll experience with individual funds. Unfortunately there's no easy way to see how groups of them would behave in a portfolio. Computing a weighted average of their returns will give you the correct average return, but standard deviation has to be computed from the yearly weighted average returns rather than from an average of the standard deviations. However, if you're so inclined, you can download monthly historical data (it's another menu option on the same page) and compute annual returns from the monthly data.

So, if standard deviation is not the appropriate measure of an asset's contribution to your portfolio's investment risk, what is? The answer is: beta, which is the topic of the next subsection.