# Using Standard Deviation And The Sharpe Ratio: Tools Of The Pros

If you're choosing investments based on total returns over specific time periods (i.e., 1yr, 3yrs, 5yrs, and 10yrs) without assessing the risk, it's time to add another component to your selection process.

Standard Deviation and the Sharpe Ratio are two basic tools that are used by investment professionals for determining risk and, with a little practice, you can be using them too.

Although standard deviation isn't limited to the area of investments, it is a measurement of volatility that translates into risk. High standard deviations denote a wide range of investment returns and low deviations denote a narrow range of returns.

A word of caution: standard deviation won't do you much good unless you're using it to compare standard deviations among other like investments. Taking things a step further, if you compare the standard deviation to a benchmark (i.e. an indices standard deviation), you can see how closely those investments are performing to their benchmark on a risk adjusted basis.

Now for the fun part. Let's compute some standard deviations using hypothetical investments:

Assume Large Cap Investment A has a 9% average return over a three year period (the most common time frame for measuring standard deviation). Assume, also, that it has a standard deviation of 6.

Now also assume that Large Cap Investment B has an average return of 9% over the same three-year period, but that it has a standard deviation of 7.

To find the range of returns for either of our hypothetical investments, you need to take the average rate of return and add (or subtract) the standard deviation for that investment. The result will give you the range of returns for that investment 68% of the time.

In our hypothetical example above, while both investments have a 9% average return, Investment A has a range of returns from 3% to 15%. Investment B has a range of returns from 2% to 16%. Because Investment B has a wider range of returns, it would be deemed to be the more volatile (or riskier) of the two investments.

Now let's look at a hypothetical benchmark to compare these investments. Let's assume that the benchmark return for Large Cap Investments is 7.25%, with a standard deviation of 5.5. Using the above formula, the benchmark range of returns for Large Cap Investments would be 1.75% (7.25% minus 5.5) to 12.75% (7.25% plus 5.5).

So far so good, but now how do we compare Investment A (with a 9% average return and a standard deviation of 6) to the benchmark (with a 7.25% average return and a standard deviation of 5.5)? For that we turn to the Sharpe Ratio.

Developed by Bill Sharpe, the Sharpe Ratio attempts to quantify an investment's risk relative to its investment performance. The higher the ratio, the better the investment's performance after adjusting for its risk.

Our formula takes the difference between the return on a particular investment and the return on a risk-free investment. That difference is then divided by our standard deviation. That should give us our answer.

Although no investment is truly risk free, let's use a low-risk, 90-day Treasury Bill, with an average return of 2%.

Our Sharpe Ratio for Investment A would be as follows:

9 (Investment A's average return) minus 2 (T Bill's average return) = 7 (Excess return over a risk-free investment)

7 (Excess return over a risk-free investment) divided by 6 (Investment A's standard deviation) = 1.67 (Sharpe Ratio) Our Sharpe Ratio for the Benchmark would be as follows:

7.25 (Benchmark's average return) minus 2 (T Bill's average return) = 5.25 (Excess return over risk free)

5.25 divided by 5.5 (Benchmark's standard deviation) = .95 (Sharpe Ratio) Because Investment A has a higher Sharpe Ratio (1.67) than the benchmark (.95), it is deemed to have a better risk adjusted return.

If you want more information on standard deviation and the sharpe ratio, there are several sites on the internet that will be happy to accomodate you.

Remember, these are only two tools used in the process of selecting securities. They are not infallible, but they can be of tremendous help in keeping your portfolio in top-notch shape.
About the Author: Glenn (?Chip?) Dahlke, a senior contributor to the Living Trust Network, has 28 years in the investment business. He is a Registered Representative of Linsco/Private Ledger and a principal with Dahlke Financial Group. He is licensed to transact securities with persons who are residents of the following states: CA. CT, FL, GA, IL. MA, MD. ME, MI. NC, NH, NJ, NY.OR, PA, RI, VA, VT, WY. If you have any questions or comments, Chip would love to hear from you. You may contact him by email at dahlkefinancial@sbcglobal.net. You may also contact him by going to the Living Trust Network's web site. Its URL is http://www.livingtrustnetwork.com. Copyright 2005. Living Trust Network, LLC. All Rights Reserved. is10 Source: www.isnare.com