Using standard deviation and Sharpe Ratio: Tools of the Pros

If you're choosing investments based on total returns for specific time periods (eg, 1 year, 3 years, 5 years, and 10yrs) without assessing the risk, it's time to add another component to the selection process.

Standard deviation and Sharpe ratio are two basic tools that are used by professionals to determine the risks of investment and, with a little 'practice, you may be using too.

Although standard deviation is not restricted to the area of ​​investment, which is a measure of volatility which results in risk. High standard deviations indicate a wide range of investment returns and low deviations show a narrow range of return.

A word of caution: the standard deviation will not do you much good unless you use it to compare the standard deviations among other similar investments. Taking things a step further, comparing the standard deviation of a benchmark (ie a standard deviation index), you can see how closely these investments are performing at their point of reference in risk-adjusted basis.

Now for the fun part. We calculate the standard deviations, using hypothetical investments:

Suppose investment Large Cap A with a yield of 9% average over a period of three years (the period of time to measure the most common standard deviation). Suppose, further, that has a standard deviation of 6.

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

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

In our hypothetical example above, while both investments have an average return of 9%, Investment A has a series of returns from 3% to 15%. Investment B has a range of yields from 2% to 16%. Because the investment B has a wider range of return would be considered the most volatile (or risky) investments of the two.

Now let's look at a hypothetical reference point to compare these investments. Suppose the benchmark return for the investment of large Cap is 7.25%, with a standard deviation of 5.5. Using the formula above, the range of benchmark returns for the investment of large Cap 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 yield of 9% average and a standard deviation of 6) Benchmark (with an average yield 7.25% and a standard deviation of 5.5)? For this we turn to the Sharpe ratio.

Developed by Bill Sharpe, the Sharpe ratio attempts to quantify the risk in its investment performance of an investment. The higher the ratio, the better performance of the investment after adjusting for risk.

Our formula takes into account the difference between the yield of a given investment and the return of a risk-free investment. This difference is then divided by the standard deviation. This should give us our answer.

Although no investment is truly risk free, we use low-risk, 90 day Treasury Bill, with an average yield of 2%.

Our Sharpe Ratio for Investment A would be as follows:

9 (average return on investment of A), less than 2 (average return of Bill T) = 7 (excess return over a risk-free investment)

7 (return in excess in the course of a risk-free investment) divided by 6 (standard deviation Investment of A) = 1.67 (Sharpe Ratio)
Our Sharpe Ratio for the benchmark would be as follows:

7.25 (average yield of the benchmark), less than 2 (average return of Bill T) = 5.25 (excess return on risk free)

5.25 divided by 5.5 (SD Benchmark) = 0.95 (Sharpe Ratio)
Because the investment A has a higher Sharpe ratio (1.67) compared to the benchmark (0.95), is believed to have a better risk-adjusted return.

If you want more information about standard deviation and the Sharpe ratio, there are several sites on the Internet that will gladly welcome them.

Remember, these are just two tools used in the process of selecting securities. They are not infallible, but they can be of great help in keeping your portfolio in top-notch shape .......