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.
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 at the
Living Trust Network. Its web site is
http://www.livingtrustnetwork.com
Get a free list of internet sites that provide information on
standard deviation and the sharpe ratio - send the Living Trust
Network an email at cdahlke@livingtrustnetwork.com.