|Library||Email or Print this page|
Are you confused by some of the terms analysts use to quantify risk and performance? Here's a quick guide to some of the most common measurements.
Standard deviation measures the amount of variation in any group of numbers that make up an average. Say you and I both play basketball and we both average 10 points per game. But while you are consistent and always hit around 10 points per game, I'm unpredictable and may hit anywhere from 1 to 20 points. With standard deviation, you could measure the variance around that average. To figure out standard deviation, find the average and subtract each number in the group from the average. Square the resulting numbers so you won't have a negative number. Then add these numbers together, divide by the total number of the group, and find the square root. Then you will have the standard deviation of the numbers in the group and can compare the standard deviation of numbers in some other group. In finance, standard deviation usually calculates monthly returns over a set time period. It measures a security's volatility and helps gauge the risk of loss as compared to other securities.
Beta measures the volatility of a security relative to a relevant benchmark index, usually the S&P 500®. To determine beta, take a security's monthly returns and those of a benchmark index and plot the security's return for each month vs. the index's on an XY graph, using the index's return as the X coordinate and the security's return as the Y coordinate. Draw a "best-fit" line to roughly connect the points and measure the slope of this line to determine the beta of the security. What that means is much simpler than the process of calculating it. A beta that is greater than one means that the security is more volatile than the benchmark, while a beta of less than one means that the security is less volatile than the index.
Beta and R-squared go hand in hand. In fact, R-squared determines how reliable the beta is. R-squared measures how close all of the points on the XY graph are to the "best-fit" line you drew to determine beta. If all of the points were right on the line, a security would have an R-squared of 100, which means a perfect correlation with the index. An R-squared of zero would mean there is no correlation at all. The lower the R-squared, the less accurate the beta is as a measure of a security's volatility.
Alpha is a means for investors to compare securities on a risk/return basis. Stocks with strong returns may have varying levels of risk, and it's important to consider both when comparing investments. People sometimes refer to this as evaluating performance on a risk-adjusted basis. Securities don't necessarily produce the returns predicted by their beta values. Alpha is the difference between the expected return and the actual return. If a security performs better than what its beta predicted, it has a positive alpha. If it performs worse, it has a negative alpha. The riskier the investment, the higher the returns must be to produce a high alpha.
For example, if a stock has a beta of 2, which means it's twice as risky as its benchmark, and generates an actual return that is 1% greater than its expected return, then the stock has a positive alpha of 1%, or 100 basis points.
The Sharpe ratio measures a security's return in excess of a guaranteed investment relative to its risk. The guaranteed investment is the 90-day T-bill rate. To calculate the Sharpe ratio, divide a security's returns in excess of the 90-day T-bill rate by the standard deviation of those returns. Say a stock produced a return of 15% with a standard deviation of 10% and the T-Bill generated a 5% return. Subtract the T-Bill's return of 5% from the stock's return of 15% and then divide by the standard deviation of 10%. The Sharpe ratio would equal 1.
The higher its Sharpe ratio, the better a security's returns have been relative to the amount of risk. Using standard deviation as its volatility component, instead of an index, the Sharpe ratio doesn't have the problem of index correlation. Since standard deviation is calculated the same way for all securities, you can directly compare the risk-adjusted returns by the Sharpe ratio.
Most investors would probably agree that these measurements can be hard to understand at first. But hang in there - once you start using them frequently, you'll begin to rely on them as important tools for comparing potential investments.
S&P 500 is a registered trademark of Standard & Poor's Corporation, a division of The McGraw-Hill Companies, Inc.
Updated: January 1, 2013
This article is for informational purposes only and is not intended as an offer or solicitation for the sale of any financial product or service or as a determination that any investment strategy is suitable for a specific investor. Investors should seek financial advice regarding the suitability of any investment strategy based on their objectives, financial situations, and particular needs. This article is not designed or intended to provide financial, tax, legal, accounting, or other professional advice since such advice always requires consideration of individual circumstances. If professional advice is needed, the services of a professional advisor should be sought.
© 2013 Wilmington Trust Corporation.