Measuring Risk: Standard Deviation and Beta (featuring r-squared)

In previous posts we learned about investment risk and I promised we would later tackle ways to actually measure that risk. Two of the most common ways to measure investment risk are standard deviation and Beta.

Standard Deviation

Standard deviation measures how much an investment varies from its "normal" (mean) return. At the risk of over-simplifying it, I will give an analogy. Think of a roller coaster. Standard deviation would measure the ups and downs and loopty-doops. So, back to investments. If you're comparing two stocks, let's say stock A and sock B.

We'll say stock A has a normal (mean) return of 7% and a standard deviation of 9%. That would mean that in a normal distribution we would expect  stock A to fall between -2% and 16% roughly two times out of three.

Now, let's look at stock B. Stock B also has a mean return of 7% but a standard deviation of 14%. That would mean that in the same two out of three times we would see the stock fall somewhere between -7% and 21%.

You can see from this little example that, although the two stocks had the same average (mean) return, stock B's returns varied more, which would make stock B more risky, ceteris parabis.

Beta

Beta is like your neighbors the Jones--it defines its value by comparing it to another. Whereas standard deviation can tell you something about an individual investment in and of itself, Beta gets its meaning only by comparing it to another investment or benchmark. Beta's starting value is 1. Beta of 1 would mean the two investments we are comparing would be expected to move in tandem. A beta of less than one, .5 let's say, would mean the investment would be expected to increase or decrease by half as much. For example, stock A has a beta of .75 compared to the S&P 500 index. The index goes up 8%, we would expect stock A to go up only 6%. The index goes down 12%,. we would see sock A go down only 9%. The same concept holds for beta greater than one: the stock B with its beta of 1.5 would increase or decrease by 50% more than its benchmark. Beta can also be less than zero, indicating an inverse relationship. A negative Beta would mean the investment would move in the opposite direction compared to its benchmark. Beta ranges -1 to 1.

So what's a good beta? It depends on your goals. If you are more aggressive than the benchmark you're using (like an index) then a Beta >1 could be good. Conversely, if you are more conservative than the benchmark than Beta <1 might be better. Generally speaking we want the lowest Beta we can get without sacrificing returns. In practical terms, Beta is almost always used to compare an investment (stock, mutual fund, etc.) to "the market" by using broad-based indexes as proxies for the market.

Since Beta defines its value by comparing it to something else, like an index as a benchmark, the comparison has to make sense. Enter: r-squared.

R-squared (correlation coefficient)

This is not a measure of risk but rather a measure to tells us about the comparison we are making between investments. In practical terms it tells you how diversified your portfolio is. Let's say your investment has an r-squared value of .9 compared to the S&P 500. That would mean that your investment is highly correlated to the index and roughly 90% of it's variability would be connected to the benchmark. In other words, the two things you are comparing are similar enough to allow beta to do its work.

Standard Deviation or Beta?

In short, r-squared helps you determine whether standard deviation or beta is a more useful measure of risk.
Generally speaking, if your r-squared is greater than .7, then Beta becomes a useful measure of risk. If r-squared is less than .7, standard deviation would probably be a better measure. Both standard deviation and Beta will make a reappearance when we learn about risk-adjusted return and we'll use both to determine if we are getting paid for the risk we're taking.

Take a Look

Next time you look at your investments take a moment to find out the standard deviation and Beta of your positions. If you have mutual funds, including funds in your 401k, the calculation of Beta and standard deviation will be done for you and they will normally give you information on the benchmark.