Risk, Variance, Standard Deviation, Volatility… What’s What?

Standard Deviation and Variance in Investing 

Standard deviation measures how far apart the numbers are in a data set. Variance, on the other hand, gives an actual value to how much the numbers in a data set vary from the mean.

Variance

There is a tree in your backyard. Everyday in the morning, when you go and take a look at it, you see that some leaves have fallen down. As a pass time, you start counting these leaves. You also start recording these values in a diary. You do this for some time and say these are the values you get.

Day 1 - 50
Day 2 - 65
Day 3 - 35
Day 4 - 45
Day 5 - 55

Now you feel that just counting the leaves is not fun anymore. You would like to guess the number of leaves you will find the next day. You take a look at your data and say "hmm looks like some times it goes above 50 or below 50 but stays around that. Maybe it will more often than not be 50. So let's see if it is 50 tomorrow." This is your expected value for the number of leaves fallen. This is the mean of the data and in a very simple case also the expected value of it.

Now say you had a friend who did the same thing with his backyard tree. and this is the data he gets

Day 1 - 50
Day 2 - 50
Day 3 - 50
Day 4 - 50
Day 5 - 50

What do you think would be his expected value for number of leaves fallen for tomorrow? 50, right? Now who do you think is more likely to be correct? You or him? Since the mean is same for both sets of data, just quoting the mean isn’t enough and here is where variance comes in. It tells you how different is your data from your mean. More the variance, harder it is to predict the next value. It helps you describe the data better.

Standard Deviation

Standard Deviation is a measure of how spread out the numbers are. A low standard deviation means that most of the numbers are close to the average, while a high standard deviation means that the numbers are more spread out.

Standard Deviation is useful in that it tell you how far from “normal” the numbers are. “Normal” is just the average of all the numbers. What if you wanted to find out the probability that the number of leaves you will find the next day will be between 40 and 60. That’s where standard deviation come into play. The average of from both trees is 50 (add all the leaves and divide by 5). So you can say the standard is 50. Now we know.

For traders and analysts, these two concepts are of paramount importance as they are used to measure security and market volatility, which in turn plays a large role in creating a profitable trading strategy.

Standard deviation is one of the key methods that analysts, portfolio managers, and advisors use to determine risk. When the group of numbers is closer to the mean, the investment is less risky; when the group of numbers is further from the mean, the investment is of greater risk to investors.

Securities that are close to their means are seen as less risky, as they are more likely to continue behaving as such. Securities with large trading ranges that tend to spike or change direction are riskier. In investing, risk in itself is not a bad thing, as the riskier the security, the greater potential for a payout.

The Bottom Line 

The standard deviation and variance are two different mathematical concepts that are both closely related. The variance is needed to calculate the standard deviation. These numbers help traders and investors determine the volatility of an investment and therefore allows them to make educated trading decisions.