Measuring Volatility
1. Measuring Volatility
Volatility is a measure of spread, or dispersion, of the returns of a security. Now, here we have two securities, along with their daily returns for a week. They both had total returns for the week of 5%, which we can find by simply adding the daily returns. This means that they both had an average daily return of 1%. However, how could we measure how spread out the daily returns actually were? Well, we could find the average distance between the actual daily returns and the average daily return of 1%. Security two looks like it experienced much higher fluctuations in its daily returns, ranging from 5% to +7%. Now, this sounds a bit confusing, so let me show you what I mean. Let's turn our attention to security one. The first daily return is 1%. This is 2% less than the average daily return of 1%, so the difference from the mean is 2%. The second daily return is 3%. This is 2% higher than the average daily return of 1%. The next daily return of 2% is 1% higher than the daily average return. The next daily return of 2% is 3% lower than the daily average return. And the final daily return of 3% is 2% higher than the average daily return. So, if we can find the averages of these differences, this will give us a really good measure of the dispersion from the mean. But here we run into a bit of a problem. To get the average, we need to add these differences and divide by five, the number of differences or days in the week. When we add these differences up, we get zero. So, the average difference is 0% divided by five or 0%. This is because some of the differences are above the average daily return of 1%, and some of the differences are below the average daily return. We run into the same problem with security two. Now, the standard deviation solves this issue.2. Let's practice!
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