Question

The​ S&P TSX Composite index delivered annual returns of​ 10.55%, ​-8.32%, ​21.08% and​ 9.10% from 2014 to 2017. What is the standard deviation of the index returns over these four​ years?

Answer 1

To calculate the standard deviation of the index returns, first find the mean of the returns, then calculate the deviation of each return from the mean, and finally square the deviations, sum them up, divide by the number of returns minus one, and take the square root.

Step-by-step explanation:

To calculate the standard deviation of the index returns, we first need to find the mean (average) of the returns over the four years. The mean can be calculated by adding up the four returns and dividing by 4. In this case, the mean return is (10.55% - 8.32% + 21.08% + 9.10%) / 4 = 8.5825%.

Next, we calculate the deviation of each return from the mean. To do this, we subtract the mean from each return. We get (-2.9725%, -16.9025%, 12.4975%, and 0.5175%).

Finally, we square each deviation, sum them up, divide by the number of returns minus one, and take the square root. This gives us the standard deviation. Plugging in the values, the standard deviation of the index returns over the four years is approximately 9.692%.