Question

You find a certain stock that had returns of 17 percent, -24 percent, 25 percent, and 8 percent for four of the last five years. The average return of the stock over this period was 10.4 percent. What was the stock's return for the missing year? What is the standard deviation of the stock's returns?

Answer 1

Answer:

Missing year return = 26%

Standard deviation = 18.38%

Explanation:

Since the average return of the stock is the mean of all returns over the period. The stock's return for the missing year can be determined by:

$10.4=\frac{17-24+25+8+x}{5} \\x=26$

The standard deviation is given by:

$\sigma =\sqrt{\frac{\sum(x_i-X)^2}{n}}\\\sigma =\sqrt{\frac{(0.17-0.104)^2+(-0.24-0.104)^2+(0.25-0.104)^2+(0.08-0.104)^2+(0.26-0.104)^2}{5}}\\\sigma =0.1838 = 18.38\%$