You find a certain stock that had returns of 10 percent, 17 percent, 23 percent,

Question

You find a certain stock that had returns of 10 percent, 17 percent, 23 percent, and 15 percent for four of the last five years. The average return of the stock over this period was 10 percent.

What was the stock’s return for the missing year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place (e.g., 32.1).)

What is the standard deviation of the stock’s returns? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

You find a certain stock that had returns of 10 percent, 17 percent, 23 percent, and 15 percent for four of the last five years. The average return of the stock over this period was 10 percent.

Explanation / Answer

Answer: Here, we know the average stock return, and four of the five returns used to compute the average return. We can work the average return equation backward to find the missing return. The average return is calculated as:

0.10 = (0.10 – 0.17 + 0.23 + 0.15 + R) / 5

0.5 =0.10 – 0.17 + 0.23 + 0.15 + R

R=0.19 or 19%

The missing return has to be 19 percent.

Answer: Now we can use the equation for the variance to find:

Variance = 1/4[(0.10 – 0.10)2+ (–0.17 – 0.10)2+ (0.23 – 0.10)2+ (0.15 – 0.10)2+ (0.19 – 0.10)2]

Variance = 0.0251

And the standard deviation is:

Standard deviation = (0.0251)1/2

= 0.1584 or 15.84%

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