You find a certain stock that had returns of 12 percent, 19 percent, 25 percent,

ID: 2725892 • Letter: Y

Question

You find a certain stock that had returns of 12 percent, 19 percent, 25 percent, and 13 percent for four of the last five years. The average return of the stock over this period was 10.2 percent. What was the stock’s return for the missing year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Stock’s return %

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

Standard deviation %

Explanation / Answer

Solution:

Average Return of Stock = Sum of Five Year’s Stock Return / No of years

10.2% = (12% + (-19%) + 25% + 13% + Missing year Stock Return) / 5

Missing year stock return = (10.2% x 5) – 31%

= 51% - 31%

= 20%

Calculation of Standard Deviation of the stock’s return

Year

Stock Return (%)

Deviation2

(Stock Return - Average Return)2

(12 - 10.2)2 = 3.24

-19

(-19 - 10.2)2 = 852.64

(25 - 10.2)2 = 219.04

(13 - 10.2)2 = 7.84

(20 - 10.2)2 = 96.04

Average Return = 10.2%

1,178.80

Standard Deviation = (Sum of (Stock Return - Average Return)2 / n)1/2

N = no of years = 5

Sum of (Stock Return - Average Return)2 = 1178.80

Standard Deviation = (1178.80 / 5)1/2 = (235.76)1/2 = 15.35%