Question

You find a certain stock that had returns of 13 percent, −20 percent, 21 percent, and 12 percent for four of the last five years. The average return of the stock over this period was 9.3 percent.
Required:
a. What was the stock’s return for the missing year?
b. What is the standard deviation of the stock’s returns?

Answer 1

Answer:

• Mean = 20.5%
• Standard Deviation = 16.90%

Explanation:

Missing mean

9.3 = (13 +-20 + 21 + 12 + missing mean)/5

46.5 = 13 +-20 + 21 + 12 + missing mean

Missing mean = 46.5 - 13 + 20 - 21 -12

Missing mean = 20.5%

Standard deviation

Variance

Squared Deviations from mean = (( 0.13 - 0.093)² + (-0.20 - 0.093)² + (0.21 - 0.093)² + (0.12 - 0.093)² + ( 0.25 - 0.093)²) / ( 5- 1)

= 0.1142 / 4

= 0.02855‬

Standard deviation = √0.02855‬

= 16.90%

Answer 2

Answer: year 5 = 20.5

standard deviation =15.11

Explanation:

YEAR       RETURNS

Year 1        13%

year 2       -20%

year 3        21 %

year 4        12%

year 5      ??

Average return = total returns 0f year 1 to 5/ number of year

year1 + year2 + year3 + year 4 + year 5)/5

9.3% = 13% +-20% + 21%+ 12% +y

9.3% x 5 =26% + y

46.5 -26 =y

y= 20.5= year 5

Standard deviation of the stock's retrurn = ( (x -average mean)2/5))^1/2

Yr               x                x-average mean           x-average mean^2

Yr               x                   x-9.3                              (x-9.3)^2

1            13.00                  3.7                                 13.69

2       - 20.00                 29.3                             858.49

3         21.00                  11.7                               136.89

4         12.00                   2.7                             7.29

5         20.50                   11.2                           125.44

Total                                                                1,141.8

  Standard deviation  =   ( (x -average mean)2/5))^1/2 

=(1141.80/5 )^1/2                  

=228.36^1/2

=15.11