Rate of return, standard deviation, and coefficient of variation Mike is searching
for a stock to include in his current stock portfolio. He is interested in Hi-Tech,
Inc.; he has been impressed with the company’s computer products and believes
that Hi-Tech is an innovative market player. However, Mike realizes that any
time you consider a technology stock, risk is a major concern. The rule he follows
is to include only securities with a coefficient of variation of returns below 0.90.
Mike has obtained the following price information for the period 2012 through
2015. Hi-Tech stock, being growth-oriented, did not pay any dividends during these
4 years.
Stock price
Year Beginning End
2012 $14.36 $21.55
2013 21.55 64.78
2014 64.78 72.38
2015 72.38 91.80
a. Calculate the rate of return for each year, 2012 through 2015, for Hi-Tech stock.
b. Assume that each year’s return is equally probable, and calculate the average return
over this time period.
c. Calculate the standard deviation of returns over the past 4 years. (Hint: Treat
these data as a sample.)
d. Based on b and c, determine the coefficient of variation of returns for the security.
e. Given the calculation in d, what should be Mike’s decision regarding the inclusion
of Hi-Tech stock in his portfolio?
a. Calculate the rate of return for each year, 2012 through 2015, for Hi-Tech stock.
| a | Beg | End | Return | Return in % |
| 2012 | 14.36 | 21.55 | 7.19 | 50.07% |
| 2013 | 21.55 | 64.78 | 43.23 | 200.60% |
| 2014 | 64.78 | 72.38 | 7.6 | 11.73% |
| 2015 | 72.38 | 91.8 | 19.42 | 26.83% |
b. Assume that each year’s return is equally probable, and calculate the average return
over this time period.
So we will put equial probabelity in each as follow
Answer : 72.31
| b | Return in % | Probabelity | Taotal |
| 2012 | 50.07% | 0.25 | 12.52% |
| 2013 | 200.60% | 0.25 | 50.15% |
| 2014 | 11.73% | 0.25 | 2.93% |
| 2015 | 26.83% | 0.25 | 6.71% |
| 72.31% |
C . Calculate the standard deviation of returns over the past 4 years. (Hint: Treat
these data as a sample.)
Answer : 86.97%
The standard deviation formula is similar to the variance formula. It is given by:
I have calculated it by using the formulla in the excel
| c | Return in % | Std Dev |
| 2012 | 50.07% | |
| 2013 | 200.60% | |
| 2014 | 11.73% | |
| 2015 | 26.83% | 86.97% |
d. Based on b and c, determine the coefficient of variation of returns for the security.
| Avearge return over period of time | 72.31% |
| Standered Deviation | 86.97% |
Noe we will calculate coefficient of variation of returns for the security as follow
=Standered Deviation /Avearge return over period of time
=86.97 % /72.31%
=1.20
e. Given the calculation in d, what should be Mike’s decision regarding the inclusion
of Hi-Tech stock in his portfolio?
He should invest as the coefficient of variation is greater than 0.9.
