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?