Rate of return, standard deviation, and coefficient of variation Mike is searchi

Question

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?

Explanation / Answer

(a) Return = [(Price a the end - Price at the beginning)+Dividend]/Price at the beginning x 100

2012 = [(21.55-14.36)/14.36]x100 = 50.07%

  2013 = [(64.78-21.55)/21.55]x100 = 200.60%

  2014 = [(72.38-64.78)/64.78]x100 = 11.73%

  2015 = [(91.80-72.38)/72.38]x100 = 26.83%

(b) Average return = [50.07% + 200.60% + 11.73% + 26.83%]/4

= 72.31%

(c) Standard deviation = {[(50.07%-72.31%)2 + (200.60%-72.31%)2 + (11.73%-72.31%)2 + (26.83%-72.31%)2]/4}1/2

= 75.32%

(d) Cofficient Of Variation = S.D/Mean

= 75.32%/26.83%

= 2.81

(e) Mike's decision will be t not to invest on stock since cofficient of variation is more than 0.90.

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