Can you help me with this question? Thank you Rate of return, standard deviation
ID: 2735100 • Letter: C
Question
Can you help me with this question? Thank you
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
b
Using excel function Average , we get average return as below:-
c
Sum of variances. As calculated above in part a
We get Sum of variances = 2.2692
3 Sample divisor (n -1)
0.7564
Variance
86.97%
Standard deviation
d.
1.20
Coefficient of variation
e.
The stock price of Hi-Tech, Inc. has definitely gone through some major price changes over this time period. It would have to be classified as a volatile security having an upward price trend over the past 4 years. Note how comparing securities on a CV basis allows the investor to put the stock in proper perspective. The stock is riskier than what Mike normally buys but if he believes that Hi-Tech, Inc. will continue to rise then he should include it. The coefficient of variation, however, is greater than the 0.90 target
Stock Price Variance Year Beginning End Returns (Return-Average Return)^2 2012 $14.36 $21.55 50.07% 0.0495 2013 21.55 64.75 200.46% 1.6459 2014 64.78 72.38 11.73% 0.367 2015 72.38 91.8 26.83% 0.2068