# Calculating Coefficient of Variation

Mike is searching for a stock to include in his current stock portfolio. He is interested in Apple Inc., he has been impressed with the company's computer products and believes Apple is an innovative market player. However, Mike realizes that any time you consider a so-called high-tech 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 2006 through 2009. Apple stock, being growth-oriented, did not pay any dividend during these 4 years.

Stock Price

Year Beginning End

2006 $14.36 $21.55

2007 21.55 64.78

2008 64.78 72.38

2009 72.38 91.80

a. Calculate the rate of return for each year, 2006 through 2009, for Apple 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 this data as a sample.)

d. Based on b and c determine the coefficient of variation of returns for this security.

e. Given the calculations in d, what should be Mike's decision regarding the inclusion of Apple stock in his portfolio.

#### Solution Preview

Please refer attached file for better clarity of tables.

Please refer below for answer to e part.

Year Beginning End Rate of return

2006 14.36 21.55 (21.55-14.36)/14.36=50.07%

2007 21.55 64.78 (64.78-21.55)/21.55=200.60%

2008 ...

#### Solution Summary

This solution provides step-by-step calculations for average return, standard deviation and coefficient of variation for returns in the given case.