Rate of return, Standard deviation, Coefficient of variation. Mike is searching
ID: 2671567 • Letter: R
Question
Rate of return, Standard deviation, 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 .90.
Mike has obtained the following price information for the period 2006 through 2009. Apple stock, being growth oriented, did not pay any dividends 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 return over the past 4 years. (Hint: Treat this data as a sample)
d) Based in b and c determine the coefficient of variation of return for the security.
e) Given the calculation in d what should be Mike's decision regarding the inclusion of Apple stock in the portfolio?
Explanation / Answer
Year
Beginning
End
Return
Rate of return
2006
$14.36
$21.55
$7.19
50.1%
2007
$21.55
$64.78
$43.23
200.6%
2008
$64.78
$72.38
$7.60
11.7%
2009
$72.38
$91.80
$19.42
26.8%
mean
72.3%
sd
75.3%
coefficient of Variation
1.04
Since the coefficient of variation is greater than 0.9 then Apple Stock will not be included in the portfolio.
Year
Beginning
End
Return
Rate of return
2006
$14.36
$21.55
$7.19
50.1%
2007
$21.55
$64.78
$43.23
200.6%
2008
$64.78
$72.38
$7.60
11.7%
2009
$72.38
$91.80
$19.42
26.8%
mean
72.3%
sd
75.3%
coefficient of Variation
1.04
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