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.

Two stocks with actual returns as follows are being considered by me as an investor. Assist me by calculating the standard deviation and the coefficient of variation and avise me based on a comparison of risk and return.
Stock X - Actual Returns: 6%, 12%, 8%, 10%
Stock Z - Actual Returns: 9.5%, 9.25%, 8%, 9%

Based on the following information, calculate the coefficient of variation and select the best investment based on the risk/reward relationship.
Std Dev. Exp. Return
Company A 7.4

Company A is considering a proposed project whose estimated NPV is 12 million. The estimate assumes that economic conditions will be "average". However the CFO realizes that conditions could be better or worse, so a scenario analysis was performed and the following results were obtained;
Economic Scenario Prob.

1) The XYZ Company has estimated expected cash flows for 1996 to be as follows:
Probability Cash flow
.10 $120,000
.15 140,000
.50 150,000
.15 180,000
.10 210,000
a) Calculate the standard deviation
b) Calculate the coefficient of variation.

Coefficient of Variation and Standard Deviation are two measures of dispersion or spread among the data values.
Let's say we have two different sets of data.
Explain which of the two mentioned measures can more accurately find which of these two data sets have more spread or variability in their data values.
You can se

Two securities, X and Y. Determine bases on the info given the AVERAGE RETURN, STANDARD DEVIATION, and COEFFICIENT of VARIATION.
YEAR RETURN X RETURN Y
1995 16.5% 17.5%
1996 14.2%

For a sample of students in the college of business administration at mid-atlantic university, the mean grade point average is 3.10 with a standard deviation of 0.25. Compute the coefficient of variation.

Ripken Iron Works faces the following probability distribution:
State of the Probability of State Stock's Expected Return if
Economy Occurring this State Occurs
Boom 0.25 25%
Normal 0.50 15
Recession 0.25

From the below solution, tell me what the coefficient of variation implies? And would you accept this project or not? Why?
The expected NPV is
E(NPV)= sigma Prob*NPV
= 0.05*(-70) + 0.20*(-25) + 0.50*12 + 0.20*20 + 0.05*30
= 3 (million)
The variance of NPV is
VAR = sigma Prob*[NPV -E(NPV)]^2
= 0.05*(-70-3)^2 + 0.

An investigator at a diet center is interested in the habits of clients entering his center's weight loss program. Given the pairs of observations below, where X = number of hours per week spent watching television and Y = number of pounds gained in the past year:
a) Construct the scatterplot, (but first read d and e below).