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# Average return, standard deviation and coefficient of variation

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Stocks A and B have the following historical returns:

Year rA rB
2006 -22.40% -13.30%
2007 20.50 19.70
2008 19.25 22.10
2009 -3.00 -10.90
2010 22.75 28.20

a.Calculate the average rate of return for each stock during the 5-year period. Round your answers to two decimal places.

b.Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Round your answers to two decimal places.

c.Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places.

d.Calculate the coefficient of variation for each stock and for the portfolio. Round your answers to two decimal places.

https://brainmass.com/math/fractions-and-percentages/average-return-standard-deviation-coefficient-of-variation-457391

#### Solution Preview

Please refer attached file for formulas and better clarity of tables.

Year Stock A Stock B
ra rb
2006 -22.40% -13.30%
2007 20.50% 19.70%
2008 19.25% 22.10%
2009 -3.00% -10.90%
2010 22.75% 28.20%
Sum 37.10% 45.80%

a.Calculate the average rate of return for each stock during the 5-year period. Round your answers to two decimal places.
Average Return for Stock A=7.42%

Average Return for Stock B=9.16%

b.Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Round your answers to two decimal places.

Year ...

#### Solution Summary

This solution describes the steps to calculate average return, standard deviation and coefficient of variation in the given case.

\$2.19

## How to explain (put into words) my calculations for file attach

1. I am not sure as how to explain the problems (put into words)
2. I am not sure if I had to do any graphing. Can you help me?

Part A
The market portfolio is assumed to be composed of two securities, Investment X and Y as shown below. Determine based on the information given the Average return, Standard Deviation and Coefficient of Variation. Which is the better investment?

Year Return X Return Y
1997 16.5% 17.5%
1998 14.2% 13.2%
1999 13.5% 14.5%
2000 16.1% 15.1%
2001 12.2% 13.2%
2002 11.5% 10.5%

Part B
A portfolio consists of five securities with following Beta and Proportions:
What is the Beta of the portfolio?

(see data in attached file)

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