Michele Stuart, a financial analyst for Chargers Products, a manufacturer of stadium benches, must evaluate the risk and return of two assets, X and Y. The firm is considering adding these assets to its diversified asset portfolio. To assess the return and risk of each asset, Michele gathered data on the annual cash flow and beginning- and end-of-year values of each asset over the immediately preceding 10 years, 1997-2006. These data are summarized in the table below. Micheles investigation suggests that both assets, on average, will tend to perform in the future just as they have during the past 10 years. He therefore believes that the expected annual return can be estimated by finding the average annual return for each asset over the past 10 years.
Return Data for Assets X and Y, 1997-2006
| Asset X Value | Asset Y Value
Year Cash flow Beginning Ending Cash flow Beginning Ending
1997 $1,000 $20,000 $22,000 $1,500 $20,000 $20,000
1998 1,500 22,000 21,000 1,600 20,000 20,000
1999 1,400 21,000 24,000 1,700 20,000 21,000
2000 1,700 24,000 22,000 1,800 21,000 21,000
2001 1,900 22,000 23,000 1,900 21,000 22,000
2002 1,600 23,000 26,000 2,000 22,000 23,000
2003 1,700 26,000 25,000 2,100 23,000 23,000
2004 2,000 25,000 24,000 2,200 23,000 24,000
2005 2,100 24,000 27,000 2,300 24,000 25,000
2006 2,200 27,000 30,000 2,400 25,000 25,000
Michele believes that each asset's risk can be assessed in two ways: in isolation and as part of the firm's diversified portfolio of assets. The risk of the assets in isolation can be found by using the standard deviation and coefficient of variation of returns over the past 10 years. The capital asset pricing model (CAPM) can be used to assess the asset's risk as part of the firm's portfolio of assets. Applying some sophisticated quantitative techniques, Junior estimated betas for assets X and Y of 1.60 and 1.10, respectively. In addition, he found that the risk-free rate is currently 7% and that the market return is 10%.
a. Calculate the annual rate of return for each asset in each of the 10 preceding years, and use those values to find the average annual return for each asset over the 10-year period.
b. Use the returns calculated in part a to find (1) the standard deviation and (2) the coefficient of variation of the returns for each asset over the 10-year period 1997-2006.
c. Use your findings in parts a and b to evaluate and discuss the return and risk associated with each asset. Which asset appears to be preferable? Explain.
The solution calculates the annual rate of return, the standard deviation and the coefficient of variation of the returns for two assets in Excel.