**Sample Answer**

**Chapter 3 Questions**

**Question 1**

The following table lists the stock prices for Microsoft from 1989 to 1998. The company did not pay any dividends during the period

**Year Price (dollars)
**1989 1.20

1990 2.09

1991 4.64

1992 5.34

1993 5.05

1994 7.64

1995 10.97

1996 20.66

1997 32.31

1998 69.34

**a.**Estimate the average annual return you would have made on your investment.

**b.**Estimate the standard deviation and variance in annual returns.

**c.**If you were investing in Microsoft today, would you expect the historical standard deviations and variances to continue to hold? Why or why not?

Question 1 |
||||||

Year | Price | Return | %Return | R-AR | %(R-AR) | %(R-AR) SQUARED |

1989 | 1.2 | 0 | 0 | 0 | 0 | |

1990 | 2.09 | 0.741666667 | 74.16666667 | 11.94058893 | 0.119405889 | 0.014257766 |

1991 | 4.64 | 1.220095694 | 122.0095694 | 59.78349164 | 0.597834916 | 0.357406587 |

1992 | 5.34 | 0.150862069 | 15.0862069 | -47.13987084 | -0.471398708 | 0.222216742 |

1993 | 5.05 | -0.054307116 | -5.43071161 | -67.66 | -0.6766 | 0.45778756 |

1994 | 7.64 | 0.512871287 | 51.28712871 | -10.93894903 | -0.10938949 | 0.011966061 |

1995 | 10.97 | 0.435863874 | 43.58638743 | -18.6396903 | -0.186396903 | 0.034743805 |

1996 | 20.66 | 0.88331814 | 88.33181404 | 26.1057363 | 0.261057363 | 0.068150947 |

1997 | 32.31 | 0.563891578 | 56.38915779 | -5.836919947 | -0.058369199 | 0.003406963 |

1998 | 69.34 | 1.146084803 | 114.6084803 | 52.38240261 | 0.523824026 | 0.27439161 |

159.24 | 1592.4 | 560.0346997 | 560.0346997 | 5.600346997 | 1.444328043 | |

62.22607774 | ||||||

Variance | 0.180541005 | |||||

Standard Deviation | 0.424901171 |

**Question 2**

Unicom is a regulated utility serving Northern Illinois. The following table lists the stock prices and dividends on Unicom from 1989 to 1998.

**Year Price (dollars) Dividends (dollars)
**1989 36.10 3.00

1990 33.60 3.00

1991 37.80 3.00

1992 30.90 2.30

1993 26.80 1.60

1994 24.80 1.60

1995 31.60 1.60

1996 28.50 1.60

1997 24.25 1.60

1998 35.60 1.60

**a.**Estimate the average annual return you would have made on your investment.

**b.**Estimate the standard deviation and variance in annual returns.

**c.**If you were investing in Unicom today, would you expect the historical standard deviations and variances to continue to hold? Why or why not?

Question 2 |
|||||

Year | Price | Dividends | Annual Returns | Deviation= Annual Return -Average Annual Return | Deviation Squared |

1989 | 36.1 | 3 | 0.083102493 | 0.01629239 | 0.000265442 |

1990 | 33.6 | 3 | 0.089285714 | 0.089285714 | 0.007971939 |

1991 | 37.8 | 3 | 0.079365079 | 0.079365079 | 0.006298816 |

1992 | 30.9 | 2.3 | 0.074433657 | 0.074433657 | 0.005540369 |

1993 | 26.8 | 1.6 | 0.059701493 | 0.059701493 | 0.003564268 |

1994 | 24.8 | 1.6 | 0.064516129 | 0.064516129 | 0.004162331 |

1995 | 31.6 | 1.6 | 0.050632911 | 0.050632911 | 0.002563692 |

1996 | 28.5 | 1.6 | 0.056140351 | 0.056140351 | 0.003151739 |

1997 | 24.25 | 1.6 | 0.065979381 | 0.065979381 | 0.004353279 |

1998 | 35.6 | 1.6 | 0.04494382 | 0.04494382 | 0.002019947 |

0.066810103 | 0.601290926 | 0.003989182 | |||

STANDARD DEVIATION (Square root Variance) | 0.063159973 |

**Question 11**

Every investor in the capital asset pricing model owns a combination of the market portfolio and a riskless asset. Assume that the standard deviation of the market portfolio is 30% and that the expected return on the portfolio is 15%. What proportion of the following investor’s wealth would you suggest investing in the market portfolio and what proportion in the riskless asset? (The riskless asset has an expected return of 5%)

**a. **An investor who desires a portfolio with no standard deviation.

**b. **An investor who desires a portfolio with a standard deviation of 15%.

**c. **An investor who desires a portfolio with a standard deviation of 30%.

**d. **An investor who desires a portfolio with a standard deviation of 45%.

**e. **An investor who desires a portfolio with an expected return of 12%.

Question 11 |
||||

A | Portfolio with no standard deviation in market portfolio | 0% | 15% | 0% |

Proportion in riskless asset | 1 | 0% | 100% | |

B | Portfolio with standard deviation of 15% in market portfolio | 15% | 15% | 100% |

Proportion in the riskless asset | 1 | 100% | 0% | |

C | Portfolio with standard deviation of 30% in market portfolio | 30% | 15% | 200% |

Proportion in the riskless asset | 1 | 200% | -100% | |

D | Portfolio with standard deviation of of 45% proportion the market portfolio | 45% | 15% | 300% |

Proportion in the riskless asset | 1 | 300% | -200% | |

E | Portfolio with expected return of 12% | 12% | 15% | 80.0% |

**References**

Damodaran, A. (2010). *Applied corporate finance.* John Wiley & Sons.

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**Question**

**Chapter 3 Questions**

Select three formula-driven-problems from the Chapter 3 that you wish to show case and prepare a Microsoft Excel document showing the Excel formulas used to prepare the solution for those problems.

**Question 1**

The following table lists the stock prices for Microsoftfrom 1989 to 1998. The company did not pay any dividends during the period

**Year Price (dollars)
**1989 1.20

1990 2.09

1991 4.64

1992 5.34

1993 5.05

1994 7.64

1995 10.97

1996 20.66

1997 32.31

1998 69.34

**a.**Estimate the average annual return you would have made on your investment.

**b.**Estimate the standard deviation and variance in annual returns.

**c.**If you were investing in Microsoft today, would you expect the historical standard deviations and variances to continue to hold? Why or why not?

**Question 2**

Unicom is a regulated utility serving Northern Illinois. The following table lists the stock prices and dividends on Unicom from 1989 to 1998.

**Year Price (dollars) Dividends (dollars)
**1989 36.10 3.00

1990 33.60 3.00

1991 37.80 3.00

1992 30.90 2.30

1993 26.80 1.60

1994 24.80 1.60

1995 31.60 1.60

1996 28.50 1.60

1997 24.25 1.60

1998 35.60 1.60

**a.**Estimate the average annual return you would have made on your investment.

**b.**Estimate the standard deviation and variance in annual returns.

**c.**If you were investing in Unicom today, would you expect the historical standard deviations and variances to continue to hold? Why or why not?

**Question 11**

Every investor in the capital asset pricing model owns a combination of the market portfolio and a riskless asset. Assume that the standard deviation of the market portfolio is 30% and that the expected return on the portfolio is 15%. What proportion of the following investor’s wealth would you suggest investing in the market portfolio and what proportion in the riskless asset? (The riskless asset has an expected return of 5%)

**a. **An investor who desires a portfolio with no standard deviation.

**b. **An investor who desires a portfolio with a standard deviation of 15%.

**c. **An investor who desires a portfolio with a standard deviation of 30%.

**d. **An investor who desires a portfolio with a standard deviation of 45%.

**e. **An investor who desires a portfolio with an expected return of 12%.

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