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

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Question 2

Unicom is a regulated utility serving Northern Illinois. The following table lists Unicoms stock prices and dividends 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 capital asset pricing model investor owns a combination of the market portfolio and a riskless asset. Assume that the standard deviation of the market portfolio is 30% and the expected return on the portfolio is 15%. What proportion of the following investors 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 the market portfolio	0%	15%	0%
	Proportion in the riskless asset	1	0%	100%
B	Portfolio with a standard deviation of 15% in the market portfolio	15%	15%	100%
	Proportion in the riskless asset	1	100%	0%
C	Portfolio with a standard deviation of 30% in the market portfolio	30%	15%	200%
	Proportion in the riskless asset	1	200%	-100%
D	Portfolio with a standard deviation of 45% proportion of the market portfolio	45%	15%	300%
	Proportion in the riskless asset	1	300%	-200%
E	Portfolio with an expected return of 12%	12%	15%	80.0%

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References

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

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