Question

Please answer all parts of Question 1 using the following data:

Year	IBM’s yearly stock return	Yearly return on the S&P500
1999	17.02%	21.04%
2000	-21.21%	-9.10%
2001	13.09%	-1.89%
2002	16.22%	-22.10%

The riskless rate for this period is 3.5%, and the covariance between returns on IBM stock and the S&P500 over this period is 0.02276.

1A. What is IBM’s arithmetic mean yearly return over this period?

1B. What is IBM’s geometric mean yearly return over this period?

1C. What is the variance of IBM’s yearly stock returns over this period?

1D. What is the arithmetic mean return on the S&P 500 over this period?

1E. What is the variance of the S&P500 over this period?

1F. What is IBM’s CAPM beta according to this data?

1G. What is IBM’s CAPM cost of equity according to this data?

1H. If IBM’s debt to equity ratio is 0.57, what is their unlevered cost of equity according to this model?

Answer 1

1A. Arithmetic Mean yearly return of IBM = (17.02%-21.21%+13.09%+16.22%)/4 = 6.28%

1B.Geometric mean yearly return of IBM = ((1+0.1702)*(1-0.2121)*(1+0.1309)*(1+0.1622))^(1/4)-1 = 4.9202%

1C. Variance of a stock M's return is given by

where Rmi are the yearly returns and is the arithmetic mean yearly return

So, variance of IBM stock's yearly returns

= ((0.1702-0.0628)^2+(-0.2121-0.0628)^2+(0.1309-0.0628)^2+(0.1622-0.0628)^2)/3

=0.033874

1D Arithmetic Mean yearly return on S&P = (21.04%-9.10%-1.89%-22.10%)/4 = -3.0125%