Question

Consider the following​ stocks, LOADING... ​, all of which will pay a liquidating dividend one year from now and nothing in the interim. Assume the​ risk-free rate is 4 % and the market risk premium is 7 % a. What does the CAPM predict the expected return for each stock should​ be? b. ​Clearly, the CAPM predictions are not equal to the actual expected​ returns, so the CAPM does not hold. You decide to investigate this further. To see what kind of mistakes the CAPM is​ making, you decide to regress the actual expected return onto the expected return predicted by the CAPM. What is the intercept and slope coefficient of this​ regression? c. What are the residuals of the regression in part ​(b​)? That​ is, for each stock compute the difference between the actual expected return and the best fitting line given by the intercept and slope coefficient in part ​(b​). d. What is the sign of the correlation between the residuals you calculated in part ​(c​) and market​ capitalization? e. What can you conclude from your answers to part ​(b​) of the previous problem and part ​(d​) of this problem about the relation between firm size​ (market capitalization) and​ returns? (The results do not depend on the particular numbers in this problem. You are welcome to verify this for yourself by redoing the problems with another value for the market risk​ premium, and by picking the stock betas and market capitalizations​ randomly.)

Stocks:

	Market Capitalization​($ million)	Expected Liquidating Dividend​ ($ million)	Beta	Expected Return
Stock A	854	1,000	0.91	17.0960​%
Stock B	797	1,000	1.43	25.4705​%
Stock C	951	1,000	1.48	5.1525​%
Stock D	870	1,000	0.85	14.9425​%

Answer 1

a. CAPM for stock = Risk free rate + Beta * Market risk premium

CAPM for stock A = 4% + 0.91*7% = 10.37%

CAPM for stock B= 4% + 1.43*7% = 14.01%

CAPM for stock C = 4% + 1.48*7% = 14.36%

CAPM for stock D = 4% + 0.85*7% = 9.95%

b. Doing regression of expected return on CAPM return using excel solver,

Intercept = 0.200966723340719

Slope coefficient = -0.364041678707896

c. For residual calculation:

Expected return using best fit line = Intercept + Slope coefficient *CAPM return

For stock A: Expected return using best fit line = Intercept + Slope coefficient *10.37% = 16.322%

Residual for stock A = Actual expected return - Best fit expected return = 17.0960% - 16.322% = 0.774%

Similarly, for stock B: Expected return using best fit line = 14.996%

Residual for stock B = 10.474%

Similarly, for stock C: Expected return using best fit line = 14.869%

Residual for stock C= -9.717%

Similarly, for stock D: Expected return using best fit line = 16.474%

Residual for stock D= -1.532%

d. As market cap increases, residual decreases. Hence sign of correlation is negative (minus)

e. As firm size (Market Cap) increases, return decreases.

Stock	Exp. Return	CAPM Return		SUMMARY OUTPUT				Stock	Exp. Return using best fit line	Residual	Market Cap
A	17%	10%						A	16.322%	0.7744%	854
B	25%	14%		Regression Statistics				B	14.996%	10.4741%	797
C	5%	14%		Multiple R	0.101765072			C	14.869%	-9.7165%	951
D	15%	10%		R Square	0.01035613			D	16.474%	-1.5320%	870
				Adjusted R Square	-0.484465805
				Standard Error	0.101750537
				Observations	4
				ANOVA
					df	SS	MS	F	Significance F
				Regression	1	0.000216682	0.000217	0.020929	0.898234928
				Residual	2	0.020706344	0.010353
				Total	3	0.020923025
					Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
				Intercept	0.200966723	0.310503045	0.647229	0.583851	-1.135020052	1.536953498	-1.135020052	1.536953498
				X Variable 1	-0.364041679	2.516383549	-0.14467	0.898235	-11.19116623	10.46308287	-11.19116623	10.46308287