Question

Assume that the data are representative of the future so that the returns obtained on firm A and the S&P 500 are the same as their expected returns. Complete the following questions:

a. The S&P 500 is a measure of the market. The market is average (by definition), so what is its beta?

b. The risk-free assets has no risk (by definition), so what is its beta?

c. Firm A, the S&P 500, and the risk-free asset should all be on the SML. The expected return for the risk-free asset can be calculated using the Forecast function. The X is risk-free beta, the known Ys are the returns on firm A and the S&P 500, and the known Xs are the betas for the same two.

d. Calculate the market risk premium.

e. From the results of (c) and (d) give the equation of the SML.

f. Use the SML from d to calculate the expected return on asset B in the return column in the first row for firm B.

g. Firm A the S&P 500, and the risk-free asset should all be on the SML. The return for firm B can also be calculated using the Forecast function. The X is firm B's beta, the known Ys are the returns on firm A, the S&P 500, and the risk-free asset, and the known Xs are the betas for the same three. Put the Forecast calculation in the return column in the second row for firm B. Is the result the same as (e).

	Beta	Return
Firm A	0.32	6.20%
S&P 500	A	9.70%
Risk-Free asset	B	C
Firm B	1.23	F
Firm B	1.23	G
MRP		D

Answer 1

a. Beta indicates how much will be the increase of stock return with increase of Market return by 1%. Since S&P 500 increase in return will be same as market return, the BETA of market =1. Looking in a different way Beta indicates systematic risk ( risk of return of stock compared to return of market). Since S&P return will be systematic risk same as market, the BETA of market is equal to ONE

b.Since risk free asset has no risk, its return do not change with change in market return. Hence BETA of Risk Free Asset =0

c.CAPM Equation:

Rs=Rf+Beta *(Rm-Rf)

Rs=Stock Return,

Rf=Risk Free Rate

Rm=Market Return

Rm-Rf=Market Risk Premium

Firm A

Beta =0.32, Rs=Stock return=6.20%

Rm=9.70%

6.2=Rf+0.32*(9.7-Rf)

6.2=Rf+3.104-0.32Rf

6.2-3.104=Rf(1-0.32)=Rf*0.68

0.68Rf=3.096

Rf=3.096/0.68=4.55

Risk Free Rate =4.55%

d. Market Risk Premium =Rm-Rf=9.70-4.55=5.15%

e.EQUATION OF SML

Rs=4.55+Beta *5.15

f.Expected Return of B

Beta of B=1.23

Expected Return of B=Rs=4.55+1.23*5.15

Return of B=10.88%