Question

In the CAPM world, two securities, A and B, are priced efficiently, i.e., they fall on the SML. The expected return of A is 20%, and its beta is 1.6. The expected return of B is 11%, and its beta is 0.7. What is the slope of the SML?

	A.	0.15
	B.	0.2
	C.	0.1
	D.	0.12
	E.	0.08

Answer 1

Security Market Line (SML) is a graph between Expected return (E[R]) on Y-axis and beta (β) on X-axis

The equation of SML is

E[Rs] = RF + βs*(RM - RF)

where, E[Rs] = Expected return on security, β = beta of the security, RF = Risk-free rate, RM - RF = Market risk premium = MRP

SML can be written as:

E[Rs] = RF + βs*MRP

The slope of SML is (RM - RF) or MRP. We need to calculate the market risk premium (MRP)

It is given that securities A and B fall on SML. Therefore,

E[RA] = RF + βA*MRP and E[RB] = RF + βB*MRP

We have, E[RA] = 20%, βA = 1.6 and E[RB] = 11%, βB = 0.7

20% = RF + 1.6*MRP

11% = RF + 0.7*MRP

Solving the above two equations and put RF = 20% - 1.6*MRP in the second equation, we get,

11% = 20% - 1.6*MRP + 0.7*MRP

9% = 0.9*MRP

MRP = 9%/0.9 = 10% = 0.1

Slope of SML = MRP = RM - RF = 0.1

Answer -> 0.1 (Option C)