Question

Using the properties of the capital market line (CML) and the security market line (SML), determine which of the following scenarios are consistent or inconsistent with the CAPM. Explain your answers. Let A denote arbitrary securities while F and M represent the riskless asset and the market portfolio respectively.

a.

Security	E[R]	σ(R)
A	25%	30%
M	15%	30%

b.

Security	E[R]	σ(R)
A	25%	55%
F	5%	0%
M	15%	30%

Answer 1

As per the CAPM ,

Expected return (E(R)) = Rf +Beta * [ ER(M)-Rf]

Rf = risk free rate

ER(M)= expected return in market

SML line represents CAPM return.

If CAPM holds, then the security will be on the SML line.

CML line=

E(R) =

Case-A.

Security	E[R]	σ(R)
A	25%	30%
M	15%	30%

Here Rf or risk free rate is not given.

Hence lets Assume Rf = 0%

Hence E(R)or expected return as per CML =

As per CML the expecter return should be 15%.

But the arbitrary ssecurity A has expected return of 25%.

Hence its is inconsistent with the CML return,SML return or CAPM.

As arbitrary security has more return than the market portfolio , hence the Market portfolio is inefficient.

Case-B

Security	E[R]	σ(R)
A	25%	55%
F	5%	0%
M	15%	30%

E(R)or expected return as per CML =

As per CML the expecter return should be 23.33%.

But the arbitrary ssecurity A has expected return of 25%.

Hence its is inconsistent with the CML return,SML return or CAPM.

As arbitrary security has more return than the market portfolio , hence the Market portfolio is inefficient.