Security Market Line and mispricing

EXERCISE 01

Gamma has a forecast expected return of 20.00% and beta 1.5. The risk-free rate is 4% and the market expected return is 12%.

A.Assess pricing under CAPM.

A.

r_i=r_f+\beta_i(E[R_M]-r_f),\quad\alpha_i=E[R_i]-r_i

r_i=0.04+1.5(0.12-0.04)=0.16

\alpha=0.2-0.16

Alpha = 4.00%. Above the SML; undervalued relative to the forecast.

Security Market Line and mispricing

EXERCISE 02

Gamma has a forecast expected return of 13.00% and beta 1.5. The risk-free rate is 4% and the market expected return is 12%.

A.Assess pricing under CAPM.

A.

r_i=r_f+\beta_i(E[R_M]-r_f),\quad\alpha_i=E[R_i]-r_i

r_i=0.04+1.5(0.12-0.04)=0.16

\alpha=0.13-0.16

Alpha = -3.00%. Below the SML; overvalued relative to the forecast.

Security Market Line and mispricing

EXERCISE 03

Gamma has a forecast expected return of 15.00% and beta 1.5. The risk-free rate is 4% and the market expected return is 12%.

A.Assess pricing under CAPM.

A.

r_i=r_f+\beta_i(E[R_M]-r_f),\quad\alpha_i=E[R_i]-r_i

r_i=0.04+1.5(0.12-0.04)=0.16

\alpha=0.15-0.16

Alpha = -1.00%. Below the SML; overvalued relative to the forecast.

Security Market Line and mispricing

EXERCISE 04

Gamma has a forecast expected return of 18.00% and beta 1.5. The risk-free rate is 4% and the market expected return is 12%.

A.Assess pricing under CAPM.

A.

r_i=r_f+\beta_i(E[R_M]-r_f),\quad\alpha_i=E[R_i]-r_i

r_i=0.04+1.5(0.12-0.04)=0.16

\alpha=0.18-0.16

Alpha = 2.00%. Above the SML; undervalued relative to the forecast.

Security Market Line and mispricing

EXERCISE 05

The market expected return is 8.5%, and the risk-free rate is 1.5%.

Portfolio	Expected return	Beta
A	2.9%	0.2
B	8.5%	1
K	5.0%	2

A.Which portfolios lie on the SML?

A.

r_i=r_f+\beta_i(E[R_M]-r_f)

r_A=0.015+0.2(0.085-0.015)=0.029

r_B=0.015+1(0.07)=0.085,\quad r_K=0.015+2(0.07)=0.155

A and B lie on the SML; K lies below it.

Security Market Line and mispricing

EXERCISE 06

Asset A has expected return 14% and beta 1.1 and lies on the SML. The risk-free rate is 5.2%. Asset B has beta 1.4 and expected return 18%.

A.Is B correctly priced?

A.

MRP=(0.14-0.052)/1.1=8\%

r_B^{CAPM}=5.2\%+1.4(8\%)=16.4\%

B offers 18%: above the SML and undervalued.

Security Market Line and mispricing

EXERCISE 07

Correlation with the market is 0.8; asset volatility is 10.000%, market volatility 5.000%, risk-free return 3.000% and market risk premium 6.000%.

A.Calculate beta and the CAPM required return.
B.Assess another security with the same beta and an expected return of 15.000%.

A.

\beta_i=\rho_{iM}\frac{\sigma_i}{\sigma_M},\quad E[R_i]=r_f+\beta_i(E[R_M]-r_f)

\beta_i=0.8\frac{0.1}{0.05}\approx 1.6

E[R_i]=0.03+(1.6)(0.06)\approx 0.126

Beta = 1.60000; required return = 12.600%.

B.

\alpha=0.15-0.126\approx 0.024

It lies above the SML and is undervalued, assuming the inputs and CAPM are correct.

Security Market Line and mispricing

EXERCISE 08

Correlation with the market is 0.6; asset volatility is 30.000%, market volatility 15.000%, risk-free return 3.000% and market risk premium 5.000%.

A.Calculate beta and the CAPM required return.
B.Assess another security with the same beta and an expected return of 8.000%.

A.

\beta_i=\rho_{iM}\frac{\sigma_i}{\sigma_M},\quad E[R_i]=r_f+\beta_i(E[R_M]-r_f)

\beta_i=0.6\frac{0.3}{0.15}\approx 1.2

E[R_i]=0.03+(1.2)(0.05)\approx 0.09

Beta = 1.20000; required return = 9.000%.

B.

\alpha=0.08-0.09\approx -0.01

It lies below the SML and is overvalued, assuming the inputs and CAPM are correct.

Security Market Line and mispricing

EXERCISE 09

Correlation with the market is 0.8; asset volatility is 25.000%, market volatility 15.000%, risk-free return 4.000% and market risk premium 6.000%.

A.Calculate beta and the CAPM required return.
B.Assess another security with the same beta and an expected return of 11.000%.

A.

\beta_i=\rho_{iM}\frac{\sigma_i}{\sigma_M},\quad E[R_i]=r_f+\beta_i(E[R_M]-r_f)

\beta_i=0.8\frac{0.25}{0.15}\approx 1.333333

E[R_i]=0.04+(1.333333)(0.06)\approx 0.12

Beta = 1.33333; required return = 12.000%.

B.

\alpha=0.11-0.12\approx -0.01

It lies below the SML and is overvalued, assuming the inputs and CAPM are correct.