Question

Suppose Intel stock has a beta of 1.6, whereas Boeing stock has a beta of 1. If the risk-free interest rate is 4% and the expected return of the market portfolio is 10%, according to the CAPM,

1. What is the expected return of Intel stock?
2. What is the expected return of Boeing stock?
3. What is the beta of a portfolio that consists of 60% Intel stock and 40% Boeing stock?
4. What is the expected return of a portfolio that consists of 60% Intel stock and 40% Boeing stock? (Show both ways to solve this.)

Answer 1

Sol:

Beta of Intel stock (Bi) = 1.6

Beta of Boeing stock (Bb) = 1

Risk free interest rate (Rf) = 4%

Return on market (Rm) = 10%

a)

To compute expected return of Intel (ERi) stock as per CAPM:

ERi = Rf + (Bi x (Rm - Rf))

ERi = 4% + (1.6 x (10% - 4%))

ERi = 0.04 + (1.6 x (0.10 - 0.04))

ERi = 0.04 + (1.6 x 0.06)

ERi = 0.04 + 0.096 = 0.136 or 13.6%

b)

To compute expected return of Boeing (ERb) stock as per CAPM:

ERb = Rf + (Bb x (Rm - Rf))

ERb = 4% + (1 x (10% - 4%))

ERb = 0.04 + (1 x (0.10 - 0.04))

ERb = 0.04 + (1 x 0.06)

ERb = 0.04 + 0.06 = 0.10 or 10%

c)

To compute beta (Bp) of a portfolio:

Weight of Intel = 60% = 0.60

Weight of Boeing = 40% = 0.40

Bp = (Weight of Intel x Bi) + (Weight of Boeing x Bb)

Bp = (0.60 x 1.60) + (0.40 x 1)

Bp = 0.96 + 0.40 = 1.36

d)

1st method

To compute expected return of a portfolio (ERp) by using CAPM and portfolio beta:

ERp = Rf + (Bp x (Rm - Rf))

ERp = 4% + (1.36 x (10% - 4%))

ERp = 0.04 + (1.36 x (0.10 - 0.04))

ERp = 0.04 + (1.36 x 0.06)

ERp = 0.04 + 0.0816 = 0.1216 or 12.16%

2nd method

To compute expected return of a portfolio (ERp) by using weighted average expected return of each stock:

Weight of Intel = 60% = 0.60

Weight of Boeing = 40% = 0.40

ERp = (Weight of Intel x ERi ) + (Weight of Boeing x ERb)

ERp = (0.60 x 0.136) + (0.40 x 0.10)

ERp = 0.0816 + 0.04 = 0.1216 or 12.16%

Result will be same using both the method.