Question

You have a portfolio that is invested 11 percent in Stock R, 56 percent in Stock S, and the remainder in Stock T. The beta of Stock R is .84, and the beta of Stock S is 1.39. The beta of your portfolio is 1.47. What is the beta of the Stock T?

Answer 1

Answer: Stock T has a beta of 1.82

Step-by-step explanation:

GIVEN the following:

PORTFOLIO:

Weight of each stock in portfolio :

Stock R(wR) = 11% = 0.11

Stock S(wS) = 56% = 0.56

Stock T(wT) = 1 - (Stock R + Stock S)

BETA value:

Stock R(bR) = 0.84

Stock S(bS) = 1.39

Portfolio Beta(Pb) = 1.47

Stock T(bT) =?

Portfolio Beta(Pb) is calculated using the formula :

Pb = WeightA×BetaA + WeightB×BetaB +.... WeightN×BetaN

Stock T = 1 - (0.11 + 0.56)

Stock T(wT) = 1 - 0.67 = 0.33

For this question, portfolio Beta =

Pb = (wR × bR) + (wS × bS) + (wT × bT)

1.47 = (0.11 × 0.84) + (0.56 × 1.39) + (0.33 × bT)

1.47 = 0.0924 + 0.7784 + (0.33 × bT)

1.47 = 0.8708 + (0.33 × bT)

1.47 - 0.8708 = 0.33 × bT

0.5992 = 0.33 × bT

bT = 1.8157

bT = 1.82

Answer 2

The beta of stock T is 1.82

Step-by-step explanation:

The portfolio beta is made up of the weighted average of the individual stock betas in the portfolio.

The formula for portfolio beta is,

Portfolio beta = wA * beta of A + wB * beta of B + ... + wX * beta of X

The weight of stock T in the portfolio is = 1 - (0.11 + 0.56) = 0.33 or 33%

Let beta of Stock T be x. The beta of Stock T is:

1.47 = 0.11 * 0.84 + 0.56 * 1.39 + 0.33 * x

1.47 = 0.0924 + 0.7784 + 0.33x

1.47 - 0.0924 - 0.7784 = 0.33x

0.5992 / 0.33 = x

x = 1.815 rounded off to 1.82