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?

Stock T has a beta of 1.82

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

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