Question

# Use a risk-free rate of 3% and a market return of 7%. You have a portfolio...

Use a risk-free rate of 3% and a market return of 7%. You have a portfolio with \$10,000 invested in Stock A with a beta of 0.9, \$20,000 in Stock B with a beta of 1.8, and \$20,000 in Stock C with a beta of 2.0. What is the beta and required return of the portfolio?

Given about a portfolio

Investment in stock A = \$10000

Beta of stock A, Ba = 0.9

Investment in stock B = \$20000

Beta of stock B, Bb = 1.8

Investment in stock C = \$20000

Beta of stock C, Bc = 2.0

So, weight of stock A, Wa = investment in A/(investment in A + B + C) = 10000/(10000 + 20000 + 20000) = 20% or 0.20

Similarly weight of stock B, Wb = investment in B/(investment in A + B + C) = 20000/(10000 + 20000 + 20000) = 40% or 0.40

Similarly weight of stock C, Wc = investment in C/(investment in A + B + C) = 20000/(10000 + 20000 + 20000) = 40% or 0.40

So, beta of portfolio is weighted average beta of its assets

=> Beta of portfolio = Wa*Ba + Wb*Ba + Wc*Bc = 0.2*0.9 + 0.4*1.8 + 0.4*2 = 1.7

required return on portfolio is calculated using CAPM

Required return on portfolio = Rf + beta*(Rm - Rf)

Rf = 3%

Rm = 7%

Required return on portfolio = 3 + 1.7*(7-3) = 9.80%

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