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Assume the market risk is 8% and risk-free rate is 2%. You have a portfolio with...

Assume the market risk is 8% and risk-free rate is 2%. You have a portfolio with $15,000 invested in Stock A with a beta of 1.2, $8,000 in Stock B with a beta of 1.8, and $12,000 in Stock C with a beta of 2.0. What is the beta and expected return of the portfolio?

Solutions

Expert Solution

Given about a portfolio,

Investment in stock A = $15000

Beta of stock A, Ba = 1.2

Investment in stock B = $8000

Beta of stock B, Bb = 1.8

Investment in stock C = $12000

Beta of stock C, Bc = 2.0

Total investment is (Investment in stock A + Investment in stock B + Investment in stock C)

=> total investment = 15000 + 8000 + 12000 = $35000

Weight in stock A, Wa = investment in stock A/total investment = 15000/35000 = 0.4286 or 42.86%

Weight in stock C, Wb = investment in stock B/total investment = 8000/35000 = 0.2286 or 22.86%

Weight in stock C, Wc = investment in stock C/total investment = 12000/35000 = 0.3428 or 34.28%

So, beta of portfolio is weighted average beta of stock = Wa*Ba + Wb*Bb + Wc*Bc

=> Beta of portfolio = 0.4286*1.2 + 0.2286*1.8 + 0.3428*2 = 1.61

So, Beta of portfolio is 1.61

Risk free rate Rf = 2%

Market risk premium MRP = 8%

So, expected return on stock using CAPM = Rf + beta*MRP

=> Expected return of the portfolio = 2 + 1.61*8 = 14.89%

jeff jeffy answered 2 years ago
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