Assume that you hold a diversified $90,000 portfolio with a beta of 1.20, and th

Question

Assume that you hold a diversified $90,000 portfolio with a beta of 1.20, and that you are in the process of buying 1,000 shares of a high-tech stock at $10 a share with a beta of 1.70, and adding it to this portfolio. Also assume that risk-free rate is 2%, and that the expected rate of return co the market is 8.6%. Based on the CAPM, what would be the expected rate of return for your portfolio after the purchase of this stock? Your answer should be between 7.45 and 16.30, rounded to 2 decimal places, with no special characters

Explanation / Answer

Beta of a portfolio is the weighted average of the betas of the stocks of the portfolio. This is calculated in the following table

So, as per the above calculations, portfolio beta is 1.25

Now, as per capital asset pricing model,

Re = Rf + (Rm – Rf) x Beta

Where,

Re = Expected return

Rf = Risk – free rate of return = 2%

Rm = Expected return on market = 8.6%

Beta = Beta of the portfolio = 1.25

So, Re = 2 + (8.6 – 2) x 1.25

= 2 + 8.25

= 10.25%

Calculations A B = A / 100,000 C D = B x C Stock Investment Weight Beta Weighted average beta A            90,000 0.9 1.2 1.08 B            10,000 0.1 1.7 0.17 Total          100,000 Total 1.25

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