Question

Q4

1.With a risk-free rate of 2.4% and a market risk-premium of 8.6%, a stock's expected rate of return is 10.7%. The following year, the market-risk premium decreases by 1% but the stock's beta and the risk-free rate remain the same. What will be the expected rate of return on the stock for that year? Answer as a percent return to the nearest hundredth of a percent as in xx.xx without entering a percent symbol.  For negative returns include a negative sign.

2.In your two-stock portfolio, you invest $25 in stock A and $75 in stock B. If the beta of stock A is 0.97 and the beta of stock B is 0.74, your portfolio beta will be: Input your answer two places to the right of the decimal point as in x.xx

Answer 1

1) Risk free rate = 2.4% ; Market Risk premium = 8.6% ; Required rate of return = 10.7%

Firstly we need to calculate beta of the stock, the formula is as follows

required rate return = risk free rate + beta * market risk premium

10.7% = 2.4% + beta * 8.6%

10.7% - 2.4% = beta * 8.6%

beta = 8.3% / 8.6%

beta = 0.965

Now in the folowing year the Market Risk premium falls by 1% , risk free rate & beta remain same

So the expected rate of return comes out to be

= risk free rate + beta * market risk premium

= 2.4% + 0.965 * 7.6%

= 2.4% + 7.33%

= 9.73 %

So, the required rate of return comes out to be 9.73.

2) Investment in Stock A = $ 25 ; Investment in Stock B = $ 75

Beta of Stock A = 0.97 ; Beta of Stock B = 0.74

Total Investment = $ 100

Weightage of A = Investment in A / Total Investment

= 25 / 100 = 25%

Weightage of B = Investment in B / Total Investment

= 75 / 100 = 75%

Beta of Portfolio = Weighted Beta of Stock A + Weighted Beta of Stock B

Weighted Beta of Stock A = Beta of Stock * Weightage of Stock

= 0.97 * 25%

= 0.2424

Weighted Beta of Stock B = Beta of Stock * Weightage of Stock

= 0.74 * 75%

= 0.555

Beta of Portfolio = 0.2424 + 0.555

= 0.797 or 0.80

So beta of the portfolio is 0.80.

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