1) An individual has $55,000 invested in a stock with a beta of 0.7 and another
ID: 2709655 • Letter: 1
Question
1) An individual has $55,000 invested in a stock with a beta of 0.7 and another $40,000 invested in a stock with a beta of 1.6. If these are the only two investments in her portfolio, what is your portfolio’s beta?
2) Suppose you manage the $4 million fund that consists of four stocks with the following investments:
a) Calculate the Porforlio Beta. Assuming the following market conditions:
Risk Free Rate of Return: 2%
Anticipated Market Return this Year: 15%
b) Under the CAPM model, what is the Required Rate of return for each asset in the portfolio and the portfollio overall
c) Confirm that the weighted average required return for the individual assets is equal to the required portfolio return calculated using the portfolio beta
3) You have the $2 million portfolio consisting of $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.2. You are considering selling $100,000 worth of one stock with a beta of 1.6 and using the proceeds to purchase another stock with a beta of 0.9. What will be the portfolio’s new beta after these transactions?
Stock Investment Beta A $400,000 1.2 B 600,000 -0.2 C 1,000,000 1.4 D 2,000,000 0.9 Total $4,000,000Explanation / Answer
1.
1.08
Portfolio Beta = 1.08
2.(a)
Portfolio beta = 0.89
b. Required rate of return as per CAPM = Riskfree Rate + Portfolio Beta(Expected Market rate-Riskfree Rate)
= 0.02 + 0.89(0.15-0.02)
=13.57%
c.
Required rate of return as per weighted average of individual assets = 13.57% (same as b above)
3.
Therefore, Portfolio's new beta = 1.2-.035 = 1.165
STOCK Beta Percentage of Portfolio Beta times % of Portfolio Stock A 0.7 58% 0.41 Stock B 1.6 42% 0.67 Portfolio Beta1.08
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