Question

Assume that CAPM holds. You are given the following information about the riskless rate f, stock X and the market portfolio, M:

	E(r)	σ
Riskless Asset (f)	0.05 (5%)	0.00
Stock X	?	0.40
Market Portfolio (M)	0.10	0.20

You are not given the expected return of stock X. The correlation of the returns on stock X and the market portfolio is equal to 0.35. Assume that stock X is part of the market portfolio.

1)

Assume that the beta of stock X is equal to 1.2. What is the firm-specific risk (in standard deviation units) of stock X?

Group of answer choices

32%

45%

25%

18%

40%

2)

You have $1,000 to invest efficiently in some combination of the risk-free asset, stock X, and the market portfolio. You are thinking of investing $400 in the risk free asset. How much should you invest in stock X and the market portfolio if you want to achieve a beta of 0.60 in your portfolio?

Group of answer choices

$300 in market portfolio and $300 in stock X

$280 in market portfolio and $320 in stock X

$0 in market portfolio and $600 in stock X

$500 in market portfolio and $100 in stock X

$600 in market portfolio and $0 in stock X

3)

Imagine that your uncle Bob holds a portfolio that has a standard deviation of 35% and expected return of 10%. If he wants to keep his current level of total risk, what is a plausible increase in expected return that you can promising your uncle?

Group of answer choices

3.75%

5.75%

8.05%

4.6%

1.55%

4)

Assume that the beta of stock X is equal to 1.2. Your friend Tim Tom is not paying attention to the Investments class and decides to invest $300 in market portfolio, $400 in stock X and $300 in the risk free asset. What is the standard deviation of the efficient portfolio that delivers the same expected return?

Group of answer choices

27.2%

20.3%

30.0%

18.8%

15.6%

Answer 1

1.
=sqrt((0.40)^2-(1.2*0.20)^2)
=32.0000%

2.
x*1+(600-x)*1.2+400*0=1000*0.60
=>x=(1000*0.60-600*1.2)/(1-1.2)
=>x=600.00000

$600 in market portfolio and $0 in stock X

3.
=0.35/0.20*0.10+(1-0.35/0.20)*0.05-10%
=3.7500%

4.
=(0.30*0.10+0.40*(0.05+1.2*(0.10-0.05))+0.30*0.05-0.05)/(0.10-0.05)*0.20
=15.6000%