1. You own a stock portfolio invested 15 percent in Stock Q, 20 percent in Stock
ID: 2715604 • Letter: 1
Question
1. You own a stock portfolio invested 15 percent in Stock Q, 20 percent in Stock R, 35 percent in Stock S, and 30 percent in Stock T. The betas for these four stocks are 1.1, 0.8, 1.2, and 0.9, respectively. What is the portfolio beta? (Round your answer to 3 decimal places.)
2. You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.95, and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio? (Round your answer to 2 decimal places.)
Beta
3. A share of stock sells for $38 today. The beta of the stock is 1, and the expected return on the market is 17 percent. The stock is expected to pay a dividend of $1.10 in one year. If the risk-free rate is 3.7 percent, what should the share price be in one year? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Share price
$
4. A stock has a beta of 0.7 and an expected return of 9 percent. A risk-free asset currently earns 4 percent.
a.
What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Expected return
%
b.
If a portfolio of the two assets has a beta of 0.6, what are the portfolio weights?(Round your answers to 2 decimal places. Omit the "%" sign in your response.)
Weight
xS
%
xrf
%
c.
If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Round your answer to 2 decimal places.)
Beta
d.
If a portfolio of the two assets has a beta of 2.80, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Omit the "%" sign in your response.)
Weight
xS
%
xrf
%
5. Asset W has an expected return of 8 percent and a beta of 2. If the risk-free rate is 5.5 percent, what is the market risk premium? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Market risk premium
%
6. Stock Y has a beta of 1.5 and an expected return of 12 percent. Stock Z has a beta of 0.8 and an expected return of 8 percent. What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Risk-free rate
%
PLEASE SHOWING WORKING!!!
2. You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.95, and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio? (Round your answer to 2 decimal places.)
Explanation / Answer
ANSWER 1
PORTFOLIO BETA => 1.015
ANSWER 2
I believe that the Beta of a portfolio is a weighted average of the betas of the stocks it comprises. Since the portflio is equally weighted with three components, each component gets a weighting of 33.33%.
The risk free asset has no correlation to the market portfolio and therefor is given a beta of 0. The formula used to determine the Beta of the remaining stock is thus:
Portfolio Beta = (weight asset 1 * Beta 1) + (weight asset 2 * Beta 2) + (weight risk free asset * Beta risk free asset).
Note that the third term in the equation (weight risk free asset * Beta risk free asset) is equal to zero because the Beta of the risk free asset is 0.
Also, probably the most important point is that the market has a Beta of 1 (Always!), so a portfolio equally as risky as the market will have a Beta of 1 also.
Thus, building on the formula I gave above:
1 = (0.3333 * B1) + (0.3333 * 1.95) + 0, breaks down to:
1 - 0.6499 = 0.3333B1,
B1 = 1.05
ANSWER 3
CAPM => 3.7 + (17-3.7) *1
=> 17%
ANSWER 4
a) the expected return on a portfolio that is equally invested in the two assets => 0.5 * 9% +0.5*4% => 6.5%
b) weight of a stock => 0.6/0.7=> 0.8571 ie 85.71%
weight of a risk free asset => 100-85.71 => 14.29%
c)
Risk premium of beta we know => (9-4) /0.7 => 7.14%
now beta =>
8% = 4% + (7.14)*b
beta => 0.5602
d)
2.80 = 0.7(weight stock "X") + 0 (1- weight of stock), reduces to:
2.80 = 0.7X
X= 4 <weight of stock...= 400%, means "weight" of RFR is: 1 - 4 = (3.00) or NEGATIVE 3.00%...(this essentially means you have borrowed at the risk free rate, perhaps to help finance the purchase of the stock in the portfolio - i.e. a leveraged portfolio)
ANSWER 5
8% => 5.5% + (RM - 5.5% ) 2
RM => 6.75
RISK PREIMUM => 6.75 -5.5 => 1.25%
answer 6
12% = rf + 1.5(rm - rf)
8% = rf + 0.8 (rm - rf)
=>
12 = -0.5rf + 1.5rm
8 = -0.2rf + 1.2 rm
by solving both equations => rf = 8%
risk free rate = 8%
STOCKS WEIGHT BETA PORTFOLIO BETA Q 0.15 1.1 0.165 R 0.20 0.8 0.16 S 0.35 1.2 0.42 T 0.30 0.9 0.27 TOTAL 1.015Related Questions
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