Question

1.You are contemplating investing in a portfolio made up of two stocks, A and B. The beta of Stock A is 1.4, and the beta of Stock B is -1.3. Assume you plan to invest X% in Stock A, and the rest of your capital (that is, 1-X) in Stock B. What should X be so that the beta of the resulting portfolio is zero?

2. Consider an amortizing loan. The amount borrowed initially is $89202, the interest rate is 6% APR, and the loan is to be repaid in equal monthly payments over 13 years. As we know, while each monthly payment will be the same, the amounts of interest and principle paid will change from payment to payment. How much of the very first payment is interest?

3. The index model has been estimated for stocks A and B with the following results:

R(A) = 0.02 + 1.1Rm

R(B) = 0.02 + 1.2Rm

Additionally, the standard deviation of the market index is 16%.

What is the covariance between stocks A and B?

Answer #1

1.

Resulting portfolio Beta is Zero

0 = 1.40 × X - 1.30 × (1 - X)

0 = 1.40 × X - 1.30 + 1.30 × X

1.30 = 2.70 × X

X = 48.15%

Value of X is 48.15%.

2.

Monthly payment on loan is calculated in excel and screen shot provided below:

Monthly Payment on loan is $824.87.

Interest on first month payment = $89,202 × 6% / 12

= $446.01

Interest on first payment is $446.01.

A portfolio is made up of Stocks A, B, C, and D in the
proportion of 20%, 30%, 25%, and 25% respectively. The
nondiversifiable risks of the stocks as measured by their betas are
0.4, 1.2, 2.5, and 1.75 for Stock A, B, C, and D respectively. The
expected returns of the stocks are 12%, 24%, 30%, and 28%
respectively. Measure the beta of the portfolio.

Suppose that a portfolio is made up of the following three
stocks:
Stock
Ace Bees Seas
Investment Beta
$ 3,000 0.75 $ 4,500 1.5 $ 7,500 1.4
The expected rate of return on the market is 13% and the
risk-free rate is 7%.
a) Compute the beta of the portfolio.
b) Compute the required rate of return on the portfolio.
c) If the expected return on the portfolio is 18%, would you
invest in it? Why or why not?

7.You have a $1,000 portfolio which is invested in stocks A and
B plus a risk-free asset. $400 is invested in stock A. Stock A has
a beta of 1.3 and stock B has a beta of 0.7. You want a portfolio
beta of 0.9.
a.How much needs to be invested in stock B?
b.How much needs to be invested in the risk-free asset?

You form a portfolio by investing 55% of your money in a risky
stock with a beta of 1.4 and the rest of your money in a risk-free
asset. The risk-free rate and the expected market rate of return
are 0.06 and 0.12, respectively. According to capital asset pricing
model (CAPM), the expected return of the resulting portfolio
is:
A.
10.62%
B.
14.40%
C.
9.78%
D.
9.30%
E.
6.60%

Find the standard deviation of a portfolio made up of 50% Stock
A and 50% Stock B
Stock
Expected Return
Beta
Standard Deviation
Correlation Coefficient ρ A,B
A
12%
1.3
0.26
0.7
B
13%
1.4
0.25
A firm falls on hard times and with no payment of dividends to
both preferred and common shareholders, they later chose to
reinstitute the payment of dividends. Is it true that the firm
cannot pay a dividend to common shareholders without first paying
dividends...

1) Suppose you have $100,000 to invest in a PORTFOLIO OF TWO
stocks: Stock A and Stock B. Your analysis of the two stocks led to
the following risk -return statistics:
Expected Annual Return
Beta
Standard Deviation
A
18%
1.4
25%
B
12%
0.6
16%
The expected return on the market portfolio is 7% and the risk
free rate is 1%. You want to create a portfolio with NO MARKET
RISK.
a) How much (IN DOLLARS) should you invest IN...

You are putting together a portfolio made up of four different
stocks. However, you are considering two possible
weightings:
Portfolio
Weightings
Asset Beta First Portfolio
Second Portfolio
A 2.20 12% 38%
B 0.80 12% 38%
C 0.55 38% 12%
D -1.30 38% 12%
a. What is the beta on each portfolio?
b. Which portfolio is riskier?
c. If the risk-free rate of interest were 3 percent and the
market risk premium were 7 percent, what rate of...

9. You have two stocks in your portfolio, A and B.
??=1,??=1.4,?(??)=10%,?(??)=12%. You notice that there is a third
stock in the market with expected return 13% and beta 1.2. You
should
(a) Sell D (b) Buy D (c) Ignore D (d) None of the above
10. In question 9, what are the weights on A and B in the
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You are trying to develop a strategy for investing in two
different stocks. The anticipated annual return for a $1,000
investment in each stock under four different economic conditions
has the probability distribution shown to the right. Complete
parts (a) through (e) below.
Returns
Probability
Economic Condition
Stock X
Stock Y
0.1
Recession
−40
−170
0.3
Slow growth
20
60
0.4
Moderate growth
90
140
0.2
Fast growth
150
190
a. Whats the expected return for stock X?
b. Whats...

Suppose that the index model for stocks A and B is estimated
from excess returns with the following results:
RA = 4.5% + 1.40RM +
eA
RB = –2.2% + 1.70RM +
eB
σM = 24%;
R-squareA = 0.30;
R-squareB = 0.20
Assume you create a portfolio Q, with investment
proportions of 0.50 in a risky portfolio P, 0.30 in the
market index, and 0.20 in T-bill. Portfolio P is composed
of 60% Stock A and 40% Stock B.
a....

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