Question

Problem 2 [3pts] Suppose portfolios A and B are both well-diversified with the following properties: Portfolio β1 on F1 β2 on F2 Expected return A 0.7 1.1 9.6% B -0.2 0.9 3.4% There are two independent economic factors, F1 and F2. The risk-free rate is 1%. What is the expected return-beta relationship in this economy? (Hint: find risk premium for each factor)

Answer #1

Consider an economy with two factors. You identify three
well-diversified portfolios A, B and C. Their details are:
Portfolio
Expected return
Beta (1st factor)
Beta (2nd factor)
A
28%
0.75
1.8
B
18%
0.25
1.1
C
28%
1.25
1.5
What is the risk-free rate in this economy? Show your
calculations

Suppose that there are two independent economic factors,
F1 and F2. The risk-free
rate is 10%, and all stocks have independent firm-specific
components with a standard deviation of 40%. Portfolios A
and B are both well-diversified with the following
properties:
Portfolio
Beta on F1
Beta on F2
Expected Return
A
1.6
2.0
30
%
B
2.5
–0.20
25
%
What is the expected return-beta relationship in this economy?
Calculate the risk-free rate, rf, and the
factor risk premiums, RP1 and...

Consider the multifactor APT. There are two independent economic
factors, F1 and F2. The
risk-free rate of return is 6%. The following information is
available about two well-diversified portfolios:
Portfolio
ββ on F1
ββ on F2
Expected Return
A
1.0
2.0
19
%
B
2.0
0.0
12
%
Assuming no arbitrage opportunities exist, the risk premium on
the factor F1 portfolio should be

Assume both portfolios A and B are well
diversified, that E(rA) = 14% and
E(rB) = 14.8%. If the economy has only
one factor, and βA = 1 while
βB = 1.1, what must be the risk-free rate?

a) Assume that the risk-free rate of interest is 4% and the
expected rate of return on the market is 14%. A share of stock
sells for £68 today. It will pay a dividend of £3 per share at the
end of the year. Its beta is 1.2. What do investors expect the
stock to sell for at the end of the year?
b) Suppose that there are two independent economic factors, F1
and F2. The risk-free rate is 6%....

Assume that both portfolios A and B are
well-diversified, that E(rA) = 16%,
and E(rB) = 11%. If the economy has
only one factor, and βA = 1.1, whereas
βB = 0.6, what must be the risk-free rate?
(Do not round intermediate calculations.)
Risk-Free Rate

Assume that both portfolios A and B are well
diversified, that E(rA) = 10%, and
E(rB) = 7%. If the economy has only
one factor, and βA = 1.2, whereas
βB = 0.7, what must be the risk-free rate?
(Do not round intermediate calculations. Round your answer
to two decimal places.)

Suppose there are two independent economic factors, M1 and M2.
The risk-free rate is 5%, and all stocks have independent
firm-specific components with a standard deviation of 52%.
Portfolios A and B are both well diversified. Portfolio Beta on M1
Beta on M2 Expected Return (%) A 1.6 2.5 31 B 2.4 -0.7 12 What is
the expected return–beta relationship in this economy? (Do not
round intermediate calculations. Round your answers to 2 decimal
places.) Expected return–beta relationship E(rP) =...

Suppose there are two independent economic factors,
M1 and M2. The risk-free
rate is 6%, and all stocks have independent firm-specific
components with a standard deviation of 50%. Portfolios A
and B are both well diversified.
Portfolio
Beta on
M1
Beta on
M2
Expected
Return (%)
A
1.6
2.5
40
B
2.4
-0.7
10
What is the expected return–beta relationship in this economy?
(Do not round intermediate calculations. Round your answers
to 2 decimal places.)
Expected return–beta relationship
E(rP) = %...

Suppose there are two independent economic factors,
M1 and M2. The risk-free
rate is 6%, and all stocks have independent firm-specific
components with a standard deviation of 50%. Portfolios A
and B are both well diversified.
Portfolio
Beta on M1
Beta on M2
Expected Return (%)
A
1.6
2.5
40
B
2.4
-0.7
10
What is the expected return–beta relationship in this economy?
(Do not round intermediate calculations. Round your answers
to 2 decimal places.)
Expected return–beta relationship E(rP) =6.00%...

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