Question

Consider a one factor economy where the risk free rate is 5%, and portfolios A and B are well diversified portfolios. Portfolio A has a beta of 0.6 and an expected return of 8%, while Portfolio B has a beta of 0.8 and an expected return of 10%. Is there an arbitrage opportunity in this economy? If yes, how could you exploit it?

Answer #1

For an Arbitrage Opportunity, there should be 2 Portfolios with SAME BETA.

In this case, Beta of A is 0.6 and Beta of B is 0.8

Therefore, By Weight of 1 to Portfolio A will have a Beta of 0.6*1 = 0.6 and Weight of 0.75 to Portfolio B will have a Beta of 0.8*0.75 = 0.6

**Now, we have 2 Portfolios as follows:**

**1)** 1 unit of A, which has an **Expected
Return of 8%** and **Beta of 0.6**

**2)** 0.75 of B, which has an **Expected
Return of 10*0.75 = 7.5%** and **Beta of
0.6**

**Therefore, To make an
Arbitrage Gain, Portfolio (1) should be BOUGHT and Portfolio (2)
should be SOLD. Arbitrage Profit = 8%-7.5% =
0.5%**

Consider a one factor economy where the risk free rate is 5%,
and Portfolios A and B are well diversified portfolios.
Portfolio A has a Beta of 0.6 and an expected return of 8%
Portfolio B has a Beta of 0.8 and an expected return of 10%
Is there an arbitrage opportunity in this economy? If yes, how
could you exploit it?
Please explain the steps

a.) Consider a one-factor economy. Portfolio A has a beta of 1.0
on the factor, and portfolio B has a beta of 2.0 on the factor. The
expected returns on portfolios A and B are 11% and 17%,
respectively. Assume that the risk-free rate is 6%, and that
arbitrage opportunities exist. Suppose you invested $100,000 in the
risk-free asset, $100,000 in portfolio B, and sold short $200,000
of portfolio A. What would be your expected profit from this
strategy?
b.)...

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

A.) Assume that the risk-free rate of interest is 6% and the
expected rate of return on the market is 16%. A stock has an
expected rate of return of 4%. What is its beta?
B.) Assume that both portfolios A and B are well diversified,
that ?(?a ) = 12%, and ?(?b ) = 9%. If the
economy has only one factor, and ? a = 1.2, whereas ? b = 0.8,
what must be the risk-free rate?

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 48%. Portfolios A
and B are both well diversified.
Portfolio
Beta on M1
Beta on M2
Expected Return (%)
A
1.6
2.3
38
B
2.2
-0.6
8
What is the expected return–beta relationship in this economy?
(Do not round intermediate calculations. Round your answers
to 2 decimal places.)

Consider the one-factor APT. Assume that two portfolios, A and
B, are well diversified. The betas of portfolios A and B are 0.5
and 1.5, respectively. The expected returns on portfolios A and B
are 12% and 24%, respectively. Assuming no arbitrage opportunities
exist, what must be the risk-free rate?

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

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 40%. Portfolios A
and B are both well diversified.
Portfolio
Beta on M1
Beta on M2
Expected Return (%)
A
1.8
2.2
30
B
2.1
-0.5
8
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...

What is the required return of the following well-diversified
portfolio if the risk-free rate is 2% and the return on the market
is 9%?
Stock
Amount
Beta
Expected Return
A
$100,000
1.2
10
B
$200,000
0.8
8
C
$100,000
1.4
12

1)Consider the multifactor APT with two factors. The risk
premium on the factor 1 portfolio is 3%. The risk-free rate of
return is 6%. The risk-premium on factor 2 is 7.75%. Suppose that a
security A has an expected return of 18.4%, a beta of 1.4 on factor
1 and a beta of .8 on factor 2. Is there an arbitrage portfolio? If
not, prove it, if yes exhibit it?
2)In the APT model, what is the nonsystematic standard deviation...

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