Question

Stock prices are determined by a 2 factor APT model. You have 3 investments available to you:

Portfolio | Expected Excess Return | Beta 1 | Beta 2 |

A | 4.9% | 1 | 0 |

B | 4.0% | 0 | 1 |

C | 4.9% | 0.5 | 0.5 |

What would the expected excess return be on an arbitrage portfolio, given this information?

Answer #1

**For an Arbitrage opportunity, Betas of 2 portfolios
should be same.**

Beta of Portfolio C is 0.5 & 0.5, whereas Beta of Portfolio A & B are 1 & 0 and 0 & 1 respectively.

If we make an Portfolio with 50% in A and 50% in B, then Beta of that combined Portfolio will become 0.5 & 0.5 i.e. same as Portfolio C.

Expected Return of above portfolio i.e. combination of A
& B = Sum of [Weight*Return] = [0.5*4.9] + [0.5*4] =
**4.45****%**

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

**1)** A+B, which has an **Expected Return of
4.45%** and **Beta of 0.5 & 0.5**

**2)** C, which has an **Expected Return of
4.9%** and **Beta of 0.5 & 0.5**

**Therefore, To make an Arbitrage Gain, Portfolio (1)
should be Sold and Portfolio (2) should be Bought.**

**Expected Excess Return =** 4.9%-4.45% **=
0.45%**

Consider the single factor APT. Portfolio A has a beta of 0.5
and an expected return of 12%. Portfolio B has a beta of 0.4 and an
expected return of 13%. The risk-free rate of return is 5%. If you
wanted to take advantage of an arbitrage opportunity, you should
take a short position in portfolio _________ and a long position in
portfolio _________.

We have two economic factors F1 and F2 in
a two-factor APT model. We have the following data on three
well-diversified portfolios.
Stock
Expected return
bi1
bi2
A
7%
2
-1
B
17%
1
2
C
12%
1
?
If the risk free rate is 2%, what is stock C's bi2 so
that there is no arbitrage opportunity in the market?
Group of answer choices
0.5
-1
2
1

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...

Consider the following multifactor (APT) model of security
returns for a particular stock. Factor Factor Beta Factor Risk
Premium Inflation 1.1 9 % Industrial production 0.7 11 Oil prices
0.3 7 a. If T-bills currently offer a 6% yield, find the expected
rate of return on this stock if the market views the stock as
fairly priced. (Do not round intermediate calculations. Round your
answer to 1 decimal place.) b. Suppose that the market expects the
values for the three...

Consider the single factor APT. Portfolio A has a beta of 0.55
and an expected return of 11%. Portfolio B has a beta of 0.90 and
an expected return of 16%. The risk-free rate of return is 3%. Is
there an arbitrage opportunity? If so, how would you take advantage
of it?

Assume that you are in the two-factor exact APT world. There are
two portfolios (portfolio 1 and portfolio 2) which have loadings on
the two factors as follows:
Loadings
factor 1
factor 2
portfolio 1
1.5
0.55
portfolio 2
1.41
-1.1
The expected return on portfolio 1 is 8.04% and the expected
return on portfolio 2 is 14.09%. The risk-free rate is 2.1%.
There is a new portfolio just formed (portfolio 3). It has
loadings of 3 and 1.5 on...

In an APT world, there may be multiple factors. Suppose there
are two - industrial production and balance of payments. The
expected excess return on these factors are 0.1 and 0.05 and the
riskless rate is 0.05. The betas for the first stock are 2 and 0.5
and for the second stock they are 1 and 3 respectively.
Find the expected return on the stocks if the APT is true.
Find a portfolio with a zero beta on industrial production....

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.)...

There are two assets following single-factor model, Asset 1 and
Asset 2. Their model parameters are given as follow,
Asset αi βi
1 0.10 1.5
2 0.08 0.5
Assume E[f]=e1=e2=0.
a) Construct a zero-beta portfolio from these two risky
assets.
b) Find the factor risk premium λ using the principle of
no-arbitrage.
c) What is the meaning of factor risk premium in single-factor
models?

Suppose stock returns can be explained by the following
three-factor model:
Ri = RF +
β1F1 + β2F2 −
β3F3
Assume there is no firm-specific risk. The information for each
stock is presented here:
β1
β2
β3
Stock A
1.11
.43
.06
Stock B
.73
1.28
−.18
Stock C
.64
−.10
1.17
The risk premiums for the factors are 5.9 percent, 5.6 percent,
and 6.3 percent, respectively. You create a portfolio with 20
percent invested in Stock...

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