Question

Security A has a beta of 1.0 and an expected return of 12%. Security B has a beta of 0.75 and an expected return of 11%. The risk-free rate is 6%. Both these two securities are in the same market. Explain the arbitrage opportunity that exists; explain how an investor can take advantage of it. Give specific details about how to form the portfolio, what to buy and what to sell (we assume that the company-specific risk can be neglected). I need a detailed answer for 20 marks.

Answer #1

An arbitrage opportunity is existing between security A and security B, because it is possible to form a Portfolio of security A and risk free assets that has a beta of. 75 and a different expected return than security B.

The investor can use the the differential weight as building a Portfolio by choosing. 75 as weight in security A and.25 of weight in risk free assets.

So then the portfolio will have Expected Rate of Return-

E(rp)=[ [.75×12%]+ [.25×6%]]

=[ 9%+1.5%]

= 10.5%

This expected rate of return of 10.5% is lesser than expected rate of return of security B which is 11%.

There is an arbitrage opportunity existing which could be exploited by buying of security B and financing the purchase of security B by short selling of security A and borrowing the risk-free Asset.

Security A has a beta of 1.0 and an expected return of 12%.
Security B has a beta of 0.75 and an expected return of 11%. The
risk-free rate is 6%. Both these two securities are in the same
market. Explain the arbitrage opportunity that exists; explain how
an investor can take advantage of it. Give specific details about
how to form the portfolio, what to buy and what to sell (we assume
that the company-specific risk can be neglected)....

security
beta
Standard deviation
Expected return
S&P 500
1.0
20%
10%
Risk free security
0
0
4%
Stock d
( )
30%
13%
Stock e
0.8
15%
( )
Stock f
1.2
25%
( )
5) A complete portfolio of $1000 is composed of the risk free
security and a risky portfolio, P, constructed with 2 risky
securities, X and Y. The optimal weights of X and Y are 80% and 20%
respectively. Given the risk free rate of 4%....

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?

23) Portfolio A has a beta of 1.3 and an expected return of 21%.
Portfolio B has a beta of .7 and an expected return of 17%. The
risk-free rate of return is 9%. If a hedge fund manager wants to
take advantage of an arbitrage opportunity, she should take a short
position in portfolio ____ and a long position in portfolio
____.
Multiple Choice
A; B
B; A
B; B
A; A

security
beta
Standard deviation
Expected return
S&P 500
1.0
20%
10%
Risk free security
0
0
4%
Stock d
( )
30%
13%
Stock e
0.8
15%
( )
Stock f
1.2
25%
( )
4) You form a complete portfolio by investing $8000 in S&P
500 and $2000 in the risk free security. Given the information
about S&P 500 and the risk free security on the table, figure
out expected return, standard deviation, and a beta for the
complete...

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wanted to take advantage of an arbitrage opportunity, you should
take a short position in portfolio _________ and a long position in
portfolio _________.

A security with a beta of 1.0 should offer a return
Greater than the return on the market portfolio
Equal to the risk-free interest rate
Equal to the return on the market portfolio
Between the return on the market portfolio and the risk-free
interest rate

Suppose that the S&P 500, with a beta of 1.0, has an
expected return of 11% and T-bills provide a risk-free return of
4%.
a. What would be the expected return and beta
of portfolios constructed from these two assets with weights in the
S&P 500 of (i) 0; (ii) 0.25; (iii) 0.50; (iv) 0.75; (v) 1.0?
(Leave no cells blank - be certain to enter "0" wherever
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(LO12-2)
a. What would be the expected return and beta of portfolios
constructed from these two assets
with weights in the S&P 500 of (i) 0; (ii) .25; (iii) .5; (iv)
.75; (v) 1.0?
b. On the basis of your answer to (a), what is the trade-off
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Suppose that the S&P 500, with a beta of 1.0, has an
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