MUST HAVE ANSWERS TODAY June 28, 2005 by 4:30 pm pacific time.

ANSWER THE FOLLOWING:
1.  	A portfolio that combines the risk free asset and the market
portfolio has an expected return of 25% and a standard deviation of
4%.  The risk free rate is 5%, and the expected return on the market
portfolio is 20%.  Assume the capital asset pricing model holds.  What
expected rate of return would a security earn if it had a 0.5
correlation with the market portfolio and standard deviation of 2%?

2.  	Johnson paint stock has an expected return of 19% and a beta of
1.7, while Tire stock has an expected return of 14% and a beta of 1.2.
 Assume the capital asset preicing model holds.  What is the expected
return on the market?  What is the risk free rate?

3.  	Suppose you have invested $30,000 in the following four stocks:
Security		Amount Invested		Beta
Stock A		$5,000				0.75
Stock B		$10,000				1.1
Stock C		$8,000				1.36
Stock D		$7,000				1.88

The risk free rate is 4% and the expected return on the market
portfolio is 15%.  Based on the capital asset pricing model, what is
the expected return on the above portfolio?

COMMENT ON THE FOLLOWING:
4.	Suppose the expected return and standard deviations of stocks A and
B are E(R A) = 0.15, and E(R B) = 0.25, ? A = 0.1 and ? B = 0.2
respectively.
a.  	calculate the expected return and standard deviation of a
portfolio that is composed of 40% A and 60%  B when the correlation
between the returns on A and B is 0.5.
b.	calculate the standard deviation of a portfolio that is composed of
40% A and 60% B when the correlation coefficient between the returns
on A and B is -0.5.
c.	how does the correlation between the returns on A and B affect the
standard deviation o the portfolio?

5.	You enter into a forward contract to buy a 10-year, zero-coupon
bond that will be issued in
one year.The face value of the bond is $1,000, and the 1-year and
11-year spot interest rates
are 3 percent per annum and 8 percent per annum, respectively. Both of
these interest rates
are expressed as effective annual yields (EAYs).
a. What is the forward price of your contract?
b. Suppose both the 1-year and 11-year spot rates unexpectedly shift
downward by 2 percent.
What is the price of a forward contract otherwise identical to yours?

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Clarification of Question by ginger8-ga on 28 Jun 2005 14:05 PDT

For questions 4 and 5, the comments need to answer the following questions:
a. 	what financial concept or principle is the problem asking you to solve?
b.	in the context of the problem scenario, what are some business
decisions that a manager would be able to make after solving the
problem?
c.	is there any additional information missing from the problem that
would enhance the decision making process?
d.	without showing mathematical calculations, explain in writing how
you would solve the problem.

SHOW ALL CALCULATIONS FOR QUESTIONS 1, 2, 3

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Request for Question Clarification by livioflores-ga on 28 Jun 2005 14:47 PDT

Hi!!

I have found the answer to the first four questions, but I cannot
answer the last one. If you like you can lower the price accordingly
to this and I will post the answer of the questions 1 to 4.

Note that you can post the question 5 as a separate question to give
another researcher the opportunity to answer it.

Regards.
livioflores-ga

---

Request for Question Clarification by livioflores-ga on 28 Jun 2005 15:16 PDT

You have lowered the price from $120 to $80, this means that you
accept asa complete answer the solution for questions 1 to 4 only?

Hi!!


1.  	A portfolio that combines the risk free asset and the market
portfolio has an expected return of 25% and a standard deviation of
4%.  The risk free rate is 5%, and the expected return on the market
portfolio is 20%.  Assume the capital asset pricing model holds.  What
expected rate of return would a security earn if it had a 0.5
correlation with the market portfolio and standard deviation of 2%?


First, we must calculate the standard deviation of the market
portfolio using the Capital Market Line (CML):
The risk-free rate asset has a return of 5% and a standard deviation
of zero and the portfolio has an expected return of 25% and a standard
deviation of 4%. These two points must lie on the Capital Market Line.

The slope of the Capital Market Line is:

Slope of CML = Increase in Expected Return / Increase in Standard Deviation
             = (0.25? 0.05) / (0.04 - 0)
             = 5

According to the Capital Market Line we have that:
E(ri) = rf + SlopeCML * STDi

where
E(ri) = the expected return on security i
rf = risk-free rate
SlopeCML = slope of the Capital Market Line
STDi = the standard deviation of security i

Since we know the expected return on the market portfolio is 20%, the
risk-free rate is 5%, and the slope of the Capital Market Line is 5,
we can solve for the standard deviation of the market portfolio
(STDm).
E(rm) = rf + SlopeCML * STDm  ==>
==> 0.20 = 0.05 + 5 * STDm  ==>
==> STDm = (0.20 ? 0.05) / 5 = 0.03  or 3%

Now we can use the found STDm to find the beta of a security that has
a correlation with the market portfolio of 0.5 and a standard
deviation of 2%.

Beta of security = [Correlation * STD of Security)] / STDm
		= (0.5 * 0.02) / 0.03
		= 0.3333

According to the CAPM we have that:

E(r) = rf + Beta_s * [E(rm) - rf]

where 
E(r) = expected return on the security
rf = risk-free rate
Beta_s = beta of the security
E(rm) = expected return on the market portfolio

In this problem we have that:
rf = 0.05
Beta_s = 0.3333
E(rm) = 0.20

E(r) = rf + Beta_s * [E(rm) - rf] =
     = 0.05 + 0.3333 * (0.20 - 0.05) =
     = 0.10  or 10%

The expected rate of return of a security that have a 0.5 correlation
with the market portfolio and standard deviation of 2% is 10% .

------------------------------------------------------

2.  	Johnson paint stock has an expected return of 19% and a beta of
1.7, while Tire stock has an expected return of 14% and a beta of 1.2.
 Assume the capital asset preicing model holds.  What is the expected
return on the market?  What is the risk free rate?

Since the CAPM holds, both securities must lie on the Security Market
Line (SML); then if we call:
SlopeSML = slope of the Security Market Line
E(rJ) = expected return on Johnson Paint?s stock
E(rT) = expected return on Tire?s Stock
Beta_J = beta of Johnson?s stock	
Beta_T = beta of Tire?s stock

we have that:
SlopeSML = [E(rJ) ? E(rT)] / (Beta_J - Beta_T) =
         = (0.19 ? 0.14) / (1.7 ? 1.2) =
         = 0.10

A security with a beta of 1.7 has an expected return of 0.19. Moving
along the SML from a beta of 1.7 to a beta of 1.0, beta decreases by
0.7 (= 1.7 ? 1.0). Since SlopeSML = 0.10, as beta decreases by 0.7,
expected return decreases by 0.07 (= 0.7 * 0.10). Then, the expected
return on a security with a beta of 1.0 equals 12% (= 0.19 - 0.07).
Since the market portfolio has a beta of one, the expected return on
the market portfolio is 12%.


According to the CAPM we have that:

E(r) = rf + Beta_s * [E(rm) - rf]

where 
E(r) = expected return on the security
rf = risk-free rate
Beta_s = beta of the security
E(rm) = expected return on the market portfolio

In this problem we have that:
E(r) = 0.19
rf = unknown
Beta_s = 1.7
E(rm) = 0.12

0.19 = rf + 1.7 * [0.12 - rf] ==> (solving for rf)
==> rf = [0.19 - (1.7 * 0.12)] / (-0.7) =
       = 0.02  or 2%

The risk-free rate is 2%.

------------------------------------------------------

3.  	Suppose you have invested $30,000 in the following four stocks:
Security		Amount Invested		Beta
Stock A		$5,000				0.75
Stock B		$10,000				1.1
Stock C		$8,000				1.36
Stock D		$7,000				1.88

The risk free rate is 4% and the expected return on the market
portfolio is 15%.  Based on the capital asset pricing model, what is
the expected return on the above portfolio?


To start we need to find the beta of the portfolio (Beta_p)

Total Invest = $5,000 + $10,000 + $8,000 + $7,000 = $30,000

Weight of Stock A = $5,000 / $30,000 = 1/6
Weight of Stock B = $10,000 / $30,000 = 1/3
Weight of Stock C = $8,000 / $30,000 = 4/15
Weight of Stock D = $7,000 / $30,000 = 7/30

Recall that the beta of a portfolio is the weighted average of the
betas of its individual components:

Beta_p = (1/6)*(0.75) + (1/3)*(1.1) + (4/15)*(1.36) + (7/30)*(1.88) =
       = 1.293

According to the CAPM we have that:

E(r) = rf + Beta_p * [E(rm) - rf]

where 
E(rp) = expected return on the portfolio
rf = risk-free rate
Beta_p = beta of the portfolio
E(rm) = expected return on the market portfolio

In this problem we have that:
rf = 0.04
Beta_p = 1.293
E(rm) = 0.15

E(r) = rf + Beta_s * [E(rm) - rf] =
     = 0.04 + 1.293 * [0.15 - 0.04] =
     = 0.1822  or 18.22%

The expected return on the portfolio is 18.22%.

-------------------------------------------------------

COMMENT ON THE FOLLOWING:
4.	Suppose the expected return and standard deviations of stocks A and
B are E(R A) = 0.15, and E(R B) = 0.25, ? A = 0.1 and ? B = 0.2
respectively.
a.  	calculate the expected return and standard deviation of a
portfolio that is composed of 40% A and 60%  B when the correlation
between the returns on A and B is 0.5.
b.	calculate the standard deviation of a portfolio that is composed of
40% A and 60% B when the correlation coefficient between the returns
on A and B is -0.5.
c.	how does the correlation between the returns on A and B affect the
standard deviation o the portfolio?


a. 	what financial concept or principle is the problem asking you to solve?

We need to use the concepts of weighted average summation/Expected
Return, and the relationship between Correlation, Variance of the
return, and Standard Deviation of the return.


b.	in the context of the problem scenario, what are some business
decisions that a manager would be able to make after solving the
problem?

For example he will try to make a portfolio with a proper correlation
between stocks that make the expected return more predictible, by
lowering the STD.
Also try to find the correct weights of the different stocks to build
a less risky portfolio.


c.	is there any additional information missing from the problem that
would enhance the decision making process?

If possible, historical data could help to stimate correlations
between different stocks, this would help to build a better portfolio.


d.	without showing mathematical calculations, explain in writing how
you would solve the problem.

First we need to use the weighted average summation to get the
expected return on the portfolio:
E(rp)	= (WA)*[E(rA)] + (WB)*[E(rB)]

Then we need to use the Variance formula to get the variance of the portfolio:
Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)2 +
2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(rA, rB)]

Finally to get the STD of the portfolio (STDp) we use:
STDp = sqrt(Variance of the portfolio)

--------------------------------------------------------

I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards.
livioflores-ga

---

Clarification of Answer by livioflores-ga on 28 Jun 2005 16:54 PDT

Note that I posted the answer in the assumption that you have accepted
the "only four questions" deal, I assumed that because you have
lowered the price as I suggested you. due the proximity of the dead
line I did not wait for a clarification.

Sincerely,
livioflores-ga

Hi!!


1.  	A portfolio that combines the risk free asset and the market
portfolio has an expected return of 25% and a standard deviation of
4%.  The risk free rate is 5%, and the expected return on the market
portfolio is 20%.  Assume the capital asset pricing model holds.  What
expected rate of return would a security earn if it had a 0.5
correlation with the market portfolio and standard deviation of 2%?


First, we must calculate the standard deviation of the market
portfolio using the Capital Market Line (CML):
The risk-free rate asset has a return of 5% and a standard deviation
of zero and the portfolio has an expected return of 25% and a standard
deviation of 4%. These two points must lie on the Capital Market Line.

The slope of the Capital Market Line is:

Slope of CML = Increase in Expected Return / Increase in Standard Deviation
             = (0.25? 0.05) / (0.04 - 0)
             = 5

According to the Capital Market Line we have that:
E(ri) = rf + SlopeCML * STDi

where
E(ri) = the expected return on security i
rf = risk-free rate
SlopeCML = slope of the Capital Market Line
STDi = the standard deviation of security i

Since we know the expected return on the market portfolio is 20%, the
risk-free rate is 5%, and the slope of the Capital Market Line is 5,
we can solve for the standard deviation of the market portfolio
(STDm).
E(rm) = rf + SlopeCML * STDm  ==>
==> 0.20 = 0.05 + 5 * STDm  ==>
==> STDm = (0.20 ? 0.05) / 5 = 0.03  or 3%

Now we can use the found STDm to find the beta of a security that has
a correlation with the market portfolio of 0.5 and a standard
deviation of 2%.

Beta of security = [Correlation * STD of Security)] / STDm
		= (0.5 * 0.02) / 0.03
		= 0.3333

According to the CAPM we have that:

E(r) = rf + Beta_s * [E(rm) - rf]

where 
E(r) = expected return on the security
rf = risk-free rate
Beta_s = beta of the security
E(rm) = expected return on the market portfolio

In this problem we have that:
rf = 0.05
Beta_s = 0.3333
E(rm) = 0.20

E(r) = rf + Beta_s * [E(rm) - rf] =
     = 0.05 + 0.3333 * (0.20 - 0.05) =
     = 0.10  or 10%

The expected rate of return of a security that have a 0.5 correlation
with the market portfolio and standard deviation of 2% is 10% .

------------------------------------------------------

2.  	Johnson paint stock has an expected return of 19% and a beta of
1.7, while Tire stock has an expected return of 14% and a beta of 1.2.
 Assume the capital asset preicing model holds.  What is the expected
return on the market?  What is the risk free rate?

Since the CAPM holds, both securities must lie on the Security Market
Line (SML); then if we call:
SlopeSML = slope of the Security Market Line
E(rJ) = expected return on Johnson Paint?s stock
E(rT) = expected return on Tire?s Stock
Beta_J = beta of Johnson?s stock	
Beta_T = beta of Tire?s stock

we have that:
SlopeSML = [E(rJ) ? E(rT)] / (Beta_J - Beta_T) =
         = (0.19 ? 0.14) / (1.7 ? 1.2) =
         = 0.10

A security with a beta of 1.7 has an expected return of 0.19. Moving
along the SML from a beta of 1.7 to a beta of 1.0, beta decreases by
0.7 (= 1.7 ? 1.0). Since SlopeSML = 0.10, as beta decreases by 0.7,
expected return decreases by 0.07 (= 0.7 * 0.10). Then, the expected
return on a security with a beta of 1.0 equals 12% (= 0.19 - 0.07).
Since the market portfolio has a beta of one, the expected return on
the market portfolio is 12%.


According to the CAPM we have that:

E(r) = rf + Beta_s * [E(rm) - rf]

where 
E(r) = expected return on the security
rf = risk-free rate
Beta_s = beta of the security
E(rm) = expected return on the market portfolio

In this problem we have that:
E(r) = 0.19
rf = unknown
Beta_s = 1.7
E(rm) = 0.12

0.19 = rf + 1.7 * [0.12 - rf] ==> (solving for rf)
==> rf = [0.19 - (1.7 * 0.12)] / (-0.7) =
       = 0.02  or 2%

The risk-free rate is 2%.

------------------------------------------------------

3.  	Suppose you have invested $30,000 in the following four stocks:
Security		Amount Invested		Beta
Stock A		$5,000				0.75
Stock B		$10,000				1.1
Stock C		$8,000				1.36
Stock D		$7,000				1.88

The risk free rate is 4% and the expected return on the market
portfolio is 15%.  Based on the capital asset pricing model, what is
the expected return on the above portfolio?


To start we need to find the beta of the portfolio (Beta_p)

Total Invest = $5,000 + $10,000 + $8,000 + $7,000 = $30,000

Weight of Stock A = $5,000 / $30,000 = 1/6
Weight of Stock B = $10,000 / $30,000 = 1/3
Weight of Stock C = $8,000 / $30,000 = 4/15
Weight of Stock D = $7,000 / $30,000 = 7/30

Recall that the beta of a portfolio is the weighted average of the
betas of its individual components:

Beta_p = (1/6)*(0.75) + (1/3)*(1.1) + (4/15)*(1.36) + (7/30)*(1.88) =
       = 1.293

According to the CAPM we have that:

E(r) = rf + Beta_p * [E(rm) - rf]

where 
E(rp) = expected return on the portfolio
rf = risk-free rate
Beta_p = beta of the portfolio
E(rm) = expected return on the market portfolio

In this problem we have that:
rf = 0.04
Beta_p = 1.293
E(rm) = 0.15

E(r) = rf + Beta_s * [E(rm) - rf] =
     = 0.04 + 1.293 * [0.15 - 0.04] =
     = 0.1822  or 18.22%

I've done this equation several times and come up with .0147 or 1.47%