Made an investment of $30,000 in the following stocks.
A) $5,000 with a beta of 0.75
B) $10,000 with a beta of 1.10
C) $8,000 with a beta of 1.36
D) $7,000 with a beta of 1.88
The risk-free rate is 4 percent and the expected return on the market
portfolio is 15 percent.  Based on the CAPM, what is the expected
return on the above portfolio?

doogie59 --

Your answer is 16.93%.


Here is how you can reproduce it for yourself.  

Since you know the risk-free rate, the expected market return and the
beta(a) of the assets in your portfolio, you can use the calculator at
this linked site to quickly determine the return on each stock in the
portfolio:

Money Chimp: CAPM Calculator
http://www.moneychimp.com/articles/valuation/capm.htm


Using that calculator, the expected return for each of the stocks in
your posited portfolio are:

A) 11.5%
B) 15%
C) 17.6%
D) 22.8%


To determine the return on the entire portfolio, I first calculated
the amounts in dollars of the expected return on each stock in the
portfolio,  The results of this calculation are as follows:

A) $575
B) $1500
C) $1408
D) $1596


I then added these amounts and calculated the percentage that their
sum ($5079) represents of the value of the entire portfolio ($30,000).
The result of this calculation was 16.93%


Additional Information:

Here, from Forbes Financial Glossary, is the definition of "Expected Return":
 
"Expected return  
The expected return on a risky asset based on a probability
distribution for the possible rates of return. Expected return equals
some risk free rate (generally the prevailing U.S. Treasury note or
bond rate) plus a risk premium (the difference between the historic
market return, based upon a well diversified index such as the S&P 500
and the historic U.S. Treasury bond) multiplied by the assets beta.
The conditional expected return varies through time as a function of
current market information."


Search Strategy:

I found the calculator (and much other information about expected
rates of return) using the following Google search:

expected market return equals beta
://www.google.com/search?num=100&hl=en&lr=&safe=off&c2coff=1&rls=GGLD%2CGGLD%3A2004-01%2CGGLD%3Aen&q=expected+market+return+equals+beta
  

I am confident that this is answer you are seeking.  If anything is
unclear, please ask for clarification before rating the answer.


markj-ga

---

Clarification of Answer by markj-ga on 29 Mar 2005 14:08 PST

doogie59 --

While my methodology was right on, I misread your question and used
the wrong figure as the expected market return in my calculation. 
(Thanks to r0ug2-ga for noticing the (critical typo.  The correct
answer in 18.2% and here is a rewrite of the answer with the corrected
breakdown of the calculations:

Your answer is 18.2%.


Here is how you can reproduce it for yourself.  

Since you know the risk-free rate, the expected market return and the
beta(a) of the assets in your portfolio, you can use the calculator at
this linked site to quickly determine the return on each stock in the
portfolio:

Money Chimp: CAPM Calculator
http://www.moneychimp.com/articles/valuation/capm.htm


Using that calculator, the expected return for each of the stocks in
your posited portfolio are:

A) 12.25%
B) 16.10%
C) 18.96%
D) 24.68%


To determine the return on the entire portfolio, I first calculated
the amounts in dollars of the expected return on each stock in the
portfolio,  The results of this calculation are as follows:

A) $612.50
B) $1610
C) $1516.80
D) $1727.60


I then added these amounts and calculated the percentage that their
sum ($5466.90) represents of the value of the entire portfolio ($30,000).
The result of this calculation was 18.2%


Additional Information:

Here, from Forbes Financial Glossary, is the definition of "Expected Return":
 
"Expected return  
The expected return on a risky asset based on a probability
distribution for the possible rates of return. Expected return equals
some risk free rate (generally the prevailing U.S. Treasury note or
bond rate) plus a risk premium (the difference between the historic
market return, based upon a well diversified index such as the S&P 500
and the historic U.S. Treasury bond) multiplied by the assets beta.
The conditional expected return varies through time as a function of
current market information."


Search Strategy:

I found the calculator (and much other information about expected
rates of return) using the following Google search:

expected market return equals beta
://www.google.com/search?num=100&hl=en&lr=&safe=off&c2coff=1&rls=GGLD%2CGGLD%3A2004-01%2CGGLD%3Aen&q=expected+market+return+equals+beta
  

I am confident that this is answer you are seeking.  If anything is
unclear, please ask for clarification before rating the answer.


markj-ga

The first answer was not correct, but the correct answer came through
very soon after the first response from the same researcher.  I think
that is fantastic!

Damned. Maybe I miss the point but it seams to me that you use '14%'
as the return rate on the benchmark portfolio instead of 15%

4 + (15-4) * 0.75 = 12.25
and
4 + (14-4) *.0.75 = 11.5

Cheers