Any help solving the following problem is appreciated.  Any websites,
formulas, etc. to help explain calculations needed to solve problem is
helpful.


Use the data below and consider portfolio weights of .60 in stocks and
.40 in bonds.

		Rate of Return	
Scenario	Probability	Stocks	Bonds
Recession	0.2	           -5%	  14%
Normal	        0.6                15%     8% 
Boom	        0.2	           25%	   4%
			
Calculate the rates of return for each scenario and the expected
return on the portfolio.

			Weights
Stocks			  0.6
Bonds			  0.4

a. What is the rate of return on the portfolio in each scenario?

Racession
Normal
Boom

b. What is the expected return and standard deviation of the
portfolio?

Expected return
Variance
Standard Deviation

c. Would you prefer to invest in the porfolio of stocks only or in
bonds only?

Stocks:  	Expected Return: 13.00% and Standard Deviation 9.8
Bonds    	Expected Return:  8.40% and Standard Deviation 3.2
Portfolio: 	Expected Return: 10.24% and Standard Deviation 4.6

Hello again boobee,

First, the answers to your questions:

A.  Recession 2.6%; Normal 12.2%; Boom 16.6%

B. Expected return 11.16%; Variance 20.30; Standard Deviation 4.51

C. Given the expected returns and standard deviations, investing in
all stocks would lead to the highest overall rate of return in the
long run, but requires taking on the most risk in the short term. 
Investing in all bonds leads to a lower rate of return the long run,
but requires much less risk in the short term.  The portfolio
demonstrates the principal that buying multiple types of securities
rather than just one reduces the variability of the return on
investment.  By buying a mixture of both stocks and bonds, the
investor captures a significantly higher rate of return than the
bonds-only portfolio while taking on significantly less risk than the
stocks-only portfolio.  Assuming the investments are not perfectly
correlated, diversification reduces risk.  Which mixture of asset
types an individual would prefer to invest in depends on the rate of
return they need and how much risk they are comfortable with.

Now, the formulas used:

To calculate the rates of return for Questions A. and B., I used the
formula mu(x)=x1p1 + x2p2 + x3p3 where xn are the rates of return for
each asset class and pn are the weights in Question A. (obviously,
there is no x3 and p3 in Question A.), and xn are the scenario rates
of return from Question A. and pn are the scenario probabilities in
Question B.

To calculate the variance, I used the formula Sigma^2
(x)=[x1-mu(x)]^2p1+[x2-mu(x)]^2p2+[x3-mu(x)^2p3 where mu(x) is the
expected return calculated for the first part of Question B., xn are
the scenario rates of return, and pn are the scenario probabilities.

The standard deviation is calculated by taking the square root of the
variance.

I couldn't identify an equation that is necessary to answer Question
C., so I provided relevant information so that you can identify your
investment preference and support it.  Are you sure the question isn't
asking you whether you would prefer to invest in the portfolio, in
stocks only, or in bonds only?  It reads a little strange as posted.

I hope you find the above material helpful.

Sincerely,

Wonko

Thanks again.....