I need help with another formula.

The data is:
                                     Rate of Return

Scenerio          Probability         Stocks    Bonds
Recession              .20              -5%       -14%
Normal Economy         .60              +15        +8
Boom                   .20               +25        +4


COnsider a protfolio with wieghts of .60 in stocks and .40 in bonds,
what would the rate of return on the porfolio be for each scenerio?
Also what would be the expected rate of return and standard devation
of the portfolio?

Hi!!


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

If we call RP the rate of return on the portfolio, then:

Rp = Weight of Stocks * Stocks rate + Weight of Bonds * Bonds rate 


For example:
-Normal Economy:
Rp = 0.60 * 15% + 0.40 * 8% =
   = 12.2%



What is the expected rate of return and standard deviation of the portfolio?

Expected Return = Weighted sum of the expected returns of each scenario =
                = 0.20*Recession rate + 0.60*Normal rate + 0.20*Boom rate
                

Now recall the formula for the Variance:
Variance = summatory over all scenarios of [Scenario probabilty *
(Correspondent rate of return - Expected return)^2 ]

Now Standard Deviation is easy to find, it is simply the square root
of the variance or sqrt(Variance) .


Note about the statement of the problem: for the recession scenario
the bond rate is -14%, you have posted a question with a very similar
statement with the only difference in this minus sign (+14% for bonds
on recession). Check this sign in order to confirm it, the positive
sign is more in agreement with the reality.


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

Regards,
livioflores-ga