What formula would I use to find the expected rate of return and
standard deviation for each investment.

                                            Rate of Return
Scenerio                  Probability        Stocks   Bonds
Recession                    .20              -5%        +14%
Normal economy               .60              +15%      +8
Boom                         .20              +25       +4


I do not expect an answer, rather a formula or explanation as to how
to solve. Thanks.

Hi!!

The formula for the Expected Rate of Return (Er) of each investment is
the summatory over all scenarios of [Scenario probabilty *
Correspondent rate of return]

For example for the stocks you have:

Er = P(recession)*(-5%) + P(normal)*(15%) + P(boom)*25% =
   = 0.20 * (-5) + 0.60 * 15 + 0.20 * 25 =
   = 13%

The investment in stocks has an expected rate of return of 13%.

Using the same formula for the bonds you will get Er = 8.4%

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

To calculate the standard deviation (STD), first we need to find the variance:

Variance = summatory over all scenarios of [Scenario probabilty *
(Correspondent rate of return - Er)^2 ]

For example for the stocks you have:
Variance = 0.20 * (-5-13)^2 + 0.60 * (15-13)^2 + 0.20 * (25-13)^2 =
         = 0.20 * (-18)^2 + 0.60 * (2)^2 + 0.20 * (12)^2 =
         = 0.20 * 324 + 0.60 * 4 + 0.20 * 144 =
         = 64.8 + 2.4 + 28.8 =
         = 96

The STD is simply the square root of the variance:
STD = sqrt(96) = 9.80

For the bonds you will get a STD equal to 3.2%


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

Regards,
livioflores-ga

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Request for Answer Clarification by baseball2-ga on 25 Jul 2005 17:24 PDT

I once again sorry livioflore. I get the first calculation however (I
copied and pasted your note for STD. How did you figure the -13 in the
calculation.

To calculate the standard deviation (STD), first we need to find the variance:

Variance = summatory over all scenarios of [Scenario probabilty *
(Correspondent rate of return - Er)^2 ]

For example for the stocks you have:
Variance = 0.20 * (-5-13)^2 + 0.60 * (15-13)^2 + 0.20 * (25-13)^2 =
         = 0.20 * (-18)^2 + 0.60 * (2)^2 + 0.20 * (12)^2 =
         = 0.20 * 324 + 0.60 * 4 + 0.20 * 144 =
         = 64.8 + 2.4 + 28.8 =
         = 96

The STD is simply the square root of the variance:
STD = sqrt(96) = 9.80

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Request for Answer Clarification by baseball2-ga on 25 Jul 2005 19:36 PDT

Never mind. Once again I figured it out.

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Clarification of Answer by livioflores-ga on 25 Jul 2005 20:01 PDT

Glad to know that!!

Thank you for the good rating.