Portfolio AB is formed by investing 50% of the funds in each of the assets A and B. A similar (equally weighted) portfolio has also been created from A and C, called AC. Find the rates of return not given for AB and AC. (Partial answers are given below.)   Econ                                                        AB=                             AC= Conditions      Probability                    .50A+.50B                     .50A+.50C Boom                 .30                                  55%                                35%  Normal             .40                                      ?                                    ? Bust                   .30                                 15                                     ?    (For example, the highlighted return of 55% for Portfolio AB under “Boom” is found as follows: .50 x 60% + .50 x 50%.  That is, 50% is invested in A, with A having a return of 60% and the remainder (50%) invested in B, with B having a return of 50%, together they give a return of 55% under Boom.)   Find the expected return and standard deviation of AB and AC. (The formulas are given in 1 above.) Do you see any evidence of risk reduction from the numbers you obtain? If so, what do you think is the underlying reason for it?

Essentials Of Investments
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ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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  1. Portfolio AB is formed by investing 50% of the funds in each of the assets A and B. A similar (equally weighted) portfolio has also been created from A and C, called AC. Find the rates of return not given for AB and AC. (Partial answers are given below.)

 

Econ                                                        AB=                             AC=

Conditions      Probability                    .50A+.50B                     .50A+.50C

Boom                 .30                                  55%                                35% 

Normal             .40                                      ?                                    ?

Bust                   .30                                 15                                     ? 

 

(For example, the highlighted return of 55% for Portfolio AB under “Boom” is found as follows: .50 x 60% + .50 x 50%.  That is, 50% is invested in A, with A having a return of 60% and the remainder (50%) invested in B, with B having a return of 50%, together they give a return of 55% under Boom.)

 

  1. Find the expected return and standard deviation of AB and AC. (The formulas are given in 1 above.) Do you see any evidence of risk reduction from the numbers you obtain? If so, what do you think is the underlying reason for it?
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