in order to fund her retirement, Glenda requires a portfolio with an expected re

Question

in order to fund her retirement, Glenda requires a portfolio with an expected return of 12 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 1 and 2 have expected returns of 9 percent and 10 percent per year, respectively, then what is the minimum expected annual return for Stock 3 that will enable Glenda to achieve her investment requirement cna you use the fromula that have given you. I have the answers I did a chart in excel not goning to work. but It has to be in this formula. plese help me thank you.

Return 1

Stock 1

25%         

9%

Stock 2

50%

10%

Stock 3

25%

X%

12%

E(Rportfolio) = 12%

Required to find: E(R3)

E(Rportfolio) = x1 x E(R1) + x2 x E(R2) + x3 x E(R3)

E(R3) = [E(Rportfolio) – (x1 x E(R1)) – (x2 x E(R2))] ÷ x3

Return 1

Retur2

Stock 1

25%         

9%

Stock 2

50%

10%

Stock 3

25%

X%

12%

E(Rportfolio) = 12%

Required to find: E(R3)

E(Rportfolio) = x1 x E(R1) + x2 x E(R2) + x3 x E(R3)

E(R3) = [E(Rportfolio) – (x1 x E(R1)) – (x2 x E(R2))] ÷ x3

Explanation / Answer

E(Portfolio) = x1*E(R1) + x2*E(R2) + x3*E(R3); E(R3) = [E(Portfolio) – x1*E(R1)–x2*E(R2)]/x3; x1=0.25 x2=0.5 x3=0.25 x1,x2,x3 are portfolio weights and hence can be written as percentages; Portfolio weights indicate the fraction of the portfolio’s total value held in each asset, i.e. xi=(value held in the ith asset)/(total portfolio value); Also Portfolio weights must sum to one: x1+x2+…+xn = 1; E(Portfolio)=0.12; E(R1)=0.09; E(R2)=0.1; Substituting these, we get E(R3) as 0.19 or 19% expected returns on Stock 3

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