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{"sheet":"A,B,C","index":0,"n_rows":28,"n_cols":9,"rows_kept":28,"cut":false,"hidden":false,"merged":[[0,1,0,8]]}
[null,"Juggling a Portfolio"]
[]
[null,"Shares in companies A, B, and C have expected rates of return over the next"]
[null,"year of 10%, 11%, and 15%, respectively. One standard-deviation’s-worth of"]
[null,"uncertainty in what each stock will return is 6%, 8%, and 10%. The returns on"]
[null,"the stocks vary independently."]
[]
[null,"What is the expected value and standard deviation of the rate of return (over"]
[null,"the next year) on a portfolio consisting of equal dollar amounts invested in all"]
[null,"three stocks?"]
[]
[null,null,null,"A","B","C"]
[null,null,"E[ROR]",0.1,0.11,0.15]
[null,null,"StdDev(ROR)",0.06,0.08,0.1]
[]
[null,null,"allocation",{"$f":"1/3","v":0.33333333333333331},{"$f":"1/3","v":0.33333333333333331},0.33333333333333331,null,{"$f":"SUM(D16:F16)","v":1},{"$f":"showformula(H16)","v":"=SUM(D16:F16)"}]
[]
[]
[null,"E[RORportfolio]",null,{"$f":"SUMPRODUCT(D16:F16,D13:F13)","v":0.12},{"$f":"showformula(D19)","v":"=SUMPRODUCT(D16:F16,D13:F13)"}]
[null,"StdDev(RORportfolio)",null,{"$f":"SQRT(SUMPRODUCT(D16:F16^2,D14:F14^2))","v":4.7140452079103175E-2},{"$f":"showformula(D20)","v":"=SQRT(SUMPRODUCT(D16:F16^2,D14:F14^2))"}]
[]
[null,"Var( a∙RORA + b∙RORB + c∙RORC ) = a2∙Var(RORA) + b2∙Var(RORB) + c2∙Var(RORC)"]
[]
[null,"since the rates of return vary independently."]
[]
[]
[]
[null,"The Solver setup below can be used to find the least-risk portfolio which returns 12%  in expectation."]

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[null,"Juggling Another Portfolio"]
[]
[null,"Shares in companies D and E have expected (annual) rates of return of 10%"]
[null,"and 13%, respectively, and standard deviations of 6% and 10%. The correlation"]
[null,"between their rates of return is 0.4 . What is the expected value and standard"]
[null,"deviation of the rate of return (over the next year) on a portfolio consisting of"]
[null,"a 75% : 25% dollar mix of these two stocks?"]
[]
[null,null,null,"D","E"]
[null,null,"E[ROR]",0.1,0.13]
[null,null,"StdDev(ROR)",0.06,0.1]
[null,null,"correlation",0.4]
[]
[null,null,"allocation",0.75,0.25,{"$f":"showformula(E14)","v":"0.25"}]
[]
[]
[]
[null,"E[RORportfolio]",null,{"$f":"SUMPRODUCT(D14:E14,D10:E10)","v":0.10750000000000001},{"$f":"showformula(D18)","v":"=SUMPRODUCT(D14:E14,D10:E10)"}]
[null,"StdDev(RORportfolio)",null,{"$f":"SQRT(SUMPRODUCT(D14:E14^2,D11:E11^2)+2*D14*E14*D11*E11*D12)","v":5.9581876439064929E-2},"=SQRT(SUMPRODUCT(D14:E14^2,D11:E11^2)+2*D14*E14*D11*E11*D12)"]
[]
[null,"Var( d∙RORD + e∙RORE ) = d2∙Var(RORD) + e2∙Var(RORE) + 2∙de∙Cov(RORD, RORE) ,"]
[null,"and  Cov(RORD, RORE) = StdDev(RORD)∙StdDev(RORE)∙Corr(RORD,RORE) ."]
[]
[null,"Note: If we had three stocks, we'd need to extend our formula for the variance of a sum"]
[null,"of random variables:"]
[]
[null,"Var(X+Y+Z) = Var(X) + Var(Y) + Var(Z) + 2∙Cov(X,Y) +  2∙Cov(X,Z) + 2∙Cov(Y,Z) ."]
[]
[]
[]
[null,"The Solver setup below can be used to find the least-risk portfolio which returns 12%  in expectation."]