58. A retired partner from a large brokerage firm hasone million dollars available to invest in particularstocks or bonds. Each investment’s annual rate ofreturn depends on the state of the economy in thecoming year. The file P09_58.xlsx contains thedistribution of returns for these stocks and bonds asa function of the economy’s state in the coming year.As this file indicates, the returns from stocks andbonds in a fair economy are listed as X and Y. Thisinvestor wants to allocate her one million dollars tomaximize her expected value of the portfolio oneyear from now.a. If X 5 Y 5 15%, find the optimal investment strategy for this investor. (Hint: You could try a decisiontree approach, but it would involve a massive tree.It is much easier to find an algebraic expression forthe expected final value of the investment whena percentage p is put in stocks and the remainingpercentage is put in bonds.)b. For which values of X (where 10% , X , 20%)and Y (where 12.5% , Y , 17.5%), if any, willthis investor prefer to place all of her availablefunds in stocks? Use the same method as in part afor each combination of X and Y.
58. A retired partner from a large brokerage firm has
one million dollars available to invest in particular
stocks or bonds. Each investment’s annual rate of
return depends on the state of the economy in the
coming year. The file P09_58.xlsx contains the
distribution of returns for these stocks and bonds as
a function of the economy’s state in the coming year.
As this file indicates, the returns from stocks and
bonds in a fair economy are listed as X and Y. This
investor wants to allocate her one million dollars to
maximize her expected value of the portfolio one
year from now.
a. If X 5 Y 5 15%, find the optimal investment strategy for this investor. (Hint: You could try a decision
tree approach, but it would involve a massive tree.
It is much easier to find an algebraic expression for
the expected final value of the investment when
a percentage p is put in stocks and the remaining
percentage is put in bonds.)
b. For which values of X (where 10% , X , 20%)
and Y (where 12.5% , Y , 17.5%), if any, will
this investor prefer to place all of her available
funds in stocks? Use the same method as in part a
for each combination of X and Y.
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