qn. you are considering investing $1000 in a complete portfolio. the complete po
ID: 2728672 • Letter: Q
Question
qn. you are considering investing $1000 in a complete portfolio. the complete portfolio is composed of treasury notes that pay 5% and a risky poryfolio, P, constructed with two risky securities X and Y.
The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 10%.
required,
1. assume that you wish to obtain an expected return of11% from your complete portfolio, calculate the investment proportions of your overall portfolio .
2. What would your investment proportions of your complete portfolio if your expected return from the complete portfolio is 60%?
Explanation / Answer
Return of portfolio is the weighted average return of all the securities in the portfolio.
Return of portfolio P = 0.60 * 14 + 0.40 * 10 = 12.40 %
Q .1 ) Equation for Return of complete portfolio consisting of Treasury notes and risky porfolio P consisting of X & Y Stock when the return of complete portfolio is 11 % as given in question:-
Let A denotes investment portion of Treasury notes and (1 - A) denotes to risky porfolio P.
11 = A * 5 + 12.40 * ( 1 - A)
11 = 5A + 12.40 - 12.40A
7.4A = 1.4
A = 1.4 / 7.4 = 0.189 (Treasury notes)
1 - A = 1 - 0.189 = 0.811 (Risky portfolio P)
Conclusion:- The investment proportion of Treasury notes = 0.189 and of risky portfolio P = 0.811
Q . 2) Equation for Return of complete portfolio consisting of Treasury notes and risky porfolio P consisting of X & Y Stock when the return of complete portfolio is 60 % as given in question:-
Let A denotes investment portion of Treasury notes and (1 - A) denotes to risky porfolio P.
60 = A * 5 + 12.40 * ( 1 - A)
60 = 5A + 12.40 - 12.40A
(-) 7.4A = 47.60
A = (-) 47.60 / 7.4 = (-) 6.4324 (Treasury notes) [ Negative reflects amount to be borrowed.]
1 - A = 1 - (-) 6.4324 = 1 + 6.4324 = 7.4324 (Risky portfolio P)
Conclusion:- The investment proportion of Treasury notes = (-) 6.4324 i.e., reflecting amount to be borrowed and of risky portfolio P = 7.4324.
Verification:- = 5 * (-) 6.4324 + 12.40 * 7.4324
= (-) 32.162 + 92.162 (approx)
= 60 % (approx)
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