Assume that you manage a risky portfolio with an expected rate of return of 20% and astandard deviation of 46%. The T-bill rate is 5%.A client prefers to invest in your portfolio a proportion (y) that maximizes the expectedreturn on the overall portfolio subject to the constraint that the overall portfolio'sstandard deviation will not exceed 35%a. What is the investment proportion, y? (Do not round intermediate calculations. Enteryour answer as a percentage rounded to two decimal places.)Investment proportion yb. What is the expected raintermediate calculations. Enter your answer as a percentage rounded to twodecimal places.)of return on your client's overall portfolio? (Do not rounRate of return

Question
Asked Oct 1, 2019
Assume that you manage a risky portfolio with an expected rate of return of 20% and a
standard deviation of 46%. The T-bill rate is 5%.
A client prefers to invest in your portfolio a proportion (y) that maximizes the expected
return on the overall portfolio subject to the constraint that the overall portfolio's
standard deviation will not exceed 35%
a. What is the investment proportion, y? (Do not round intermediate calculations. Enter
your answer as a percentage rounded to two decimal places.)
Investment proportion y
b. What is the expected ra
intermediate calculations. Enter your answer as a percentage rounded to two
decimal places.)
of return on your client's overall portfolio? (Do not roun
Rate of return
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Assume that you manage a risky portfolio with an expected rate of return of 20% and a standard deviation of 46%. The T-bill rate is 5%. A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 35% a. What is the investment proportion, y? (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) Investment proportion y b. What is the expected ra intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) of return on your client's overall portfolio? (Do not roun Rate of return

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check_circleExpert Solution
Step 1

a.

Given,

Standard Deviation of Portfolio = 46%

New Standard Deviation of Portfolio = 35%

 

Calculation of Investment Proportion y:

New Standard Deviation of Portfolio
Investment Proportion
Standard Deviation of Portfolio
35%
46%
= 76.09%
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New Standard Deviation of Portfolio Investment Proportion Standard Deviation of Portfolio 35% 46% = 76.09%

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Step 2

b.

Investment Proportion = 76.09%

Expected Rate of Return = 20%

T-Bill Proportion = 23.91%

T-Bill Rate = 5%

 

Calculation of Expected Rate of Return of Client’s Portfolio:

(Investment Proportion x Expected Rate of Return)
Expected Rate of Return of Clients's Portfolio = |
+(T-Bill Proportion x T-Bill Rate)
(76.09%x20%)+(23.91%x 5%)
15.218%+1.1955%
=16.41%
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(Investment Proportion x Expected Rate of Return) Expected Rate of Return of Clients's Portfolio = | +(T-Bill Proportion x T-Bill Rate) (76.09%x20%)+(23.91%x 5%) 15.218%+1.1955% =16.41%

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Step 3

Working Note:

 

Calculation of T-Bill Proport...

T-Bill Proportion =100%- Investment Proportion
=100%-76.09%
= 23.91%
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T-Bill Proportion =100%- Investment Proportion =100%-76.09% = 23.91%

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