I need help with question d Q2 (Essential to cover – a, b, c, d)Suppose that the risk-free rate is 3% and that the corresponding optimal risky portfolio has anexpected return of 15% and a standard deviation of 20%. Consider an investor with preferencesrepresented by the utility function U = E(r) – 0.5A0°, where A = 2.(a) What fraction of her wealth should she invest in the risky portfolio?(b) Should she invest more or less fraction of her wealth in the optimal risky portfolio if she ismore risk-averse? Why?(c) Should she invest more or less fraction of her wealth in the optimal risky portfolio if theoptimal risky portfolio offers a higher expected return (but the same standard deviation)? Why?(d) If the risk-free rate is higher, what would you expect the optimal risky portfolio to differ fromthe current one (for 3% risk-free rate) in terms of expected return and standard deviation?(e) Now suppose that the investor faces a higher risk-free rate when borrowing (because you arefacing more borrowing constraints than the government, or people won't allow you to borrow atthe same rate as the government). Specifically, the investor may lend at a risk-free rate of 3% buthas to borrow at a risk-free rate of 5%. Assume for simplicity that the optimal risky portfolio isthe same for either 3% risk-free rate or 5% risk-free rate, i.e., with an expected return of 15% anda standard deviation of 20% (this should not be the case in reality, as you will find out inquestion (d)). What fraction of her wealth should the investor now put in the risky portfolio?Hint: The risk-free rate of 3% will imply a fraction yl of wealth invested in the optimal riskyportfolio. The risk-free rate of 5% will imply another fraction y2 of wealth invested in theoptimal risky portfolio. However, 3% is only available for the investor to lend (so she cannotborrow to invest more than her wealth to invest in the optimal risky portfolio). If she wants toborrow to invest more than her wealth to invest in the optimal risky portfolio, she will have to gowith 5% risk-free rate (but she won't be able to lend at 5% rate).The key here is: you would need to understand what weights in the optimal risky portfolio meanshe will lend, and what weights mean she will borrow.(f) What is the expected return and standard deviation of the portfolio that you found in (e)?

Introduction: The possible return on a risk-free investment is known as the risk-free rate of…

Answered: (d) If the risk-free rate is higher,…

(d) If the risk-free rate is higher, what would you expect the optimal risky portfolio to differ from the current one (for 3% risk-free rate) in terms of expected return and standard deviation?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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I need help with question d

Q2 (Essential to cover – a, b, c, d)
Suppose that the risk-free rate is 3% and that the corresponding optimal risky portfolio has an
expected return of 15% and a standard deviation of 20%. Consider an investor with preferences
represented by the utility function U = E(r) – 0.5A0°, where A = 2.
(a) What fraction of her wealth should she invest in the risky portfolio?
(b) Should she invest more or less fraction of her wealth in the optimal risky portfolio if she is
more risk-averse? Why?
(c) Should she invest more or less fraction of her wealth in the optimal risky portfolio if the
optimal risky portfolio offers a higher expected return (but the same standard deviation)? Why?
(d) If the risk-free rate is higher, what would you expect the optimal risky portfolio to differ from
the current one (for 3% risk-free rate) in terms of expected return and standard deviation?
(e) Now suppose that the investor faces a higher risk-free rate when borrowing (because you are
facing more borrowing constraints than the government, or people won't allow you to borrow at
the same rate as the government). Specifically, the investor may lend at a risk-free rate of 3% but
has to borrow at a risk-free rate of 5%. Assume for simplicity that the optimal risky portfolio is
the same for either 3% risk-free rate or 5% risk-free rate, i.e., with an expected return of 15% and
a standard deviation of 20% (this should not be the case in reality, as you will find out in
question (d)). What fraction of her wealth should the investor now put in the risky portfolio?
Hint: The risk-free rate of 3% will imply a fraction yl of wealth invested in the optimal risky
portfolio. The risk-free rate of 5% will imply another fraction y2 of wealth invested in the
optimal risky portfolio. However, 3% is only available for the investor to lend (so she cannot
borrow to invest more than her wealth to invest in the optimal risky portfolio). If she wants to
borrow to invest more than her wealth to invest in the optimal risky portfolio, she will have to go
with 5% risk-free rate (but she won't be able to lend at 5% rate).
The key here is: you would need to understand what weights in the optimal risky portfolio mean
she will lend, and what weights mean she will borrow.
(f) What is the expected return and standard deviation of the portfolio that you found in (e)?

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