QUESTION 3 Matt has inherited a large sum of money wo and is deciding how much to invest in a low interest savings account with fixed rate of return r f = 0.1 and how much to invest in his friend's new business, which is a risky asset with random rate of return ã given by with prob. 7 = 0.4 with prob. 1 – T = 0.6 S-0.6 0.9 Suppose Matt inherited wo 8000 to invest and has a utility function over final portfolio value v given by u(v) = =20.6. (a) Calculate the optimal amount a* for Matt to invest in the risky asset. (b) Now suppose that wo 20000 instead. Calculate the new optimal investment in the risky asset and compare to your answer in part (a). Is there a shortcut way to quickly determine, based on (a), how much Matt would invest in the risky asset when his wealth is higher?
QUESTION 3 Matt has inherited a large sum of money wo and is deciding how much to invest in a low interest savings account with fixed rate of return r f = 0.1 and how much to invest in his friend's new business, which is a risky asset with random rate of return ã given by with prob. 7 = 0.4 with prob. 1 – T = 0.6 S-0.6 0.9 Suppose Matt inherited wo 8000 to invest and has a utility function over final portfolio value v given by u(v) = =20.6. (a) Calculate the optimal amount a* for Matt to invest in the risky asset. (b) Now suppose that wo 20000 instead. Calculate the new optimal investment in the risky asset and compare to your answer in part (a). Is there a shortcut way to quickly determine, based on (a), how much Matt would invest in the risky asset when his wealth is higher?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:QUESTION 3
Matt has inherited a large sum of money wo and is deciding how much to invest in a low interest savings
account with fixed rate of return rf
0.1 and how much to invest in his friend's new business, which is a
risky asset with random rate of return ã given by
S-0.6 with prob. 7 = 0.4
with prob. 1 – T = 0.6
0.9
Suppose Matt inherited wo
:8000 to invest and has a utility function over final portfolio value v given by
u(v) = v0.6.
(a) Calculate the optimal amount a* for Matt to invest in the risky asset.
(b) Now suppose that wo
20000 instead. Calculate the new optimal investment in the risky asset and
compare to your answer in part (a). Is there a shortcut way to quickly determine, based on (a), how much
Matt would invest in the risky asset when his wealth is higher?
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