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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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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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?
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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