Consider an individual who has Dollars to invest in two risky assets. The means and variances of the two rates of return are given by: µ₁ < µ2 and 0² < o². In other words, asset 1 is less risky. Show that the minimum variance his portfolio may achieve is lower than what it would be if he invests all his money in asset 1.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.9P
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25. Consider an individual who has A Dollars to invest in two risky assets. The means
and variances of the two rates of return are given by: µ₁ < µ₂ and 0² < 0². In
other words, asset 1 is less risky. Show that the minimum variance his portfolio
may achieve is lower than what it would be if he invests all his money in asset 1.
26. Consider an individual whose uncertain income is w. Let his utility function and
measure of absolute risk aversion be given by U(w) and Ra(w), respectively. Show
that in order for his measure of absolute risk aversion to be decreasing it must be
the case that
J³U (w)
> 0.
Iw³
Transcribed Image Text:25. Consider an individual who has A Dollars to invest in two risky assets. The means and variances of the two rates of return are given by: µ₁ < µ₂ and 0² < 0². In other words, asset 1 is less risky. Show that the minimum variance his portfolio may achieve is lower than what it would be if he invests all his money in asset 1. 26. Consider an individual whose uncertain income is w. Let his utility function and measure of absolute risk aversion be given by U(w) and Ra(w), respectively. Show that in order for his measure of absolute risk aversion to be decreasing it must be the case that J³U (w) > 0. Iw³
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