Suppose you have $1000 to invest in two assets. The first is a risk-free bond that will return 5 percent with probability 1, i.e. you will will have 1.05× the amount you invest. The second is a hot new startup that will will return 20 percent with probability 1 2 , and will go bankrupt (i.e. you will lose your entire investment) with probability 1 2 . If your utility of wealth function is U(W) = ? W, how much should you invest in the bond, and how much should you invest in the startup?
Suppose you have $1000
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