Consider a risky asset with return expressed by Return =0.5 with probability p and Return of...
Consider a risky asset with return expressed by
Return =0.5 with probability p
and Return of 0.05 with probability1−p
It has a utility function U(WT)=ln(WT), where WT is the final value from investing wealth W.
a) Find the Certainty Equivalent of the investment for such
utility as a function of probability p and invested wealth W. How
does it depend on p? Comment on your result.
b) Compute the Certainty Equivalent for a probability p=50%
c) Compute the Risk Premium for a probability p=50%
d) What is the risk premium if p=0? And if p=1? Comment on your
results, and show how the risk premium is a non-monotonic function
of probability p.
e) Find the probability p that maximises the risk premium (for this
it may be useful to know that logb(x)=ln(x)/ln(b)
Homework Answers
As p rises, Probability of good return rises, so CE , (Minimum amount of wealth, which if provided with certainty,providing same EU as that of the gamble,) will rise naturally
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Consider a risky asset with return expressed by
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