View the step-by-step solution to:

Question

Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r

∼ N(μ,σ^2). Show that the mean-variance utility function is equivalent to the CARA utility u(r) = −e^−Ar (they are representations of the same preferences). Use the fact that if a random variable x is distributed normally with mean μx and variance σ^2 x, then

E[e^ax] = e^aμx+ 1/2^a2 sig,a^2 x

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes