Risk attitudes For each of these utility functions, determine whether the agent is ri

1Risk attitudes

For each of these utility functions, determine whether the agent is risk-averse, risk-neutral, or risk-loving. (Assume that wealth is always positive: w > 0).

• u(w) = 2w³ + w.
• u(w) = 5ln(w) − 4. (ln is the natural logarithm function.)

2Now you see it, now you don’t

A student has $900 in total wealth, consisting of a $500 laptop as well as $400 in cash, but

√ there is a 5% chance that her laptop gets stolen during the quarter. Her utility is u(w) = w, where w is her wealth at the end of the quarter.

• Compute the expected value and variance of the student’s end-of-quarter wealth.
• Compute the student’s expected utility, given the risk of having her laptop stolen. Then compute her certainty equivalent.
• A startup called Swipe provides full insurance against the risk of laptop theft. What is the actuarially fair price of this insurance policy? Would the student buy such a policy at the actuarially fair price?
• Explain how Swipe’s insurance contract might create an adverse selection problem. Explain how the contract might create a moral hazard problem.

Copyright2018 by Brendan M. Price. All rights reserved.1

3Portfolios

Explain why each of the following investment strategies reduces, but doesn’t eliminate, the investor’s exposure to risk.

• Investing in several different clean-energy technologies (wind, solar, and hydrogen) instead of just investing in solar.
  

  1 Risk attitudes

  For each of
  these utility functions, determine whether the agent is risk-averse,
  risk-neutral, or risk-loving. (Assume that wealth is always positive: w > 0).

  a.
  u(w)
  = 2w³ + w.

  b.
  u(w)
  = 5ln(w) − 4. (ln is the natural
  logarithm function.)

  2 Now you see it, now
  you don’t

  A student has $900 in total wealth, consisting of a $500 laptop as
  well as $400 in cash, but

  √ there is a 5% chance that her laptop gets stolen during the quarter.
  Her utility is u(w) = w, where w is her wealth at the end of the
  quarter.

  a.
  Compute the expected value and
  variance of the student’s end-of-quarter wealth.

  b.
  Compute the student’s expected
  utility, given the risk of having her laptop stolen. Then compute her certainty
  equivalent.

  c.
  A startup called Swipe provides
  full insurance against the risk of laptop theft. What is the actuarially fair
  price of this insurance policy? Would the student buy such a policy at the
  actuarially fair price?

  d.
  Explain how Swipe’s insurance
  contract might create an adverse selection problem. Explain how the contract
  might create a moral hazard problem.

  Copyright 2018 by
  Brendan M. Price. All rights reserved. 1

  3 Portfolios

  Explain why
  each of the following investment strategies reduces,
  but doesn’t eliminate, the investor’s
  exposure to risk.

  a.
  Investing in several different
  clean-energy technologies (wind, solar, and hydrogen) instead of just investing
  in solar.