Utility An economic term referring to the total satisfaction received from consuming a good or service. A consumer's utility is hard to measure. However, we can determine it indirectly with consumer behavior theories, which assume that consumers will strive to maximize their utility. Utility is a concept that was introduced by Daniel Bernoulli. He believed that for the usual person, utility increased with wealth but at a decreasing rate. Investopedia 1 Exposition of a New Theory on the Measurement of Risk

Utility and Risk Aversion  An individual may value expected outcome differently based on their risk aversion which may be based on wealth or preferences  The utility of a financial gain or loss to an individual is likely dependent on current wealth U(w)=ln(1+w)

Utility and Risk Aversion  An individual has wealth of 1000 and has the opportunity to participate in a fair ‘financial game.’ 50% chance to gain 100 or lose 100. Assume her utility function is the natural log of her wealth What probability of winning 100, p, would motivate her to play the financial game?

Risk – Return Utility Curve Note the same utility for these assets u = 10% s = 20% u = 7% s = 14% u = 4% s = 0% A=3

Attitude Towards Risk  A>0  Risk decreases utility of return  Individual is risk averse and is thus an ‘investor’  Investor will not participate in a ‘fair financial game’  A=0  Risk does not effect the utility of return  Individual is risk neutral and will participate in a ‘fair financial game’  A<0  Risk increases utility of return  Individual will participate in an “unfair financial game” Las Vegas

Indifference Curves

Risk – Return Indifference Curve Note the investor’s indifference between these assets u CE = 11% s = 0% u = 12% s = 8% u = 14% s = 14%

Optimal Portfolio  CAL line contains all possible portfolios  What’s your allocation of funds between assets  Depends on your “A” and say its 5  Set the shape and orientation of indifference curve  Your optimal portfolio is at the tangent point  Equal slopes Asset A Asset P Asset F CAL Indifference curve with A=5 tangent to the CAL u CE

9 Portfolios With Two Risky Assets  AB =1  AB =0  AB =-.5  AB =-1 A B

10 Now Determine Your Optimal Portfolio Indifference curves A=2, 4, 7 T: Optimal Risky Portfolio F P: Your optimal portfolio A B V

11 Portfolio with 2 Risky Assets Indifference curves A=4 T: Optimal Risky Portfolio F P: Your optimal portfolio A B V