# 2007 a exam december.pdf - This exam consists of 8 numbered...

• No School
• AA 1
• 9

This preview shows page 1 - 3 out of 9 pages.

This exam consists of 8 numbered pages Erasmus University Rotterdam Master Quantitative Finance Exam FEW2614 “Asset Pricing” Thursday December 21, 2007, 9h30–12.30h This exam consists of 9 questions. Please formulate your answers in a clear, compact, to-the-point matter (no more than 5 sentences or 100 words per essay question). You are allowed to use a calculator. Avoid speculating or including details that are beyond the point. The total points of the exam equals 70. For each question, it is indicated how many points a good answer produces. The sum of your points divided by 7 determines your grade. You need at least 39 points to pass the exam. Good Luck! Part I: Theory (35 points) 1. ( 8 points ) Consider an agent with a concave utility function u ( c ). His sub- jective discount factor is equal to 1. The economy has two periods, and can be in four states of the world in the future. The probabilities of the different states to occur are (0.3, 0.3, 0.2, 0.2). The agent has determined his optimal consumption and investment accordingly. His marginal utility in the different future states of the world is given by (105, 95, 120, 70). (a) ( 1 point ) Rank the states from good to bad. As the utility function is concave, marginal utility is low if utility is high. Consequently, the rank should be 4, 2, 1, 3. 1

Subscribe to view the full document.

(b) ( 3 points ) Write the risk-free rate as a function of his current marginal utility. Is the risk-free rate increasing or decreasing in current consump- tion? The pricing kernel for each state s is given by u 0 ( c s ) /u 0 ( c 0 ) . The risk-free rate is equal to 1 / E[ m ] , and E[ m ] = 4 s =1 m s π s = 4 s =1 u 0 ( c s ) π s /u 0 ( c 0 ) , so R f = u 0 ( c 0 ) / 4 s =1 u 0 ( c s ) π s . Substitution yields R f = u 0 ( c 0 ) / 98 . If cur- rent consumption goes up, it’s marginal utility goes down, so the risk-free rate is decreasing in current consumption. (c) ( 2 points ) Assume the risk-free rate is equal to 1.05. Value an asset A with pay-off (20, 10, 25, 15). What is the expected return on this asset? (If you cannot find the values of the pricing kernel for different states of the world, assume they are given by (1.03, 0.9, 1.1998, 0.6671).) If the risk-free rate is 1.05, current marginal utility is 1 . 05 × 98 = 102 . 90 . The different values for the pricing kernel can subsequently be found as (1.0204, 0.9232, 1.1662, 0.6803). Contingent claims prices can be found as p c s = m s π s , which yields (0.3061, 0.2770, 0.2332, 0.1361). The asset’s price can be found as p A = 4 s =1 p c s x A s = 16 . 76 . The expected pay-off is equal to 17. The expected return is hence 17 / 16 . 76 = 1 . 014 . Under the alternatively given pricing kernel, the contingent claim prices would be (0.309, 0.27, 0.23996, 0.13342), and the price of the asset would be 16.88. The return would be 17 / 16 . 88 = 1 . 007 . (d) ( 2 points ) Under the same assumption, value an asset B with pay-off (40, 25, 60, 15). What is the expected return on this asset? Which asset is judged on returns the best hedge against future variation in consump- tion?

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

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