Part 1: Reservation Prices and Equilibrium

(RE-)EXAMINATION IN INVESTMENTS

Friday May 16, 2008. 3 pages. 3 hours. “Open book”, ie. all books, notes, calculators, computers (with internet connection disabled) are allowed.

Each of the 10 numbered questions (Q.number.letter) is worth 10 points, and has a 1 page answer limit.

Part 1: Preferences, state-prices and trades

Consider a state-preference model specified by the tables below:

The last tableof the model description specifiesall agents have marginal utility functions of the form

.

(Q.1.a) What are (up to the usual positive affine transformations) the utility functions of the agents?

(Q.1.b) Show that all agents have constant relative risk aversion, and decreasing absolute risk aversion.

(Q.1.c) Calculate Agent2’s reservation price for Sec1 (at the initial portfolios compositions above).

(Q.1.d) A market maker quotes a price of 1.00 for Sec2. At that price, suppose that: Agent1 wants to buy 10 units, Agent2 wants to buy 2 units, Agent3 wants to sell 3 units, and Agent4 wants to sell 15 units. Explain carefully which trades are made.

Part 2: Equilibrium

Running the model from Part 1 through APSIM produces this output:

(Q.2.a) Argue that this is indeed an equilibrium.

(Q.2.b) Do all agents hold portfolios that a combinations of the risk-free asset (Bond) and the market portfolio of risky assets (Sec1-3)?

(Q.3.c) Determine the “price per chance” (PPC) for the different states and plot the pricing kernel. What is (at least to a very close approximation) the functional form of this curve?

Part 3: Options

(Q.3.a) One of the risky securities in the model from parts 1 and 2 is a call-option. Which one, on what, and what is its strike price?

(Q.3.b) Supposeput options with the same strike price as in (Q.3.a) are introduced into the market, and assume they are in 0 net supply. What is a reasonable equilibrium price of the put options, and why?

(Q.3.c) Call-options are often used as part of the salary for the top management of a company; so-called executive options. A few years ago, one could read this quote in a Danish newspaper:

People who are opposed to executive options believe that they make the top management too risk-seeking because options can only increase in value, not decrease like ordinary stocks.

Comment on the quote. (The statement contains a conclusion and argument for reaching it; you may want to look at the two parts separately.).