2006 Day 1 239A Question

I was going over question I1 on the 2006 exam this evening. I think it would be worth discussing (1) sufficient conditions for uniqueness of equilibria and (2) situations of effective market completeness.

I know this is a little vague, but I'll try to flesh out the details and revise this post before the next meeting.

Theorems to memorize

I think it might be useful if we could all brainstorm theorems/derivations that we should memorize. I'll start, but others should feel free to edit this post.

Theorey

1. CAPM and 2 fund separation (monetary and zero-beta)
2. APT
3. First and Second fundamental Theorems of Asset Pricing
3.1 Conditions for Complete Markets Equilibrium
4. First and Second Welfare Theorems - Complete Markets
5. Milgrom and Stokey No Trade Theorems

Continuous Time

1. Ito's Lemma
2. Martingale Representation Theorem
3. Girsanov's Theorem
4. Black-Scholes Formula

Corporate

1. Modigliani Miller
2.

Microstructure

1. Kyle Model
2. Revenue Equivalence Theorem
3. Direct revelation principle

Butterfly (strategy using options) and Arrow-Debreu Securities

Assume that the only state variable is the S&P500 index levels. Assume that you have a continuum of strike prices of options over the S&P500 index. Show how to construct a state contingent claim that pays $1 in a given state (say, S&P500 is at 1500 a year from now). This is a question discussed in Prof. Rubinstein's lecture.

CAPM & Black Scholes

The second part of the "Does the CAPM price options" question from the 2006 2nd day asks: Why is it that beta appears in the CAPM but volatility appears in the Black-Scholes forula?

Convenience Yield, Forwards and Futures

Define and relate the following terms: convenience yield, forward price, and futures price. Is it possible to have a non zero convenience yield when storage is free?

Efficient Markets and No Aribtrage

Relate the following concepts: efficient markets and no arbitrage. If markets are efficient can there be arbitrage opportunities?

Problem 5 on Jacob

I spoke with Jacob in the hallway about problem 5 and this is what he had to say:

1) Its not necessarily the case that CRRA utility plus lognormal gives you mean variance optimization. This is true if you can continually rebalance or if you are not perturbed by small shocks. (I'm not entirely clear on what this means). The crux of this arguement relies on the fact that a linear combination of log normal assets is not lognormal. In continuous time, the mean and variance dominate over the sqrt(delta t) term so its better there (Again unclear on details here).
2) Having one investor find it optimal to hold the market portfolio implies that you can use the market portfilio to do pricing (maybe not necessarily Beta pricing). This is because optimality gives us a ratio of utilities and thus a SDF. This SDF need not be unique. Its likely not in problem 5.

3) Now its also possible that every investor might want to hold the market portfolio, but its not necessary that the pfolio be MVE. In fact, if you have 2 fun seperation through utility restrictions, unless you have MV utility, the funds may not be MVE. IF you have distributional constraints leading to 2 fund sep, then all utility maximizers (including MV optimizers) will want to hold the funds, so they will have to be MVE.


He recommended reading Dybvig and Ross (?) 1980(?) paper in Econometrica. It has something to do with the fact that investors might want to hold specific assets because its optimal for them to do so but the linear combination of these assets is SSD (dominated) by something else in the economy.

I know this probably did not clear up many of your questions, but perhaps you can be more prepared when you speak with him.

2 Fund Seperations

In a two fund monetary seperation, is the risky fund always Mean Variance Efficient?
If so, is it necessarily the tangency portfolio (defined by the line between the Risk free and the Frontier) or can it be any mean variance efficient fund?

Options and The CAPM

In a CAPM world would anyone buy options?

Efficient Markets and Exchange Rates

In an efficient Market, is the floating exchange rate a martingale?

Notes/Questions on the CAPM.

In skimming Jacobs notes on 2 fund seperation, I noticed that HARA only leads to 2 fund sep if all investors have the same power (thus the same risk aversion?). Is that true (Cass and Stiglitz)? Still dont see any use for Options in a static CAPM. - Nish



With regard to the first question Nish, the power in the marginal utility for HARA class is not exactly the risk aversion. HARA includes utility functions with non-constant risk aversion. See Ingersoll p.146 for a statement of sufficient conditions on marginal utility for monetary two-fund separation.

This blog can act as an alternative to the google doc

I think this might be a better way to keep track of comments/questions concerning preparation for the finance prelim than the previously suggested google doc.