Outstanding questions

I - Random walk == efficient market?
II- treasury yield curve relationship to mortgage yield curve
III- concrete example of incompleteness arising from transactions costs.

Let's start with 2005.II.5 tomorrow?

Market Efficiency and the Expectations Hypothesis

Is the expectations hypothesis a consequence of the efficient markets hypothesis? Is so explain why. If not explain how the two concepts are related.

B&S and CAPM Redux

I created a new post about this because the previous one is already in the "older posts" section. To refresh your memory, this is about 2005, II.4.

Here are my 2 cents, let me know if it makes sense:

Answer to first question: you can use CAPM to estimate expected excess returns of options under certain assumptions: HARA class of utility functions.

Answer to second question:

(Preliminary note: CAPM is about expected excess returns and and is mute about price levels. B&S is about arbitrage free price levels and is mute about expected excess returns.)

Role of Beta in CAPM: quantifies the amount of the priced factor in an asset, to measure its expected excess return. The price of risk is given by the expected market premium.

In that sense, sigma in B&S is analogous to the expected market premium and not to beta. The delta of an option is analogous to beta. Making sigma = 0, the option is worth its intrinsic value (something analogous to the risk free rate).

Investment-cash flow sensitivity

We spent quite a lot of time in 239D discussing investment-cash flow sensitivity. It is not clear to me why this is an interesting/important topic. What is the significance of Inv-CF sensitivity? Is it simply a proxy for financial constraints (i.e. firms that are constrained have investment that is more sensitive)?

Over(under) stated estimates/t-stats

This is related to problem II.13 from 2005 day 2. Do we have a good list of cases where estimates are over or understated, or where the t-stats are? perhaps we can discuss this next time.

When is the next meeting/what is the group meeting schedule now?

thanks,

Javed

Complete Markets with BM

I was looking at PS3 Problem 2 in 239B yesterday (Black Scholes with Stochastic Interest Rates) and I noticed that the set up of the problem has two risky assets (a stock and a zero coupon bond) and two independent brownian motions. However, a unique EMM does not exist and the markets are not complete.

It seems counterintuitive to have a non complete market with two risky assets and two indep BMs. In what situations with these conditions can markets be incomplete?

Two Fund Risky Separation

I am trying to solve Jacob's Prelim 2002 Problem (IIB). It is a two fund risky separation question with distributional assumptions (jointly normal asset returns). I can't make the portfolio weights independent of each investor's initial wealth. Maybe I am missing a key conceptual step. Need help here!

The Revenue Equivalence Theorem

What are the conditions needed for the revenue equivalence theorem to hold in the Common Values case?

Heterogenous Beliefs, Short Selling Constraints, and Prices

All else equal, should we seeing higher or lower prices when there are short selling constraints? What are the necessary conditions for short selling constraints to matter?

SDF, State prices and the Radon-Nikodym derivative

This is a question for the group meeting. I wonder how they are all related.

A Question about Brownian Motion

Hey y'all,

I remember in our last meeting (when we were discussing the filter strategy and barrier strategies) that it was mentioned that since BMs have normally distributed increments, the value of a BM at t+1 can be anything from +inf to -inf (only in expectation is it BM(t) ).

In some sense its ridiculous to talk about t and t+1 since dt is infinitesimal. But is it the case that at each infinitesimal increment, the BM could concievably be hitting +inf or arbitrarily close and coming back to some "mean"? What happens when the BM over the next infinitesimal is arbitrarily large. Does the Martingale property now imply that it stays that large? Maybe I'm just being an idiot.

Is my understanding of this correct? Is there somewhere in Durret or Shreve I could look to figure this out (assuming I can understand Durret or Shreve)? Perhaps I can just add assorted facts about BMs to our list of things to discuss on Sunday.

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.