MS&E 444 Investment Practicea finance project class.Updated 6/2/2008 |
Lectures: Monday Wednesday 4:15-5:30, Education 206. Instructor: Kay Giesecke, Terman 414 TA: Benjamin Armbruster, Terman 499 email: lastname@stanford.edu |
Jump to Proposed Projects and Resources.
Monday June 2 at 4:00pm in building 320 room 105.
program/flyer
10 min talks + 10 min QA
4:00-4:20 Vega hedging and the shape of implied volatility term structure changes
[slides,
report]
Paul Oreto, David Starr, Matthew Dixon, Chen Zheng, Brandon Kampschuur
4:20-4:40 Structure of the implied volatility surface
[slides,
report (converted to pdf)]
M.-Günhan Ertosun, Sarves Verma, Wei Wang
4:40-5:00 Detecting insider trading
[slides,
report (converted to pdf)]
Xu Tian, Manabu Kishimoto, Li Xu
5:00-5:15 break refreshments provided
5:15-5:35 High frequency trading using order book information
[slides,
report]
Paul Merolla, Erik Anderson, Alexis Pribula
5:35-5:55 Using a behavioral model for market predictions
[slides,
report]
Sudeep Tandon, Rachit Prasad, Puneet Chhabra, Harshit Singh
5:55-6:15 Optimal trading of a mean reverting process
[slides,
report]
Wei Wang, Tony Pan, Ren Fung Yu, Chen Tze Wee
We assume there are two types of agents (with bounded rationality) that trade in a particular security: fundamentalists who base their buy or sell decisions on the notion of a ‘fair’ value of the asset and chartists who extrapolate future prices from historical trends. The fraction of agents following a particular strategy varies with their recent relative profits. We select model parameters that minimize the historical mean square error of the predicted prices and then use the model to forecast the next period's closing price. We test the model on securities from various asset classes.
In order to apply mean-reverting trading strategies to market conditions, it is important to consider practical constraints such as margin requirements and transaction costs. Furthermore, the spread between two correlated stocks does not necessarily follow a strict Ornstein-Uhlenbeck process. Our model extends Boguslavsky and Boguslavskaya's theoretical solution to account for these real world characteristics. By taking margins, transaction costs, and dynamic parameters into account, we demonstrate that a discretized trading strategy can be profitable when applied to real mean-reverting stock pairs.
VIX (volatility index) from the CBOE Indexes database.
Options prices from the OptionMetrics database.
Earnings announcements from the FirstCall database.
NYSE Trade and Quote (TAQ) database.
Course flyer. The first class is Wednesday April 2 at 4:15 in a different room than the usual one. The first class will be in 260-113.
Team applications are due 10:30am PDT on Monday April 7. See below for details.
You can use the newsgroup su.class.msande444 to form teams.
Since the enrollment in this class is limited (to approximately 30 students), we ask each team to submit an application, and then Monday afternoon we'll let people which teams were selected via email, this website, and in class. For the application we ask that each team email stanfordmsande444@gmail.com a 2-3 page pdf. Page 1 should be a description of the problem you want to tackle and the approach you want to take. If you have any preliminary results, mention them. You should also describe in a few sentences (no more than 3) how your team has the necessary skills. Page 2 should contain concise resumes of each of the team members. The optional page 3 is reserved for any figures you may want to include (possibly relating to preliminary results you mention in page 1). You should resist the temptation to cram more information on a page by messing with the font size; instead try to be concise.
Project developed in collaboration with the hedge fund EvA. Here are the slides from the first lecture describing the projects.
It's ok if multiple groups work on the same project.
The asset allocation problem is to allocate your wealth among a set of different assets (stocks, bonds, etc.) in order to obtain a good balance between risk and return. Generally this is formulated as a problem of maximizing expected utility, but behavioral economists have found that the expected utility framework does not fully capture human preferences. Prospect theory is an extension to expected utility maximization that closer models human decision making. It was developed by Kahnemann and Tversky in 1979 and won Kahnemann the Nobel prize in 2002. This New Yorker article gives a non-mathematical overview of behavioral economics / prospect theory. This project is to solve the asset allocation problem using prospect theory (instead of expected utility) to compare different return distributions.
For log-utilities, U(w)=log w, we have U(W(T))=log [W(0)] + log [W(1)/W(0)] + log [W(2)/W(1)] + · · · + log [W(T)/W(T-1)] where W(t) is the wealth at the beginning of period t. So if there are no transaction costs (no costs from moving from one portfolio to another), we maximize E[U(W(T))] by optimizing in each period, the expected log return, E[log(R)]. This myopic property is very convenient computationally since we don't need to solve a multi-period optimization problem. While a log-utility is convenient computationally, it is not as risk-averse as one would like. In these slides, Lisa Borland uses a more heavy-tailed distribution (than the true, empirical distribution) while keeping the log-utility to obtain more conservative allocations and return distributions. Using a different distribution than the true, empirical distribution is the way prospect theory differs mathematically from standard expected-utility maximization. Note that the one-period return, R=1+h_{0} x_{0}+ ··· +h_{n} x_{n} where h_{i} is the fraction of one's money invested in security i and 1+x_{i} is the return of that security. If x_{0} is the risk-free rate, then this simplifies to 1+x_{0}+h_{1} (x_{1}-x_{0})+ ··· +h_{n} (x_{n}-x_{0}). These slides only examine in detail the case of one risky asset. One project could generalize these results to the case of multiple assets. Another idea would be to abandon the log-utility and use a more risk-averse utility function in the classical expected-utility framework (i.e., using the true, empirical distribution).
This paper clearly develops and discusses the solution for an Ornstein-Uhlenbeck process assuming no transaction costs, no budget constraint, and no margin-requirements. These slides further explain the financial implications of the model. This paper has a more complicated solution for a more explicit model of trading a pair of stocks. This project will develop trading strategies for more realistic models. EvA provided us a time-series where the portf.ER column is the expected return (the signal) for that day and the unlevered.return column is the actual realized return.
Hedge-fund replication is the idea that you can get returns similar to those of hedge funds more cheaply using some simple strategies such as borrowing money and buying an index fund. This New Yorker article provides some context. This project is to determine to what extent this is possible for EvA. Is EvA market neutral or is it exposed/correlated to certain market factors/indices? Can you approximate it's return distribution with a simple strategy? Some Goldman Sachs slides. A team interested in this project should send an email to Benjamin for access to EvA's return data.
Insider trading is when people who have "inside" information (often because they work for the company) and illegally use this knowledge to trade (and make money off uninformed suckers). This is quite common and occurs both in the stock market [NY Times article] and the options markets [news article, case studies]. This can detected by looking for large trades or spikes in volume ahead of a merger or other announcement. Insider trading hurts market makers who have to give bid/ask quotes for options and is very blatant in Brazil. The project would be to replicate some of these results and answer questions such as (a) how frequent is insider trading (compared to the number of events of a given size); (b) how likely will somebody get caught; (c) what the average profit is; (d) whether insider trading is more prevalent / concentrated in some sectors; (e) whether it has gotten worse (say compared to the 90s); (f) are there currently any unusual trades indicating an imminent merger or other event; (g) and can money be made by detecting inisider trades (McMillan wrote a book on the premise that you can).
It is important but difficult to quickly and accurately detect when the characteristics of a financial time series changes. In particular we want to detect these changes (which may be due to the firing of a CEO or other events) without human intervention. Drift and volatility are examples of two characteristics we may wish to examine. Detecting a change in the drift is useful for stock picking while detecting a change in the volatility is crucial for pricing options. The project is develop methods for detecting these changes. These might come from statistics, signal processing (e.g., wavelets), etc. We expect that each method will show a trade-off between the delay in noticing a change, the accuracy of detection, and the size of the change.
Is there any relationship between the correlation mong stocks and the volatility in the market and/or the dispersion (variation) across stocks? The idea would be to explore whether there is any information that can predict extreme correlations in stock moves - as we saw in August 2007, or that can predict extreme market moves in any direction. A short description of Omega statistics.
The implied volatility of a particular option is the number one needs to plug into the volatility term of the basic Black-Scholes formula to obtain the market price of that option. (If all the assumptions of the Black-Scholes formula held, then the implied volatility would be the constant and the same for all options on the same underlying stock. However, they don't all hold.) The term-structure of implied volatility is a vector of implied volatilities for a set of options differing in their expiration dates (e.g., these options could all have at-the-money strike prices). This project would explore how this vector changes over time. If one looks at the covariance matrix of these changes, are there any common factors that can explain them? Principal components or fundamental factors? Do these changes match any theoretical model for pricing options? The papers 1, 2, 3, may be of use. This file from EvA contains time-series of implied volatilities for many options.
Volatility has a number of characteristics that have not been seen before in a single model. These are auto-correlation (decaying as a power-law), fat-tailed distribution, higher moments of returns exhibit multi-fractal scaling, and an Omori law for volatility shocks. References [1, 2, 3].
This paper for example, lists some ideas.