Research Experiences For Undergraduates (REU)

REU 2012 Projects


Incorporating Forward-Looking Signals into Covariance Matrix Estimation for Portfolio Optimization

Sponsor: Wellington Management
Advisor: Prof. Marcel Blais

Tejpal Ahluwalia    Robert Hark    Daniel Helkey    Nicholas Marshall   
Tejpal Ahluwalia    Robert Hark    Daniel Helkey    Nicholas Marshall

The widespread assumption of stationary in financial models is typically unjustified; however, there exist distinct periods during which market returns follow relatively consistent distributions. During these time periods, or regimes, it is reasonable to assume that future returns will behave similarly to those of the past. Effective trading strategies should adjust accordingly to regime changes, since an optimal portfolio during one time period may prove inefficient for a subsequent regime. A traditional approach to diversify holdings at a given time is to perform a Markowitz portfolio optimization, assigning weights to distribute investments under the assumption that asset returns exhibit stationarity. This method entails estimating the covariance matrix of asset returns with an aggregate of past data, thus ignoring the possibility of different regimes.

We adapt Markowitz portfolio optimization to take regime change into account via a method which dynamically estimates the covariance matrix of asset returns. The estimation method first adjusts the sample covariance matrix using the shrinkage transformation as described by Ledoit and Wolf in 2003. The method subsequently readjusts the transformed covariance matrix using a mixing parameter that is derived from forward-looking signals based on implied volatility. We find that our methods typically outperform the standard Markowitz portfolio optimization on stocks from both the Dow Jones Industrial Average and the S&P 500 during time periods since the collapse of the dot-com bubble in 2001.


Modeling Multidimensional Tolerance Stack-up in Excel Using Monte Carlo Simulations

Sponsor: Gillette - Procter & Gamble
Advisor: Prof. Matthew Willyard

Garrett Castle    Salil Gadgil    Michael Walker    Gregory Zajac   
Garrett Castle    Salil Gadgil    Michael Walker    Gregory Zajac

As a product is manufactured, it is subject to multiple sources of variation. Manufacturers use tolerance stack-up analysis to predict how often the accumulated variation of individual parts will compromise the functionality of the final product. Our goal is to create a model in Microsoft Excel that uses Monte Carlo methods to simulate these variations and provide information about the potential feasibility of a product. With these results, engineers can make necessary changes to the production or assembly process. We are developing such a model in Excel to make conducting simulation and tolerance stack-up analysis affordable and broadly accessible.


Modelling Cancer Stem Cell and Non-Stem Cancer Cell Population Growth

Sponsor: Center of Cancer Systems Biology
Advisor: Prof. Suzanne Weekes

Brian Barker    Sarah Bober    Karina Cisneros   
Brian Barker    Sarah Bober    Karina Cisneros
Justina Cline    Amanda Thompson
Justina Cline    Amanda Thompson

Each year cancer treatment in the US costs more than $120 billion, with over a million new people diagnosed with cancer. In order to improve cancer treatment techniques, researchers are studying tumor growth and behavior. The Center of Cancer Systems Biology has been working with a multi-compartment model based on the Non-Stem Cancer Cell Hypothesis. The Hypothesis proposes the idea that there are two types of cancer cells: cancer stem cells and non-stem cancer cells. Our first task was to simulate population growth and analyze the multi-compartment model analytically and numerically in MATLAB. We analyzed the sensitivity of the model with six parameters, and compared the proportion of cancer stem cells to non-stem cancer cells over different parameter values. We then analyzed the model.s steady states. We will proceed to develop a 2-compartment model that reflects the results of the multi-compartment model. The 2-compartment model will be more elegant and easier to use, and will allow us to further study the sensitivity of the populations and the age structure distribution of a simulated tumor.

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Last modified: Jul 22, 2012, 23:24 EDT
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