Dang Trinh ’12
Major: Mathematics
Thesis Advisor: Tanya Leise

What is your thesis about?

It’s a statistics thesis where I’m focusing on a particular branch of statistics that focuses on time series data. Specifically, I’m focusing on time series of stock prices and stock volatilities of 500 stocks in the Standard & Poor’s 500, daily data going back to 1962. So essentially I have data of about 6-7 million cells.

Is this a crossover with the economics department?

No, I could have made it that way, but I chose to do it with the math department instead.

How did you decide on this topic?

Well, there were a lot of factors. I’ve always known that I’m interested in finance and economics, and I wanted to do something that was related to that. The second semester of my junior year, I took two classes, the time-series analysis taught by Shu-Min Liao and an econ course called Dynamic Macroeconomics taught by Professor Sami Alpanda. Both of them essentially were time-series analyses, and I was really into it. It was just a new field of statistics, econometrics, that was just really, really fascinating for me, because I could see so many things that can arise out of it: the real business cycle, forecasting, the relationship between inflation and unemployment, things like that. So those were the things that really fascinated me enough to start this thesis.

What are time series, exactly?

A time series is just any series where you have observations that go through time for a specific type of observation; for example, stock prices, that’s a time series, inflation, that’s a time series, population of a state over time, that’s a time series.

How are you using them in your project?

I’m looking at this particular property of stock volatility. The property is called long memory. What it means is that observations that are far apart in time have a small but statistically significant correlation. Why am I looking at this? Two reasons: first, empirical evidence has shown that there is a certain very strong persistence in the autocorrelation of these stock volatilities. And the presence of this long memory is one of the more strong pieces of evidence against the very well-known efficient market hypothesis, because if the market is really efficient, any shock you have to the market, the effect should go away in an exponentially short period of time, rather than having that long persistence. So in that sense I’m examining these 500 stocks and estimating the long-memory parameters of it, and doing a hypothesis test on whether these estimates are statistically different from zero, which means short memory. And then the second part of my thesis looks at these stocks that have long memory in their volatility. Now, where are the factors that cause these volatilities? The way I do that is essentially, I will divide them up in terms of size and in terms of industry. Each method of division I will use a technique called canonical correlation analysis, a multi-variate data analysis technique that is used specifically to detect common trends among different series in different groups of series. And so using that technique, I will get the count data for, okay, in each of these groups divided by size, what is that average number of common factors that I get, versus what are the count data for the common factors if I divide the groups by industries. And then finally, I will perform a statistical test between these count data to see which one is statistically significantly higher than the other one. And if industry is higher, then it means that these volatilities must have been caused by the same factor, and that factor relates more to the industry that the company is in, rather than the size of the company.

Are you looking at a career in finance?

Closely related, I think. I’m joining an economic consulting firm called Analysis Group, in Boston. I’m very much excited about it, first and foremost, because they use rigorous economic and statistical analysis to answer business questions in litigations, and those are the things that I’m very much excited about. And they do work a lot of cases on finance, on mortgage-backed securities and all of the litigations involved with that dirty part of the financial crisis, they do a lot with that. Actually one thing that I think would be very much attached to it is more about options pricing or derivative pricing, which starts from the Black-Scholes Equation. One assumption that goes into the Black-Scholes equation, which anyone will say is a crappy assumption, is that variances of the stocks are constant over time, I mean come on. And so in order to improve that model, you need to find certain ways in order to model the volatility as a stochastic process, rather than as a constant process in time. These long-memory models are newer, while the more traditional models of volatilities only have short memories. Only more recently, when empirical researchers discovered this long-term persistence do these models become a lot more powerful in adding meaning to the volatility of the stocks. That’s more than likely going to be related to my job, because in economic consulting, we do a lot of valuation cases also, where we try to come up with a model to value a certain asset type, so if a company proposes a new type of security, we’re going to think of what would be right way to price those securities.

Any advice for other students thinking about considering a thesis?

Well, I will speak mostly to students writing a thesis in math, because that’s where I am. If you’re an applied, or more of like a statistician kind of person, … writing a thesis with the math department has been a wonderful experience for me. My advisor was wonderful to me, she was really helpful in actually giving me the right direction and helped my determine how much is too much. When I was pursuing one direction, and it wasn’t working, and I was crying, and she was just like, okay, let’s just take a step back, and do another thing, and then I found out that the other thing actually made more sense, and then I was smiling. If anything, another advice is to try thinking about your topic by talking to faculty, and even during your summer experience, wherever you are, try to think about it during that time. I don’t think I could have come up with this topic had I not taken those two courses that I mentioned and had I not been interested in finance for a while, I don’t think I would have written anything that is even remotely related to this.