It started as an assignment for investments class; was nearly thrown in the garbage never to be seen again; and eventually won the Administrative Sciences Association of Canada prize for best student paper at the 2007 conference.
“Multi-dimensional risk and mean-kurtosis portfolio optimization,” the award winning paper by Dr. Jim Stacey looks at portfolio optimization using kurtosis as a measure of risk.
Dr. Stacey is a recent MBA grad and current sessional instructor in finance. A physicist by training, he wanted to apply computation and mathematical analysis to markets.
“What's interesting about finance and studying the behaviour of markets is it's like a new frontier,” he explained in an interview between classes. “It’s a fascinating subject. It's not a physical science, but a social science with rational and irrational components to it.”
For an investment class with Dr. Alex Faseruk, Dr. Stacey took an enhanced approach to analyzing risk. “I wanted to look at statistics that weren't normal and look for other measures of risk in portfolio optimization. I wanted to make risk multidimensional,” he said.
Instead of focusing only on standard deviation when measuring risk, Dr. Stacey looked at the kurtosis of the distribution. “I wanted to figure out the impact of the shape of the distribution. If a distribution has a fat tail, is it riskier than or not as risky as a normal distribution? I wanted to look at shape as a dimension of risk to optimize portfolios.”
Looking for the particular shape that could signify another dimension of risk, Dr. Stacey looked at leptokurtic distributions, distributions that are more sharply peaked with fatter tails. “I was searching for stocks, that when combined, had a narrow peak and fat tail,” Dr. Stacey explained. “When the peaks are narrower and the tails are fatter, they mimic a low-risk portfolio with significantly fewer stocks than you would need if you were combining stocks following the traditional method of portfolio optimization.”
Taking a small number of stocks and putting together portfolios with leptokurtic distributions does not necessarily mean there will be a low return. Because of the shape of the tail there is a high risk component, but as the distributions become more peaked the fluctuations become smaller.
“This research may eventually lead to a viable investment strategy, and it has created a number of interesting questions that remain open. Is it possible to find a meaningful number of stocks with these properties? I found that when combined, many stocks followed the normal statistical shape. It was difficult to find stocks with a narrow peak and fat tails when combined,” he explained.
The difficulty he ran into almost led him to throw away the results. “I thought this work was a failure. I said to myself, this is hard, the computer isn't able to do what I thought-it's only fit for the garbage,” explained Dr. Stacey. “But Dr. Faseruk, my adviser, rescued it from the trash. He encouraged me to submit the paper to ASAC and it was only when I was re-writing it from assignment to submission that I realized there might be something here.”
Dr. Stacey found that it was possible to combine certain stocks and create portfolios that mimic a low-risk portfolio with fewer stocks. Because of the fat tail, these distributions do have a high risk component, but as the distributions become more peaked, the fluctuations they experience are smaller. If the probability of small fluctuations becomes much larger than the probability of large fluctuations, then the stock tends to increasingly behave like a risk-free asset. In other words, the familiar relationship that higher returns implies higher risk (and vice versa) might not apply to these stocks.
As Dr. Stacey said, “It's an intriguing result that raises fundamental questions about the nature of risk. It introduces new quantities and expands portfolio optimization using higher properties of the underlying statistics.”
“I really give kudos to Alex Faseruk for encouraging me to think outside the box. This research is totally opposite to what you'd expect when researching the issue,” said Dr. Stacey. “I found that the previous work of Markowitz (the father of modern portfolio theory) was validated while, at the same time, a hint of potentially new insights into the behaviour of risk was revealed.”
Dr. Stacey’s award is the latest in a string of successes for finance students and their professor, Dr. Alex Faseruk. At last year’s Academy of Finance annual meeting in Chicago, Dr. Faseruk accepted the Excellence in Teaching Award, as well as the Best Paper Award for “enhancing pedagogy in teaching option strategies through the use of management science techniques,” co-authored by Dr. Chris Deacon, Department of Physics and Physical Oceanography and an MBA graduate. Another recent MBA grad, Punit Anand, earned first place in the student research paper competition sponsored by the Canadian Institute of Chartered Business Valuators for his paper, “counting models for equity valuation.”