No, it doesn’t involve coconuts or rabbits or the comedy of Monty Python. It’s a simple but elusive concept for those who play the stock market. Low risk, high return — a dream for most investors. Memorial’s Dr. Jim Stacey, a physicist by trade, took a visual approach to a mathematical problem.
Can the shape of a bell curve answer the question that traditional economic formulas can’t?
Initially thrown off by early research in his MBA studies, Dr. Stacey was ready to throw out the idea until his supervisor encouraged him to approach it in a new way. Soon he was analyzing the peaks of the bell curve and exploring some fundamental questions about the nature of risk, giving new insights to a long-lived puzzle.
Dr. Stacey, a recent MBA graduate, 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 said. “It's a fascinating subject. It's not a physical science, but a social science with rational and irrational components to it.”
His research interest led to a paper for an investments class that looked for a new way to determine the measure of risk in a portfolio. Instead of focusing only on standard deviation when measuring risk, Dr. Stacey looked at the kurtosis, or shape, of the distribution.
Normally in finance, risk is measured by assessing the standard deviation of stock performance. By looking at the shape of the bell curve, Dr. Stacey was hoping to discover something new. “If you picture a bell curve, risky stocks tend to have wide peaks and relatively skinny tails. I wanted to figure out 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.”
Stocks with fat tails are generally more risky, but a narrow peak means that the fluctuations of that stock are smaller. By combining these two properties, the stocks 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.
“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. Alex 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.”