How the Father of Arbitrage Pricing Theory Influenced Wall Street

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Wharton's David Musto on the late Stephen A. Ross, this year's winner of the Wharton-Jacobs Levy Prize for Quantitative Financial Innovation.

This year’s winner of the Wharton-Jacobs Levy Prize for Quantitative Financial Innovation, an award given to leading lights in the world of finance, is former Wharton professor Stephen Alan Ross. Many in the field consider him to be one of the most important thinkers in modern finance. One of his best-known ideas, for which he is receiving this award, is arbitrage pricing theory, or APT. It has been a staple of finance since he developed it in 1976 while at Wharton.

In March, Ross died at 73, shortly after he was announced as the winner of the prize. The award will be given posthumously on September 15 at the Jacobs Levy Center’s annual conference, to be held in New York. More recently, he had been a professor at the MIT Sloan School of Management. Ross’s work covered many fields, from asset pricing to management and corporate finance.

Wharton finance professor David Musto, who will be speaking about Ross at the conference, joined Knowledge@Wharton to talk about the late professor’s research and contributions to the field.

An edited transcript of the conversation follows.

Knowledge@Wharton: Let’s start by talking about Ross’s most famous theory, APT. It was truly groundbreaking as a way to analyze risk and returns in financial markets. It looked at how to identify assets that were trading too low or too high, because of market mispricing. Can you explain how important that theory is, and the basics of how it works?

David Musto: I’d be happy to. And to understand the importance of this theory, it is also worth thinking about the contributions of the two previous winners of the Jacobs Levy Prize. And that would be (Nobel laureates) Harry Markowitz and Bill Sharpe. So, let’s rewind all the way back to the 1950s, when Harry Markowitz was finishing his PhD. His graduate work was about the risk of stocks. And in particular, the risk that an investor should care about. His point was that sure, stocks are risky. Investors are averse to risk, and so therefore they should care about the risk of stocks, and maybe discount for it when they buy.

But his additional point was that if you think about the risk that faces an investor, it’s not the risk of individual stocks. An intelligent investor is going to diversify across many stocks. And the risk that faces the investor, the risk that ultimately is going to deliver the payoff to his bank account, is going to be the risk of this portfolio. And once you think of it that way, you realize that the correct measure of risk is not a stock’s risk by itself, but instead, the risk that it’s going to add to a diversified portfolio. So, that was his point. That was a pathbreaking point, and the contribution that won him the Jacobs Levy Prize.

Now go forward from the 1950s to the 1960s. Bill Sharpe is a graduate student. And then his most famous paper, and the one that he won the Jacobs Levy prize for, is one that shows that if, in a world where investors are trying to maximize their expected return for a given unit of volatility, you can reach the conclusion that the risk that really matters about a stock is what you’d call its beta (a stock’s volatility in relation to the market). Essentially, in technical terms, it is the result you would get if you did a regression of the stock’s return on the market portfolio. You get a number, which on average is going to be one, but it can be higher or lower. That [beta] tells you the risk that the stock adds to the market portfolio.

“The correct measure of risk is not a stock’s risk by itself, but instead, the risk that it’s going to add to a diversified portfolio.”

Knowledge@Wharton: Is that a volatility measure, in a way?

Musto: Beta is telling you what today we would call the systematic portion of the stock’s return — that portion of the stock’s return that’s correlated with the market. The stock also is going to have what practitioners would call an idiosyncratic component– meaning, its own special risk from its own special thing that the company does. That is, of course, important to people at the company. It’s important to the CEO. But to a holder of a diversified portfolio, those idiosyncratic risks of the component stocks are going to average out close to zero, when you put together a big portfolio. And so that’s just not going to matter so much. This is capturing that portion that’s not going to wash out.

So, that was Bill Sharpe, in the 1960s. … Steve Ross came here to Wharton in the early 1970s and he soon developed this arbitrage pricing theory. He approached the question in a somewhat different fashion. He said, “Let’s just start by assuming that stock returns follow what you could call a factor structure — what you mean is that there’s some small number of factors, say five. There’s no specific number it has to be, but let’s say it’s five factors. Let’s say that those five factors account for most, or almost all, of the co-movement between stocks. All of the systematic portion of their stock returns is captured by those five factors. Everything that’s not captured by them is idiosyncratic.

Well, let’s say that’s true. His point was that in a world with that kind of factor structure, the risk of a stock that’s going to matter to investors is its exposure to those factors. And every factor is going to have associated with it what you would call a risk premium — so, how many units of additional expected return an investor can get for additional exposure to that factor? Exposure to those factors is going to give investors more expected return, for bearing that systematic risk associated with those factors.

“He was a great intellectual presence.”

And then, the idiosyncratic component of the stock’s return is not going to give you any additional expected return. It shouldn’t, because to an intelligent investor putting together an optimal portfolio, that’s just going to wash out. It’s the factor-driven part of the return that’s going to matter. And so that’s going to be driving expected returns.

Over time — to take this idea into practice — the way people have developed it is to think about what those factors could be that could be the underlying drivers of stock returns. They could be things like changes in expected inflation. They could be developments to GNP. They could be things having to do with interest rates — and what kind of risk premium you would need to be compensated for exposure to that factor.

Knowledge@Wharton: Those things tend to be macro-economic factors?

Musto: Yes. These would be macro-forces that can have their own separate effects on stock returns. It could be inflation. It could be about the term structure of interest rates. It could be production of the economy in general. Things like that.

Knowledge@Wharton: And so this led to predictions, or analysis that would show that an individual stock was overpriced or underpriced, and then you could make decisions for buying and selling based on that?

Musto: I actually worked for Steve Ross for a couple of years after I finished college at a money management company called Roll & Ross Asset Management. Roll being Dick Roll, another famous finance academic, who is also going to be speaking at our Jacobs Levy event, by the way.

The goal of this company was to manage equity portfolios for pension funds, endowments and the like. And the special sauce of the company was understanding expected returns via the arbitrage pricing theory. By which I mean, understanding, for a given stock, what expected return you would need to hold the stock, given its exposure to the macro factors driving stock returns. And if we could perceive, through our black box code that I was working on the whole time there, if one could perceive that here’s a stock that has maybe some additional expected return over and above the return that one would require for its macro exposures, then that was a stock to buy.

That was the goal of our software, to find expected returns over and above the returns that were required for risk, so that you’re giving people an economic profit. You’re giving them more expected return than they would normally get for bearing that much risk.

Knowledge@Wharton: It’s interesting that his theories were developed in academia and applied directly onto Wall Street, which doesn’t happen every day.

“He had a way of modeling an economic problem that was always very elegant, and yet conclusive.”

Musto: It’s true not just for the arbitrage pricing theory, but also another framework he developed that people on Wall Street would be quite familiar with — the binomial option pricing model. This is a very elegant way to price the whole range of derivative securities out there. So Steve, building on the work of [Fisher] Black and [Myron] Scholes, showed how you could take what they did and think about it as a binomial framework that would help you price a wide range of securities, and show you how you go about replicating the payoff of any derivative security you might be interested in, with this binomial trading technique.

Knowledge@Wharton: Something Professor Ross became known for was moving things from the theoretical, the abstract, maybe academic, into the real world of Wall Street. Was that a conscious thing that he did, from your observations working with him?

Musto: He had a way of modeling an economic problem that was always very elegant, and yet conclusive. In other words, he had a way of actually getting to the actual problem, modeling it in a way that just settled the question. And this is something that I saw as coming out of his exposure to the great physicists of the time, and how they would stylize a problem just enough to be able to solve it robustly. And that’s what he did, again and again. And it was impressive to watch.

Knowledge@Wharton: Any other thoughts or impressions of the man that you spent some time around?

Musto: He was a great intellectual presence. I attended the memorial service held for him at Yale. That’s where I know him from. I grew up in New Haven, [Conn.], and I met him in New Haven. And he was a professor at Yale, in between being here at Penn, and later being at MIT. His memorial service packed a very large chapel at Yale. One person after another testified about how generous and yet incisive he was. It was fun to think that a man like him, with his capabilities, had chosen our field to work in.

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