Research Discovers Breakthrough For Computing Risk And Return Measures Of Financial Securities
When investors buy fixed income securities and financial derivatives, how can they estimate the “expected returns” they hope to earn over short periods like one month or six months? How can they measure the riskiness of these returns?
A new paper co-authored by Sanjay Nawalkha, professor of finance at the University of Massachusetts Amherst Isenberg School of Management, provides the first rigorous theoretical framework for the derivation of formulas for expected returns and risk measures of fixed income securities and financial derivatives, which are worth more than $132 trillion in combined valuation globally.
Valuation and risk-return analysis are done using probability measures – either real or invented – in the finance field. Before this significant new discovery by Nawalkha and Xiaoyang Zhuo, assistant professor at the Beijing Institute of Technology School of Management and Economics, the valuation of all fixed income securities and financial derivatives relied upon a risk-neutral probability measure (“Q”) discovered in the Nobel Prize-winning papers that form the basis of the Black-Scholes-Merton model. After almost 50 years, Nawalkha and Zhuo have created a new probability measure (“R”), which, together with its variants, subsumes both the real probability measure and the risk-neutral measure and its variants.
Using the new Nawalkha-Zhuo framework, one can derive not only the valuation formulas but also the formulas for the expected returns and risk measures over an arbitrary holding period for innumerable fixed income securities and financial derivatives.
“For example, if this machinery was available in, say, 2005, there is some chance that collateralized debt obligation (CDO) fund managers would have been aware of the highly negative ‘expected returns’ in this market, which could have slowed down the bubble created in the housing market in 2008,” Nawalkha says.
Darrell Duffie
This paper was a breath of fresh air when Sanjay sent it to me a few months ago. I was kind of blown away by the fact that I hadn’t realized that I could do this for so many years, when I was doing all these kinds of calculations manually.
Darrell Duffie, Adams Distinguished Professor of Management and Professor of Finance at Stanford University, after reviewing a first draft of Sanjay Nawalkha’s research in 2020
The paper, “The Theory of Equivalent Expectation Measures for Contingent Claim Returns,” was published in the October 2022 issue of The Journal of Finance, the journal of the American Finance Association. Nawalkha presented the first draft of the paper in the fall of 2020, at the annual conference of the Center for International Securities and Derivatives Markets (CISDM), where it was discussed by Darrell Duffie, the Adams Distinguished Professor of Management and Professor of Finance at Stanford, who is one of the most cited professors in finance.
“This paper was a breath of fresh air when Sanjay sent it to me a few months ago,” Duffie said during the conference. “I was kind of blown away by the fact that I hadn’t realized that I could do this for so many years, when I was doing all these kinds of calculations manually, kind of plugging coefficients in the underlying processes to compute everything. And now all I have to do is change to a nice measure and derive the behavior of the stochastic processes of interest under that new measure, and then just go for it.”
Duffie ended his laudatory comments by saying, “I wanted to make it crystal clear that this is a big machine. It’s just waiting for applications.”
The complete paper, “The Theory of Equivalent Expectation Measures for Contingent Claim Returns,” is available online from The Journal of Finance.