Seventy years ago, an economist named Harry Markowitz received his Ph.D. from the University of Chicago, based on his doctoral thesis about the proper allocation of investments. Now known as Modern Portfolio Theory, it laid out a framework for how to get the best return on stocks in light of the risk involved.
A new upgrade to MPT, seeking to refine how to assess risk for various types of securities, comes in a working paper, “Equivalent Expectation Measures for Risk and Return Analysis of Contingent Claim Portfolios,” by two young economists.
Markowitz, who won a Nobel prize for MPT, died last June at age 95. He invented a mathematical concept to measure the risk on a collection of assets in terms of how they move up and down together. Before his research, scholars focused on individual securities, not on how they might offset one another, or on the market writ large. Other refinements to MPT have been launched since, notably the work of another Nobel winner, William Sharpe.
The two academics who penned the new paper—Sanjay Nawalkha, from the University of Massachusetts, Amherst, and Xiaoyang Zhuo, at the Beijing Institute of Technology—created a new class of probability gauges, called “equivalent expectation measures,” which produce formulas to find the future prices of virtually any financial securities over a given holding period. Their concept encompasses Treasurys, corporate bonds, mortgage-backed securities and derivatives: options, futures and swaps. These securities are collectively called “contingent claims.”
The professors’ approach allows measurement of the risk (known in economist-speak as the “variance”) on, for example, a three-month call option for the S&P 500 for a one-month holding period. The EEM concept also permits investors to measure the “covariance” (i.e., how two different securities move in relation to one another, useful when constructing a portfolio). Such as that of a three-month call option on Tesla stock and a six-month call option on Apple stock during a two-month holding period for both.
A spin-off version of this paper is already accepted by the Journal of Investment Management. This journal is also organizing a conference in March at the University of California at San Diego, to honor Markowitz.
In an interview, Nawalkha termed it “serendipitous” that the new concept “extends applications to Markowitz’s work to all contingent claims [and] coincides with the conference.”
Previously, Nawalkha and Zuo authored a paper refining another storied financial model, Black-Scholes, to calculate the expected risks and returns of derivatives over a finite period, say over three or six months.
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Tags: Black-Scholes, Derivatives, equivalent expectation measure, Harry Markowitz, Modern Portfolio Theory, Sanjay Nawalkha, University of California at San Diego, William Sharpe, Xiaoyang Zhuo