Roy’s (1952) Revisited in Today’s Investing Contexts

Abstract

A. D. Roy’s “Safety First and the Holding of Assets” (Econometrica, 1952), is not only highly regarded but also considered one of the cornerstones of portfolio theory. Roy (1952) provided a modern approach to wealth multiples, information-based risk management, which included a re-evaluation of the role of cash reserves deployed in a multiperiod setting. These ideas and the work derived from them have contributed to progress in the modeling of inventory management, money demand, and portfolio insurance (value-at-risk being a modern incarnation of Roy’s safety-first principle). However, not a single existing study in the finance literature employed a strict application of Roy’s investing approach, directly as it was laid out in his original contribution. This is exactly the objective of our study. Furthermore, at each step of the application of Roy’s model, we compare it to the corresponding step in Markowitz’s (1952, 1959) mean-variance model. We find that the most forward-looking elements in Roy’s model, mentioned above, decouple revenues from risk. Specifically, the variance-covariance matrix, a mainstay of mean-variance analysis, gets dislodged from the computations, which prevents the calculation of the efficient frontier, as noted by Markowitz (1987, p. 37). We show that revenues-risk integration takes place in Roy’s model at the level of expectations, as in expert assessments, beyond the purely descriptive statistics of the mean-variance model. What appear as limitations from the standard mean-variance model viewpoint are, therefore, turned into advantages in certain contexts such as venture capital, angel investing, and private equity.