Risk, Ownership, and Control

Conventional models view risk as an exogenously generated random process. Also, especially for financial assets, very often it is assumed that returns are normally distributed, an assumption that comes with considerable baggage. Recent innovations in numerically intensive methodology (made easier by Mathematica) allow modeling using non-normal heavy-tailed distributions. Another common—and realistic—assumption for financial assets is the separation of ownership and control. This Demonstration provides a way of thinking about how those assumptions might be relaxed for all investments but especially for individually owned investment real property.

The ownership of private real estate investment includes management burdens but combines ownership and control, providing the entrepreneur at least some opportunity to "shape" his environment. This Demonstration describes a random process that produces heavy tails because its probability (by changing the shape of the die) is influenced by an ownership efficiency factor (modeled as a taper). A standard die delivers a discrete {, , , , , } probability mass function of equal probabilities. In the alternative, the combination of ownership and control modifies the probability function to the extent the owner is efficient at managing the enterprise. In this case, the taper of the die permits different probabilities for it to land on different sides. Naturally, the preferred outcome is for a die to land on a side where the payoff on the opposite side is high. Thus, a skilled entrepreneur arranges his investment strategy so as to maximize the probability the die would land in a way that most benefits him. Other, less preferred, outcomes are also possible. The investor seeks to minimize the probabilities of those. This concept was perhaps first observed by Frank H. Knight in his path-breaking work, Risk, Uncertainty and Profit (1921).