In the movie “Cool Hand Luke”, there is a scene in which the warden, holding his rifle, wearing his mirrored sunglasses, and standing atop a hill above Paul Newman, tells him that “What we have here is a failure to communicate!” That is the metaphor for this post.
How many times have you explained an appraisal to a client and gotten a blank stare or a comment to the effect that “well, I don’t understand that at all, but you are the expert and you must know what you are doing.” I have gotten many such stares and comments, particularly regarding things like:
- Strategic acquirers and synergy not being part of fair market value.
- Asset versus stock sales.
- Build-ups of discount and capitalization rates.
- Anything involving statistics or regression analysis.
- And much, much more…
Things like these that are familiar to us because we work with and study them every day over many years may be new, foreign, and threatening to our clients. This puts the onus on us to explain them well enough that they do more than accept us on faith, even if they do not grasp every last detail or nuance.
Increasingly, however, I find myself in a position like these clients when it comes to the application of option pricing theory to valuation of stock options and quantification of the lack of marketability discount. The authors of the Black-Scholes Option Pricing Model earned Nobel Prizes for their work, their model is routinely applied on Wall Street and by sophisticated business appraisers, and there is much cutting edge academic research being published, yet…
For the life of me, despite years of reading the literature and supplemental self-study of the daunting underlying mathematics, I am no closer to understanding what is really going on with option pricing than I was when I learned of it in school 40 years ago. I am miles away from being able to explain these concepts to others. I find myself saying things like “these models and techniques are generally accepted in the financial community and the appraisal profession, well published, and applied extensively”, which is really the same as “I don’t understand that at all, but you are the expert and you must know what you are doing.” In this area, I am supposed to be expert and I do NOT know what I am doing (well enough to be comfortable).
This brings me to a request: is there a (mathematical) doctor in the house who can explain:
- The fundamental assumptions that option pricing models require and how they compare with reality. What is being assumed, why, and how does that compare with the real world? Yes, the Black Scholes model requires six inputs which are “easy” to determine, but there are many underlying structural assumptions (lognormal returns, etc.) built into those models that are not readily apparent. This is consistent with my ongoing mantra of AORTA: Assumptions OverRide The Arithmetic. But even if someone can explain and assess those assumptions, I still feel the need to…
- Understand the arithmetic itself. Option models are based on differential equations that relate the rates of change of various phenomena that determine prices. Those equations can be solved to provide general formulas for the value of the option over time. With additional assumptions (initial conditions), specific values can then calculated. To put it bluntly, I do not understand the mathematics.
I am sure there is someone out there who can explain the assumptions and mathematics in a way less sophisticated individuals like me can understand and in turn relay to clients. Please, please identify yourself and take on this challenge. You will do the appraisal community a great service! After all, failure to communicate…is not an option!