prior probability

In Memoriam: Bella Benvenutti

Our hearts are broken, yet again. My wife and I are mourning another tragic and untimely loss. My former student and dear friend Jan Rene Benvenutti lost the love of his life — his beloved daughter Bella, who was only seven years old.

In honor of my late colleague and dear friend Ray Sturm (pictured below), today I am posting a link to his most-cited work, his 2003 paper “Investor Confidence and Returns Following Large One-Day Price Changes” in which Ray identified an asymmetry in investor reaction to stock market price shocks. In Ray’s own words, “my findings indicate that investors respond differently to negative price shocks than to positive price shocks. In particular, large price decreases generally drive positive post-event abnormal returns, while large price increases do not drive positive or negative abnormal returns.” According to Google Scholar, Ray’s 2003 price-shock paper has been cited at least 50 times, a remarkable and noteworthy feat in the world of academia.

As a follow-up to my previous post in honor of my late colleague and friend Ray Sturm (pictured below), who died recently at the too-early age of 58, today I am a posting a link to his beautiful 2008 paper “Does time have value? An empirical examination of the put option embedded in refundable U.S. air fares,” a research article that Ray co-authored with Drew Winters, a respected professor of finance at Texas Tech.

To the point of this post, of the two dozen or so scholarly papers that Ray published during his academic career, his 2008 time-value paper is one my favorites because of its “Coasean spirit” — i.e. the way in which Ray and Drew combine economic theory and actual practice. Below is an excerpt (footnote omitted):

“The time value of money is a fundamental tenet of finance. Specifically, under any positive discount rate, a dollar today is unambiguously worth more than a dollar tomorrow. Equally unambiguous is the value of time in the price of an option. Specifically, all standard put and call options increase in value as the time to expiration increases. In this paper, we examine ticket pricing in the airline industry and argue that the price of a refundable airline ticket consists of two components—the price of a nonrefundable ticket plus the price of a put option. The refundable ticket is obviously more valuable than the nonrefundable because the put option component gives the owner the right to sell the ticket back to the airline at its original cost. Accordingly, we apply the standard relationship between time to expiration and the value of an option developed in option pricing theory to determine whether airlines price the value of time to expiration in the put option embedded in refundable ticket prices in a manner consistent with theory.”

How many faculty have you ever seen ride to class on a skateboard, compete in surf championships, or play in a rock band? My dear colleague and friend Dr Ray Sturm (pictured below, far right) was a one-of-a-kind scholar, bon vivant, and original researcher (see here and here) who did all these things. Our paths had crossed many times — he was a fellow “lecture capture” professor and kindred spirit at my home institution, one of the few souls who made my little corner of the world a better place. I will be devoting my Spring and Summer 2022 classes to his memory.

Alternate Title: A Simple Model of Drug Smuggling

Happy New Year! Having re-binged Narcos Colombia and Narcos Mexico during the holidays, I was inspired to develop a simple model of drug smuggling.

First off, assume that p is the probability of interdiction on any cross-border smuggling operation; as a result, the expected number of trips across the border until a drug shipment is captured is 1/p.

Next, assume that the profits are $X for each successful smuggling trip, and further assume that the value of the drugs and the value of the truck, airplane, or other vessel transporting the drugs totals $Y. (In reality, the values of X and Y may vary per trip; I, however, am holding both values constant for simplicity.)

On the last trip, the transport vehicle is captured and no profits are made. Therefore, in expectation, we will have [(1/p) – 1] smuggling operations earning $X per trip and one trip losing $Y.

According to standard price theory in economics, the ex ante expected profit in equilibrium of a rational, risk-neutral smuggler should be zero. This logic can be stated formally as follows:

Y = [(1/p) – 1]X

which can be further simplified as follows:

Y = X(1 – p)/p

Given these super-simplifying assumptions, if p = ½ (i.e. a 50% probability of interdiction), then Y = X. In other words, the smuggler’s initial investment is recouped in just one smuggling operation! Put another way, if we want to combat smuggling, the probability of detection must be greater ½.

If, however, p is below ½, smuggling will always be profitable. For example, if p = 1/10, then Y = 9X. That is to say, the smuggler will recoup nine times his initial investment when the probability of interdiction is just 10%. More generally, this simple model shows that the lower the probability of detection, the more profitable smuggling will be.

So, what is the actual rate of detection? Your guess is as good as the feds’!

Bonus (1/2): I have included an acoustic version of the Narcos theme song “Tuyo” by Rodrigo Amarante below.

I will continue with my review of Nozick in the next day or two. In the meantime, however, check out this misleadingly-titled report by Sarah Holder “The Year Basic Income Programs Went Mainstream“, which begins by noting that 20 guaranteed-income pilot programs have launched in cities and counties across the U.S. since 2018, with more than 5,400 families and individuals receiving between $300 and $1,000 per month. More accurately, Ms Holder’s report also acknowledges that these “local programs are small in scale and duration” and that calls for a federal guaranteed income policy have not yet succeeded (link in the original). That’s putting it mildly! My 2020 paper “Guaranteed Income: Chronicle of a Political Death Foretold” explains why these efforts are doomed to failure.