In 2005 I was interviewing for a job as Risk Manager with Genworth Financial. I was working a gig up in Armonk, NY so I hopped a car to the GNW office and met with Mark Griffin, at that point the Chief Risk Office (CRO) for GNW. After some small talk, Mark asked me the single most interesting interview question I’ve ever been asked. I don’t recall the exact wording, but the gist was:
[caption id="attachment_825” align="alignleft” width="250” caption="André-Louis Cholesky is my homeboy”][/caption] When I did a brief post three days ago I had no plans on writing two more posts on correlated random number generation. But I’ve gotten a couple of emails, a few comments, and some Twitter feedback. In response to my first post, Gappy, calls me out and says, “the way mensches do multivariate (log)normal variates is via Cholesky. It’s simple, instructive, and fast.
So after yesterday’s post on Simple Simulation using Copulas I got a very nice email that basically begged the question, “Dude, why are you making this so hard?” The author pointed out that if what I really want is a Gaussian correlation structure for Gaussian distributions then I could simply use the mvrnorm() function from the MASS package. Well I did a quick and, I’ll be damned, he’s right! The advantage of using a copula is the ability to simulate correlation structures where the correlation is different for different levels of values.
A friend of mine gave me a call last week and was wondering if I had a little R code that could illustrate how to do a Cholesky decomposition. He ultimately wanted to build a Monte Carlo model with correlated variables. I pointed him to a number of packages that do Cholesky decomp but then I recommended he consider just using a Gaussian Copula and R for the whole simulation.
[caption id="attachment_705” align="alignleft” width="283” caption="“as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know.” US Defense Secretary Donald Rumsfeld, February 12, 2002”][/caption] I’ve been a long time reader of the blog “Messy Matters” (which invokes terrible images now that I am potty training a toddler).
[caption id=”” align="alignleft” width="224” caption="Plymouth Rock… or something”][/caption] There’s an interesting article in the WSJ this week about poultry farmers who grow for Pilgrim’s Pride (PPC). PPC is in bankruptcy and have canceled grower contracts with 400+ poultry growers. In poultry farming the farmers own the chicken houses and provide the labor but the poultry company (Pilgrim’s Pride, Tyson, Perdue, etc) own the birds and provide the feed. The producers get paid for every pound they put on the flock and they get extra bonuses for efficiency.
Let me start by saying that I like Nassim Nicholas Taleb and Benoît Mandelbrot quite a lot. I don’t agree with them all the time, but that is generally true of people I like. I recall reading Mandelbrot’s book The Misbehavior of Markets: A Fractal View of Financial Turbulencesome years ago and being struck by how much sense Mandelbrot makes. It helped that his early work related to markets was in cotton prices and I am an agricultural economist.