I can’t tell you how much engineering I’ve learned since I started studying finance. 🙂
Perhaps I should first say that I didn’t graduate from a top engineering school. But I think (or thought) I learned the basics fairly well and managed to work my way up to Principal R&D Engineer at a digital communications firm before striking out on my own as an independent contractor.
But if I had started this CFA program earlier, I might have even made Director of R&D! I mean, I can’t believe the important stuff I’ve learned while working my way through Vol. 1 of the study guides. It’s mostly statistics, but it really would have been helpful to know some of this earlier.
Maybe I did actually learn this material in college. I’m sure I did, because I had to take statistics classes. But at the time my 19-year old brain was probably focused on short-term memorization to pass tests, not how any of this stuff might actually be useful later on and should therefore be retained.
Let me just pick a few highlights. All of you properly educated stats daddies out there, keep the heckling down to a roar.
#1: Kurtosis: Is it normal? Looks normal!
Often when examining noise in communications channels, we’d plot the probability density function (PDF) to see if it appeared to be bell-curve shaped. If it looked so, we assumed the distribution was indeed normal (we called it Gaussian) and designed our algorithms around this.
Somehow it never occurred to me that you could plug a few numbers into an equation (excess kurtosis) and get a quantity proportional to just how short-tailed, normal, or fat-tailed the distribution actually is.
Not only would I have gotten mad street cred in meetings for using the word leptokurtic, I also could have perhaps designed some algorithms to work better by identifying when impulse noise (which has a fat-tailed PDF) was present, and using different noise distribution assumptions then.
#2: Standard Deviation: Means exactly what?
Sure I’ve known for years how to compute standard deviation. And I’ve also known that it’s proportional to the spread or dispersion of individual samples around a mean. But, embarrassingly, I somehow left college without knowing (or remembering) that standard deviation allows you to explicitly define confidence intervals.
I’m talking about the stuff at the bottom of pg. 391 of Volume 1.
95% of all samples should fall within 2 standard deviations of the mean.
99% of all samples should fall within 3 standard deviations of the mean.
I always used standard deviation just to be able to compare the performance of two estimation algorithms, so that I could pick the one with the lower average error. But being able to bound the error spread with confidence intervals would have given me even greater insight into whether what I had designed so far was good enough.
And I love the Chebyshev inequality on pg. 289 that lets you describe a confidence interval even if you don’t know the underlying distribution!
#3: Median: Simple, Elegant
You’ll get a howl out of this one.
What do you do when you want to compute an average, but you may have one or two huge outliers that will bias the result? Well, if you know even high school statistics you use the median instead of the mean. But if you’re me…
(1) Compute mean of data set
(2) Set threshold some multiple above mean to identify samples with extreme values
(3) Either clip those values to the threshold or discard them altogether
(4) Repeat above steps until you no longer have outliers biasing computation
#4 Confidence Intervals: More iterations, please!
Working in R&D means doing lots of simulations. And when performing those sims I had a very black & white view about the number of iterations needed to be able to accurately estimate parameters.
In short, what I always did was run a huge sample size such that I reduced my confidence interval to an extremely small spread.
In my mind, it was either “I’ve run enough iterations to give you an accurate estimate” or “you’re going to have to wait until I can run more iterations to be able to give you an accurate estimate”.
However, using t-distributions & confidence intervals you can cover all the grey areas in between. So instead of telling the executives that I couldn’t give them an accurate figure in the time frame they needed due to long simulation time, I could have actually given them a preliminary estimate, along with say a 95% confidence interval to let ’em know how off that preliminary might be.
Well I hope you’ve enjoyed my engineering blunders. Perhaps it’s divine retribution for that annoying t-shirt I used to wear in college…
In my defense I did actually study a completely different area of engineering than I ended up working in. But the bottom line is that the CFA program is making me a better engineering contractor. 🙂
And hey, who needs to be Director of R&D when I’m now CEO…
… of my own company …
… of which I am also the sole employee …
… and therefore also the janitor.
In case you’re interested, my bookmark is currently at pg. 459 of Volume 1. Just can’t seem to make it to Volume 2…