From Jawwad Farid

UNRISK Part 2 – Understanding the distribution

Before you completely write this post off as statistical gibberish, and for those of you were fortunate enough to not get exposure to the subject, let’s just see what the distribution looks like.

Not too bad! What you see above is a simple slotting of credit scores across a typical credit portfolio. For the month of June, the scores rate from 1 to 12, with 1 good and 12 evul. The axis on the left hand side shows how much have we bet per score / grade category. We collect the scores, then sort them, then bunch them in clusters and then simply plot the results in a graph (in statistical terms, we call it a histogram). Drawn the histogram for a data set enough number of times and the shape of the distribution will begin to speak with you. In this specific case you can see that the scoring function is reasonably effective since it’s doing a good job of classifying and recording relationships at least as far as scores represent reasonable credit behavior.

So how do you understand the distribution? Within the risk function there are multiple dimensions that this understanding may take.

The first is effectiveness. For instance the first snapshot of a distribution that we saw was effective. This one isn’t?

Why? Let’s treat that as your homework assignment. (Hint: the first one is skewed in the direction it should be skewed in, this one isn’t).

The second is behavior over time. So far you have only seen the distribution at a given instance, a snapshot. Here is how it changes over time.

Notice anything? Homework assignment number two. (Hint: 10, 11 and 12 are NPL, Classified, Non performing, delinquent loans. Do you see a trend?)

The third is dissection across products and customer segments. Heading into an economic cycle where profitability and liquidity is going to be under pressure, which exposure would you cut? Which one is going to keep you awake at night? How did you get here in the first place? Assignment number three.

Can you stop here? Is this enough? Well no.

This is where my old nemesis, the moment generating function makes an evul comeback. Volatility (or vol) is the second moment. That is a fancy risqué (pun intended) way of saying it is the standard deviation of your data set. You can treat volatility of the distribution as a static parameter or treat it with more respect and dive a little deeper and see how it trends over time. What you see above is a simple tracking series that is plotting 60 day volatility over a period of time for 8 commodity groups together.

See vol. See vol run… (My apologies to my old friend Spot and the HBS EGS Case)

If you are really passionate about the distribution and half as crazy as I am, you could also delve into relationships across parameters as well as try and assess lagged effects across dimensions.

The graph above shows how volatility for different interest rates moves together and the one below shows the same phenomenon for a selection of currency pair. When you look at the volatility of commodities, interest rates and currencies do you see what I see? Can you hear the distribution? Is it speaking to you now?

Nope. I think you need to snort some more unrisk! Home work assignment number four. (Hint: Is there a relationship, a delayed and lagged effect between the volatility of the three groups? If yes, where and who does it start with?)

So far so good! This is what most of us do for a living. Where we fail is in the next step.

You can understand the distribution as much as you want, but it will only make sense to the business side when you translate it into profitability. If you can’t communicate your understanding or put it to work by explaining it to the business side in the language they understand, all of your hard work is irrelevant. A distribution is a wonderful thing only if you understand it. If you don’t, you might as well be praising the beauty of Jupiter’s moon under Saturn’s light in Greek to someone who has only seen Persian landscapes and speaks Pushto.

To bring profitability in, you need to integrate all the above dimensions into profitability. Where do you start? Taking the same example of the credit portfolio above you start with what we call the transition matrix. Remember the distribution plot across time from above.

THis has appeared previously in Jawwad’s excellent blog.