I have now been doing this “risk” business for more than a decade. Eleven years ago, right about this time, I was rudely introduced to my first risk application. Fresh from my actuarial exams, I was stumped on an interview question dealing with moments of a distribution. I have read the material, struggled with it, taken an exam on it and passed it. But in the room overlooking Fleet Street in London, in the month Russia defaulted on its domestic debt, I couldn’t explain it.

A question dealing with the moment generating function has an exact and mathematical answer. These days, across three continents, clients ask more difficult questions. “Does risk really works? Or is it smoke and mirrors” and/or “what is the one thing I can do to better manage my exposures?” While risk managers are generally stereotyped as the quite sort with short snappy answers (or little to say as some uncharitable critics suggest), it has been difficult to come up with a catchy symbolic one word answer to the above two questions.

Sometime last year while reviewing a list of competitors I came across an interesting name “Unrisk”. Same concept as insured, uninsured. Risk, unrisk. Just the word I had been looking for. Catchy, symbolic and with far more cool/mystique factor than just plain simple risk management. A bright new term for an age old profession. When I saw it for the first time, I instantly knew that Unrisk would represent a state of institutional nirvana that we would achieve when we have done all that we could possibly do to manage risk on our platforms.

Next time a client would ask for a guide to a risk based paradise, you would simply give him the road map to the Unrisk state. The real question would be what you would put on that road map? And would it really protect you from all that an evil generating function could throw at you.

Second question first. No the unrisk state won’t really guarantee immunity from the evil eye. Neither will we stop booking risk. We will keep on carrying exposures on our balance sheet and will load as much risk as we can carry, sometimes even more.

And yes it won’t stop us from falling, stumbling or faltering.

Just that the frequency and severity of our nightmares would reduce a bit; we would still degrade but we would do it far more gracefully.

My personal recipe for the state is a short one. It only has one item on it.

**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.

Here is another way of looking at it. It is called a transition matrix. All it does is track how something rated/scored in a given class moves across classes over time

How do you link to profitability?

This is how profitability is calculated generally. Take the amount you have lent, multiply it by your expected adjusted return and voila, you have expected earnings. But that is not the true picture.

What you are missing is the impact of two more elements. Your cost of funds (the money you have lent is actually not yours. You have borrowed it at a cost and that cost needs to be repaid) and your best and worst case provisions. So true profitability would look something like this.

That is a pretty picture if I ever saw one. Especially when you compare the swing from the original projected number. Back to the question clients ask. Where do projected provisions come from? From transition matrices. And where do transition matrices come from. From applying your understanding of your distribution to your portfolio.

Remember these are not my ideas. They are hardly even original. The Goldman trader who first asked me about moment generating functions wanted to understand how well I understood the distributions that were going to rule my life on Fleet street?

Full credit for posing the distribution problem goes to our friend NNT (Nicholas Nassim Taleb) who first posed this as getting comfortable with the generating function problem. He wrote all of three books on the subject and then some. Rumor has it that he also made an obscene amount of money in the process (not with book writing, but with understanding the distribution). All he suggested was that before you took a punt, try and understand how much trouble could you possibly land in based on how what you are punting on is likely to behave in the future. Don’t just look at the past and the present, look the range, likely, unlikey, expected, unexpected.