# Chocolate or Vanilla?

As always, comments are welcome.

Risk Measures basically comes in two flavors: chocolate or vanilla.  Really.  Sometimes it’s described as two styles: “Impact” or “Probability”, but I think of them as flavors.

One school of thought is that the best way to estimate a portfolio’s risk is to identify what drives each security’s value and then stress all those factors.  This tells you what impact you can expect on your portfolio for each of those different stresses.  Let’s call this Vanilla.

The chocolate school says that the best way to estimate a portfolio’s risk is not to treat each asset class separately like the plain vanilla people, but rather to estimate probabilities of various losses.

These two approaches really are as different as I’m suggesting.  The vanillas like to understand the sensitivity each security has to real markets.  Let’s work through a real life example with a simple bond.  It’s not good enough just to know that bond prices go up when interest rates drop, and vice-versa.  We also need to know by how much they’ll go up.  For this, the vanillas calculate the bond’s duration and convexity, two numbers that can be plugged into an easy formula to estimate how much the bond’s value will change when interest rates move.  Once you know the duration and convexity of every bond in your portfolio, it’s straightforward to start making some scenarios – interest rates down 1.00%, down 0.75%, down 0.50%, down 0.25%, no change, up 0.25%, up 0.50%, up 0.75%, and so on.  Since you can calculate how each bond responds to each of these changes, you can also calculate how the entire portfolio shifts in response to each of these.  See how easy risk management is?  This kind of analysis tells you what the impact is of different interest rate shifts on your portfolio, but it doesn’t tell you anything about how likely those shifts may be.

Time for chocolate.  Instead of simply estimating what happens to the portfolio if the markets do one thing or another, this approach tries to quantify how likely certain losses are.  Value-at-Risk is the poster-child chocolate calculation:  99% of the time, your portfolio’s return should be better than X.  In other words, you have a 1% chance of doing worse than X.  Calculating this X is not easy, but there are plenty of short-cut formulas to make it do-able.  Another example of a chocolate style calculation involves credit risk.  Imagine a bond issued by a company that might just go under.  The expected value of the bond is the probability of default times the expected loss if it does default (technically it’s one minus that number, but don’t worry about that).  The default probability is usually gotten from the credit rating, and the ‘loss given default’ is estimated from bonds of similar companies.  The problem with chocolate analyses is that it’s actually incredibly hard to estimate probabilities of rare events accurately.  When you go back and test the predictions / estimates of the probabilities, they don’t often pass appropriate quality tests.  In other words, doing this right is hard, takes time and effort, and not everyone will be successful.

So, what’s the best thing to do?  Go for classic vanilla or decadent chocolate?  My suggestion is simple and obvious (exactly what this food analogy is good for): have one scoop of each.  There’s no reason that a fund manager has to pick one over the other – both of them have their place in the risk management tool box.  But for some reason, different parts of the industry tend to rely on one or the other.  Maybe they’re not thinking about them in terms of flavors: because once you call them chocolate and vanilla, the fact that you want one of each becomes obvious.