Rortybomb’s DIY Stress Test 1: Background and Theory

From the Congressional Oversight Panel’s report on the Stress Test:

Because results are presented on the “more adverse” scenario alone, the ability to extrapolate results from a single set of data is impaired. Even though the “baseline” scenario was likely too optimistic, publishing the results from that scenario would have improved transparency and enabled private analysts, who can play an important role in the way information is used, to present their own predictions and analyses.

Which leads Felix Salmon to comment: “If we knew how much difference there was between the baseline test and the more-adverse test, then analysts could at least do a rough-and-ready extrapolation to any forecast they liked. With only the one set of datapoints, however, it becomes impossible…”

This sounds like a challenge, so let’s see what we can do. There’s some modeling fingerprints in the Stress Test documentation that we can extract some information from, and we’ll do that at the end when we create our own DIY Stress Test spreadsheet. First though.

What it means to be Adverse

It is starting to look like the “adverse scenario” numbers, numbers that should have only had a 10% chance of happening, are going to reflect reality. So there is a meme going around that using the adverse scenario’s values is a good way to go, since they have turned out to be pretty accurate. However, this misses a key conceptual risk management point – if for some reason we end up in a situation in the risky portion of our possibilities, we need to re-examine the tail risk given our situation at hand. We cannot assume that since things have gone bad, they are done going bad. The idea of a tail estimate, especially in capital reserving, is a big deal. There’s a reason they estimated losses at a 10% likelihood. At any moment, we want to be able to survive a turn of events up to and including that tail. (And 10% is generous. We usually want something under 1%.)

To put it in non-financial terms, if you are driving, a tail risk event is that you could get in a car accident. If you get in an accident, the tail risk is no longer you being in an accident – the tail risk is now being trapped in a burning car, or being pushed into other cars causing more accidents, or your airbag/seat belt malfunctioning. It is important to update our expectations of risk as we go forward. And to expect banks to be able to not just survive but be able to handle an adverse shock is a reasonable expectation (to say the least) for our government.

Estimating Losses

Stress test formula: TOTAL LOSSES = TOTAL AMOUNT * TIME * EXPECTED LOSS %

That’s it. You do that by each asset class (home loans, credit cards, commerical real estate loans, etc.), add up the results, and we are done. Here is the adverse scenario’s summary for Bank of America (click through for a bigger image):

boa_stress_test

Bank of America has $325bn in first-lein mortgages (it has $22.1bn of losses when it loses 6.8%, so 22.1/.068 is the total amount). This is constant for all scenarios, and something a bank can tell you after a day checking some spreadsheets. Time is 2 years (till the end of 2010), and we normalize all our loss expectations for 2 years. So those are simple.

All the drama is in figuring out expected losses. How much money will be lost in mortgages between now and 2010? As you can imagine, that’s the complicated part. Do you use statistical relationships? Do you use option pricing theory and make the factors endogenous like the Merton model? Do you use consistent numbers across banks – are Well’s Fargo’s credit card losses the same percentage as American Express? This is very complicated, and the Fed appears to have let the banks use their own models in large part. Adding all these up, across the different banks, is all the stress test is. Indeed check out this summary chart from the Fed release (page 9), which is just all of those charts above for each bank. That chart will be the backbone of our spreadsheet.

Now with one point we can’t extrapolate. However the Fed did include this (page 6):

EL_Stress_Test

Here we see expected losses per asset class per scenario per unemployment rate. More importantly, we see the difference between the two. So we can do a quick linear extrapolation between the two to get a value of expected loss % per asset class for any unemployment rate. This is really a down-and-dirty, but it is all we have. We take this change and add it to the expected losses % per bank in their adverse numbers (not the same as the average amount – unique per bank), and are then about to get new expected losses %. And since we can back out all the total amounts from the original numbers, we have everything we need. So in the next entry we’ll create a spreadsheet capable of doing that.

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One Response to Rortybomb’s DIY Stress Test 1: Background and Theory

  1. Pingback: TARP Overseer’s Dream Comes True: Rortybomb DIY Stress Test | Abnormal-Return

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