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I wish I had in my career as stressful tests as the one defined by the EBA for the European Bank Stress Test edition 2016. I would have passed them with flying colours with both hands tied behind my back.

I can’t go into the details of the report, as I am no banking expert to judge the output. All I was, almost 20 years ago, is a quant at Salomon Brothers, specialised in credits, relative value and exotic derivatives. All I know from my past banking experience is markets, and not bank ratios. Also, for reasons I will explain later, you wouldn’t judge the solidity of the banks from the test output, but from the chosen inputs. That is all you need to know. And it is not looking good, in my modest opinion.

The inputs, which defines the ‘stressful’ scenarios the banks will have to navigate and stand (and against which pretty much all of them (bar one) have gotten a ‘pass’ – even if there was no pass/fail score, that would have been your conclusion reading the newspapers-) are what really matter.

Well, the inputs then. There are a number of endogenous variables that contribute to the adverse scenario.

Here are the main ones:

- Long term interest rates
- Exchange rates
- Stock prices
- Real GDP
- House prices

I’d like to focus on interest rates, which I know better, and should be quite a critical input for banks.

The adverse scenario is defined as a shock to the baseline, in terms of basis points (100th of 1%, so 1 bp is 0.01% change in yield).

By looking at the EBA inputs table, we understand that an adverse scenario for Italy would be an increase in long term yield of 89bp (0.89%) versus the baseline scenario, and of about 120/130bp from the average yield level of 2016. The important question is whether that shock is a significant event, or a normal one. In the former case, we can genuinely talk about shock, while in the latter we cannot.

To understand the likelihood of such a shock I have taken the last 8 years of the Italian long term bond (10 year) and calculated the monthly change and its standard deviation. I am assuming changes are drift-less and normally distributed etc etc. I.e. the standard random walk theory, which is not necessarily correct if you have zero-bound interest rates, but even better it is probably conservative near the zero bound. (Plus, interests are negative today in Germany, so what do we do with the zero bound model?).

The standard deviation is 34bp/m, which means the yield is likely to change up to 0.34% up or down every month with a 67% probability. To understand the likelihood of events over 2 years, we need to extrapolate that out for 24 months. In a drift-less random walk, the variance propagates with the square root of time, hence to obtain the dispersion of prices at the 24th month we need to multiply 0.34 by Sqrt(24), which makes 167bp.

**167 is therefore a measure of rates dispersion around the average rate of 2016 (remember the drift-less assumption) for yields in 2018 taking a 10 year constant maturity Italian bond as reference.**

1-sigma captures 67% probability. Hence, we have a 67% probability that long term yields in Italy in 2018 will be between 180 (today) – 167 (1-sigma) = 13 and 180+167=347. The adverse scenario considers an yield of 300bp.

Going up to 300bp from 180bp corresponds to a +0.72 sigma event. In a normal distribution, anything below 0.72 sigma has a chance of happening of 76%, and anything above has a chance of happening of 24%.

**So a scenario that is worse than what the EBA has defined as a stress scenario (for interest rates) has a 1 in 4 chance of happening in 2 year time.** And the EBA is also assuming that only the increase of interest rates is adverse to banks, but not the decrease. So rates could go to -200bp, and banks should be OK. Yet, banks have been suffering dearly since rates went negative. Correlation is not causation, of course, but why not checking? If we consider scenarios worse than what the EBA has defined as adverse scenario in both the upside and downside, then they have a 48% probability of happening. It’s a coin toss.** 52% all is good, 48% we have a situation, Houston**. Not reassuring, if you ask me and my money.

Let’s look at real data in the market, and see if we can find some situations where yields moved substantially (in standard deviation terms).

I have only reported some cases worth of mention.

- Nov-08, the yield fell 67bp in 1 month. That is ¾ of the shock considered for the 2-year stress test.
- Nov-10 it grew 81bp, which is 90% of the 2-year shock, still in 1 month.
- Jul-11, the whole 2-year shock happened in 1 month, and in 3 months yields grew 115bp, which is 129% of the two year shock. In just 3 months!
- The month after, 80% of the shock in the other direction, and then half the 2-year shock up, in one month, and the month after 58bp, and then the month after again 95bp, almost 110% of the 2-year shock, in 1 month!
- In the months between Sep-11 and Nov-11 yields grew 195bp, which is 220% of the 2-year shock, in just 3 months.
- And then again and again, till Apr-13, with an adverse shock of almost 100% of the 2-year shock.

Yield changes of 89bp do not seem to be exceptional cases on a monthly basis, but pretty much quite a normal occurrence in the market. Imagine over 2 years.

As final proof, let’s look at 24 month historical yield changes in the IT long bond, and chart them against the adverse scenario (we use -89bp and 89bp band). It is apparent that over a 2-year horizon, rates have been more often outside of the bands than inside!

It wouldn’t be correct to generalise, but from a quick and dirty analysis, it seems that for one of the scenario inputs, and a pretty critical one for banks (long term interest rates), the stress test adverse scenario fails to meet the common sense definition of ‘stressful’ event.

With this data, I am willing to bet £100 that we will have long term Italian yield 89bp higher or lower than current level by end 2018.

I fail to be reassured knowing that banks in Europe are safe in situations that happen 76% of the time (or 52%, if you take both sides of the risk), and I have no information on whether they are safe in the remaining ‘unlikely’ 24% (or 48%) of the cases.

Using a bit of logic and game theory, the purpose of a bank stress test is to reassure markets and consumers of the solidity of the banks, to prevent a bank run. Hence, the stress test has to be positive, and cannot, under any circumstances, be negative, lest triggering the same bank run it is intended to prevent. Imagine a stress test that says that banks are insolvent. What would happen next? Bank run and bank insolvency.

Hence the solidity of the banks cannot be judged from the outcome of the test, which will surely be positive, but only from the severity of input. Because the test has to be successful, the most adverse scenario considered cannot produce negative results. For this reason, it is the severity of the adverse scenario considered in the test that defines the degree of solidity of the banks, and not the outcome of the test.

Of course, we cannot generalise these findings to all the endogenous variables, and we cannot extrapolate these limited conclusions to the whole test, but from an interest rate standpoint, having used a 0.72 standard deviation as an adverse case can only suggest me that beyond that point banks are probably not safe, and because 0.72 sigma can’t really be considered a stressful situation, but more like a run of the mill scenario in interest rate markets, I fail to feel reassured on the solidity of European banks by the stress test. At least from an interest rate shock stand point.

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