Streetwise Professor

February 2, 2013

All Large Calculations Are Wrong. So DIVERSIFY THE RISK.

A tag-team of my favorite blogs-the wonderfully sardonic (and insightful) Rhymes With Cars and Girls and the less sardonic (but equally insightful) Deus ex Macchiato-discuss the fact that model-based risk-weighted capital calculations on the same assets differ substantially between models/banks.

From this, DEM concludes the need to centralize capital calculations:

he answer is clear. Centralize and standardise capital calculation. Throw all those internal models away, and use one common, regulator developed approach. Now that a lot of progress has been made on trade reporting, the data infrastructure exists to do this — or least it wouldn’t be too hard to extend what does exist to do it. Developing the models would be a huge undertaking, but compared to having each large bank do it individually, a central infrastructure would be cheaper and more reliable, and anyway you could pick the best of individual banks’ methodologies. You could even spin out the var teams from four or five leading banks into the new central body — just don’t pick the bank whose IRC is less than 10% of the average answer…

Crimson Reach at Rhymes is more cautious, repeating his theme that All Large Calculations are Wrong.  He concludes:

In other words, it’s a Large Calculation. But as RWCG readers know, all large calculations are wrong. So, I’m skeptical that the answer to this is to ‘centralise’ the calculation – i.e., make it even larger.

I’m on Crimson’s side on this one.  (Sorry, David.)

Centralize capital calculations?  No. No. No. No. No fucking no.

Crimson is right: all Large Calculations Are Wrong.  Including those-and I would suggest, especially those-undertaken by some Centralized Authority, e.g., The Wizard of Financial Oz.

What would you rather have?  Randomly distributed mistakes, or perfectly correlated ones?

The answer, it seems to me, is gob-smackingly obvious.  Randomly distributed.  Perfectly correlated errors are a recipe for systemic risk.  All banks will crowd the risks that the model underprices and avoid the risks that it overprices.  If an adverse shock hits the crowded investment, every bank is screwed simultaneously.  All will need to liquidate their positions in that asset, or in other assets.  Every bank will have fire sales at the same time.

That’s what we want to avoid.  That’s what creates a systemic risk.

We want to diversify model risk, not concentrate it.  Centralized calculation concentrates it.  I actually see an evolutionary benefit in the wide range of model risk weights that DEM bewails.  That represents a diverse ecosystem of entities with divergent views that is less vulnerable to a single shock.  Yeah, that shock will crater some banks, but not all of them. When I think of any-ANY-centralized calculation, I think of the Socialist Calculation Debate.  I also think of monocultures that are dangerously vulnerable-systemically vulnerable-to a single shock.  Think of the devastation that smallpox wreaked on native American populations.  A single shock can crater everybody all at once.

If that happens, who is the buyer in the fire sale?  If there are no buyers in the fire sale, how low can prices go? Pretty damn low.

Crimson is right.  All Large Calculations Are Wrong.  The answer to this problem is exactly the opposite that DEM suggests.  Diversify this risk.  Don’t concentrate it.  Don’t sort on it.

We need less centralized control-freakishness.  Not more.  A lot less.  Mistakes are inevitable.  Create a system that induces them to make uncorrelated mistakes (or at least, mistakes with low correlation).  Don’t induce perfect correlation in errors.  I say again: don’t induce perfect correlation in errors.  Create a diverse ecosystem, not a monoculture.   Imposing uniformity because disagreement is unseemly and reveals the fundamental uncertainty with assessing risk is exactly-exactly-the wrong answer.  It makes errors systematic.  Systematic errors create systematic risk.

Diversified, diverse populations are far more robust than uniform, monocultural ones.  Disagreement is a feature, not a bug.  Enforced agreement is the worst bug of all.  Sort of like smallpox.

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  1. SWP – No, I agree, all large calculations are wrong. My proposal to centralise wasn’t based on the hope that doing so would mean doing it right, but rather that doing so would mean doing it equally wrong for everyone. Now you might argue, rightly, that arbitrages would result; but arbitrages result from any capital framework. That might go some way to restoring investor trust in capital ratios.

    I agree with you completely that a diverse ecology with uncorrelated errors would be good – if investors trusted it. But the problem we have right now is epistemic. No one believes capital ratios. So what we need right now isn’t a framework where capital is a robust measure with diverse errors; what we need is a framework where investors believe that capital is a robust ratio.

    Let me end with a provocative thought experiment. Suppose for a moment we could indeed come up with the right model, and impose it. (Neither you nor I think that that is possible, but run with it for a second.) In my plan, we’d use that model. In yours, we’d use it with each bank applying in addition a random small error to it…

    Comment by David — February 2, 2013 @ 5:16 pm

  2. @David. Calculations, no matter what, cannot be equally wrong for everyone – if for nothing else, then at least because of the zero-sum game character of markets – regardless of how you interpret this phenomenon. Given that for every gain there will be lose, these calculations will be “more wrong” for one side, than the other.

    Generally speaking, given that we deal with fundamental uncertainty in financial markets, there cannot be a “right” calculation. I don’t mean this on a narrowly defined technical level but on a larger model level.

    There is no right model even in physics, where one has more or less well formulated fundamental laws of conservation, how can one expect it in so much more complex financial systems?

    Even in physics we don’t claim something to be right or wrong. We just claim that this or that model performs well in view of the limited in each era set of human interactions with the nature. For example, we can rely on classic mechanics until we have to explain the nature of light. How would making everyone use Newton Laws to explain the essence and behavior of light make it right?

    So is the situation in financial systems – only more complex.

    We come up with models. And the only thing that tells us whether they are right or wrong is if they perform well. But what means something performs well?

    The formation of the dynamics of the financial systems is largely influenced by the strategic interaction of market participants. There is no divine force shaping this dynamics. The strategic behavior of markets participants cannot be modeled as if one big herd is going in the direction of its Sheppard (be it central banks, regulatory bodies or whomever) since they compete within a predefined at each time pool of limited resources and for transferring not necessarily offsetting each other exposures – for someone who wants to transfer whatever risk, someone else has to agree to carry it. If everyone has the same view of right and wrong, one of the risk transferring or carrying sides has to be just an idiot to do so.

    Not only all large calculations are wrong but such recipes are wrong and dangerous. The only outcome of such prescriptions will be to make the financial markets redundant, which implies the end of the risk transferring functionality from the underlying economy to the participants of financial markets. This will mean that instead of the financial market participants carrying them, the participants of the underlying economy will need to do so. Can they function this way? Of course. This is mostly what goes on in non-developed countries. But the first obvious outcome of this is the inability to raise capital in order to finance the basic economic activities, or funding these activities at much higher cost then they could’ve. Imagine car ownership when there are no used or new part dealers…

    Finally, how does forcing everyone to do the same wrong calculations make the investors trust capital ratios? First of all, investors should not trust the capital ratios as if a line of defense. They are wrong not because we somehow calculate them in a wrong way or each of us calculates things differently but because by definition all of them are proxies and simplifications of the actual phenomenon. The more complex the markets are the less reflective the capital ratios are of the complex phenomenon.

    So, capital ratios in no way can be a remedy for investor trust and the investors have to learn to do a better job when making investment decisions. Laziness always comes at a cost. Relying on capital ratios is a manifestation of laziness.

    Comment by MJ — February 2, 2013 @ 10:43 pm

  3. Thanks for the shout-out, SWP.

    It seems to me that investor distrust in, or at least skepticism of, ‘capital ratios’ can only be a healthy thing. And I’m not sure how focused I’d like a regulator to be on boosting financial firms’ stock prices via inducing investor ‘trust’ in them; I guess such a mandate does superficially, in some short-sighted way, protect the taxpayer (by leaving someone else holding the bag…) but still.

    Back to the original study, I’ll add a few possible mitigating factors to the optically-bad results people are reacting to:

    (1) In reality (well…we hope) no bank’s position is well described as Long An Equity Index Future, or such-and-such Pair Trade. Banks have more complex portfolios than that. So if, as the study suggests, Bank X undercounts the RWA for Trade Package #1 by 10x, they may be overcounting the RWA of some other Trade Package #2 just as much. These errors can have a cancellation effect.

    (2) Moreover, (for better or worse) these capital calculations are *nonlinear*. They don’t simply add up. So there are some trades for which you could under/overcount their VaR by huge amounts and have no material effect on your overall RWA – if your risk/capital usage is dominated by some completely-uncorrelated risk type. Relatedly, undercounting a certain trade type’s RWA by $X doesn’t necessarily mean you’re undercounting your firm’s RWA by $X.

    So, add up these factors and it’s likely that the *actual* mismatch between various banks’ capital models (e.g., imagine all banks calculating each others’ RWAs on their internal models..) would not be nearly so extreme as the 10x factors being reported in that study for particular individual one-dimensional trades.

    One can easily imagine (key informed people in) banks being in the situation of ‘knowing’ their capital calc is ‘wrong’ to some extent for Risk Type 1 but this affects longs and shorts, or is offset by some other known-wrongness on Risk Type 2, and so they are unable/unwilling to fix it without also simultaneously fixing the offsetting wrongness – because that would only make things more wrong. Oh yeah, also, in some cases banks can be DISALLOWED from (immediately) fixing known-wrong aspects of their capital calc, ‘because that would be a Model Change which requires regulator approval, which will take months’. These are just some of the hazards of large calculations, and they would be *amplified* were they centralized and performed by a regulator grappling (in an even less-informed way) with position data being fed to them by all the banks.

    Comment by The Crimson Reach — February 3, 2013 @ 8:02 am

  4. @David @MJ @Crimson Thanks for your comments. I hesitate to reply, because I know by doing so I will reduce the average IQ of the commenters 😛 Hell, I’ll lower the left support of the distribution. Anyways, here it goes.

    I still have to push back, David. Pace Hume, skepticism is highly warranted in most things, especially large calculations about opaque financial institutions. Why do we want people to have confidence in something that is wrong? You almost seem to be advocating a religious/theological position; robust capital ratios as the opiate of the masses.

    I much prefer that people understand what are those things that cannot be understood. That is the proper epistemological position here, IMO.

    @MJ. Your point re the nature of financial markets, and in particular the feedback mechanisms is spot on. And models have a role in this. Models affect the nature of feedbacks in the system. In particular, VaR type models induce a destabilizing feedback mechanism because of their inherent procyclicality. That tendency is exacerbated, the greater the number of institutions that use the same model.

    @Crimson-no problem re the shout-out. Deserved. Thanks for the details re the study. Yes. . . errors are diversified within a given bank’s model, so presumably the study overstates the true variability in the bottom line number. The nonlinearity point is also an important one.

    One of the most interesting issues relates to your last paragraph: the extent to which there are moral hazard/adverse selection problems because of information asymmetries about the risk number. I think an implication of your statement is that a centralized calculation would exacerbate this problem. I fully agree. I’ve made a big deal about that wrt Basel II. A centralized mechanism with banks that can understand what risks are mispriced by the calculation induces everyone to crowd the same trade in order to exploit the errors in the capital costs. That increases systemic risk. Yes, prices adjust to mitigate this, but that’s another bug added to the mix.

    Thanks again for the comments. Very illuminating.

    The ProfessorComment by The Professor — February 3, 2013 @ 9:39 am

  5. @David. You are way off on your thought experiment. If your hypothetical was true, I too would go with the model. Assume away the problem, and I won’t have any problem with centralization.

    The ProfessorComment by The Professor — February 3, 2013 @ 11:50 am

  6. Right there with you on a central metric causing everyone to tune/crowd into the same trade(s). People need to understand that this is NOT a hypothetical concern: ‘Gee our VaR is dominated by [Distressed Loans? JPYUSD? Mortgage OAS?] but hey looky what also coincidentally lost a lot of money on those same VaR dates: [silver futures? natgas? Russell 2K?]. Looks like that would be a cheap way to reduce our capital and still keep our core trade on!’ If folks don’t think businesses within banks are doing this NOW, they need to think again. (To some extent, this is also what the ‘London Whale’ was doing.)

    So the real question is do you want ALL banks reverse-engineering and overtuning to the SAME capital model and pouring into the SAME trade(s) for non-economic reasons? At least in the former (current) situation, the market-distorting effects, and systematic risks, are capped by any given bank’s size.


    Comment by The Crimson Reach — February 3, 2013 @ 12:36 pm

  7. […] in turn prompted a response from Craig in Houston ( which can be summarised (in a nice way without malice) “No. No. No. No. No fucking […]

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  8. […] model-based capital calculations are wrong because they confuse the first issue with the second. SWP says:We want to diversify model risk, not concentrate it. Centralized calculation concentrates it. I […]

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  9. […] In posts like the above, everything is generalized.  Sometimes it helps to have a concrete example and Craig Pirrong from Streetwise Professor provides a timely one right here. […]

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  10. Decentralized markets are always smarter than individuals. Period. Even if the calculations are wrong by both the market and the individual. Less people are hurt when it’s a market.

    Comment by Jeff — February 4, 2013 @ 10:24 am

  11. Maybe some old Gosplan personnel could be brought in to consult on this model. It sounds as though they would have just the right skill set to get this bad boy running.

    Comment by pahoben — February 4, 2013 @ 1:43 pm

  12. Accurate summary?

    The upshot is that all the risk models suck, and so do the derived capital ratios, and it’s better if they don’t all suck in exactly the same way and if people don’t put too much faith in them.

    The response from the Terrible Simplifiers is to get rid of all opaque financial complexity, on the grounds that at best it generates a constant-sum casino luring smart people into unproductive activity and at worst it’s a hugely negative-sum game due to occasional systemic crises.

    The response from the SWP and others is that allowing markets to shift risks around the economy is hugely productive, so the complexity is worthwhile even if once in a while we get a big crisis. Crises are probably inevitable, but financial regulations have tended to be neutral or negative in preventing them, and the new regulations look to be even worse. Don’t just do something, sit there!

    The response from the Technocrats is to standardize and centralize regulations and products to maintain “transparency,” and then to deal with the occasional crises by the use of unbridled discretionary powers wielded by government officials. If this regime further empowers TBTF institutions over smaller ones, so much the better because we’d rather watch over a few big firms than a multitude of small ones (and the rent-seeking opportunities are better).

    My tentative response: We need pre-established circuit-breakers that can clearly and objectively distinguish systemic liquidity crisis situations from both run-of-the-mill individual entity failures and widespread solvency problems. These circuit-breakers should not be complex regulatory rules, which can be gamed in multiple ways, but instead fundamental modifications to financial contract enforcement. The exact implementation needs to be studied carefully, but the idea would be to recognize that during a general liquidity crisis contracts requiring immediate and full payment in cash are unenforceable as written. General liquidity crises are like Acts of Market God. You might peg the existence of a liquidity crisis to a key interest-rate spread or some other hard-to-manipulate general market indicator, and you might give creditors an incentive to delay their payment demands by making the haircut decline with patience (or even go negative for enough patience). The devil would be in the details, of course, and the interaction of such changes with the Living Will regulations now being proposed would also have to be looked at carefully. But I can’t see any other way to restore a decentralized, automatic market response in the face of these occasional systemic crises. Otherwise the Technocrats or the Terrible Simplifiers are going to win the argument and we’ll all pay for it later.

    Comment by srp — February 4, 2013 @ 7:02 pm

  13. @srp. Somehow I don’t see the circuit-breakers dissipating the accumulated “energy.” It the risk has been systematically dislocated, aggregated and trapped, something has to happen – some explosion must take place. And in fact, the circuit-breaker may be the very detonator that might be needed for the explosion.

    Comment by MJ — February 4, 2013 @ 10:50 pm

  14. […] Professor took up the mantle against the push to centralize (Large) capital calculations here, and I endorse those comments.  Perfectly correlated errors are a recipe for systemic risk.  All […]

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  15. @MJ: I”m almost sorry I used the analogical term “circuit-breaker” because it has all those irrelevant associations with both energy (and with previous ill-considered regulations imposed on stock exchanges). But it does convey the general idea quickly. What I would love are specific suggestions about good or bad ways to go about altering contract enforcement to deal with systemic crises. (We already have rules to prevent straightforward enforcement within pyramid schemes, for example, so the idea of partly invalidating agreements that are inherently not executable has precedent.)

    I agree that if done badly these measures could actually create more frequent (although not necessarily more severe) crises. Fears of not getting paid back because a general crisis might happen could lead to hoarding of cash and a speeding up or creation of a liquidity jam. That could widen the “basin of attraction” pulling the system into a crisis. (On the other hand, I’m not sure that a world where people are occasionally reminded, without being ruined, that they need to watch out for liquidity crises wouldn’t be better than a world with rare but catastrophic deviations from perfect liquidity.) But, logically, when we have a whole bunch of mutually inconsistent demands for immediate cash payment we can either 1) have an outside party with sufficient liquidity bail everybody out or 2) reduce the demands to what is consistent with the amount of liquidity available. Path 1), bailouts by a lender of last resort with the power to levy taxes or print money, leads straight down the path we don’t like–dumb centralized regulations, rent-seeking, ambiguous executive powers and behavior, etc. So perhaps exploring path 2) would be a good idea.

    Comment by srp — February 5, 2013 @ 3:59 pm

  16. @srp. I don’t think the issue at stake here is the “bad” analogy. My issue rather is how does halting the trade for a period of time – short, moderate or long – eliminate the risk – be it volumetric (aka liquidity) or price risk. Are you claiming that the market cataclysms are resulted from the overreaction of hot-headed traders/investors and they need time to cool and, then, everything will go back to normal?

    Comment by MJ — February 6, 2013 @ 1:17 am

  17. @srp . Your analysis focuses on what is the best way to structure private liquidity supply in a way that is run free. You rightly conclude that this is a very hard task. One way is to suspend payment during “generalized” liquidity runs. The other is to have a LOLR. As you note, both alternatives have problems.

    Towards the bottom of this John Cochrane post, he suggests jettisoning private liquidity supply altogether. For various purposes, there is a high demand for claims that have a fixed nominal value. Banks and shadow banks structure liabilities in an attempt to do this. But all of these structures are run prone, and trying to fix them (e.g., deposit insurance) create moral hazard problems. So Cochrane suggests that the government freely supply short term floating rate debt that will have a fixed nominal value, but will not be subject to run risk. He credits the basic idea to Milton Friedman, and argues that a perfectly elastically supplied liability of this sort will eliminate reliance on fragile private liabilities structured to have fixed nominal value. (Holmstrom and Tirole make a similar argument in their work on liquidity.)

    There’s something to be said for this. A lot actually. I basically view it as Central Bank 2.0. Instead of issuing reserves only to banks at 0 interest, like Central Bank 1.0 does, issue interest bearing reserves to anyone. I guess there is the question of the optimal quantity of these reserves. I’ll have to go back and read Friedman’s paper. But if the goal of this is to meet the demand for fixed-nominal value liabilities, i.e., to meet the demand for liquidity, a sufficient condition to conclude that the supply of these liabilities is too small is that private parties will try to create substitutes.

    I’ll have to think some more about potentially hidden flaws.

    The ProfessorComment by The Professor — February 6, 2013 @ 5:06 pm

  18. I have to think about that Cochrane/Friedman proposal. It’s certainly a bold one. The first thing I wonder about is whether the “money-like” property of Treasury debt would persist after this policy was instituted.

    Why does he keep putting “liquidity” in scare quotes?

    Comment by srp — February 6, 2013 @ 7:12 pm

  19. Dunno re the scare quotes. I’ll look again.

    My main reservation is that he is implicitly assuming that variable rate Treasury debt will be default free, and hence not subject to runs . . . . or that the amount of such debt will not influence the incentive to run on longer maturity debt. That seems to be a heroic assumption, and not necessarily consistent with other things he’s written about government debt and inflation.

    The ProfessorComment by The Professor — February 6, 2013 @ 9:13 pm

  20. @srp. Tho the best I can figure, Cochrane puts “liquidity” in quotes because the term is used in so many ways, and is often somewhat ambiguous in its meaning.

    The ProfessorComment by The Professor — February 6, 2013 @ 10:02 pm

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