• 07 May 2012 at 5:47 PM
  • Banks

Markets Are Telling Us That Too Big To Fail Is All Better

Oh am I a sucker for this sort of thing:

This paper proposes a theoretically sound and easy-to-implement way to measure the systemic risk of financial institutions using publicly available accounting and stock market data. The measure models credit risk of banks as a put option on bank assets, a tradition that originated with Merton (1974). We extend his contribution by expressing the value of banking-sector losses from systemic default risk as the value of a put option written on a portfolio of aggregate bank assets whose exercise price equals the face value of aggregate bank debt. We conceive of an individual bank’s systemic risk as its contribution to the value of this potential sector-wide put on the financial safety net. To track the interaction of private and governmental sources of systemic risk during and in advance of successive business-cycle contractions, we apply our model to quarterly data over the period 1974-2010. Results indicate that systemic risk reached unprecedented highs during the years 2008-2010, and that bank size, leverage, and asset risk are key drivers of systemic risk.

A “theoretically sound and easy-to-implement way to measure the systemic risk of financial institutions” sounds pretty good! Is it easy to implement? Well let’s implement it to find out. [Pounds head against Google Spreadsheets.] Umm. Okay, I guess it was easy? I don’t know, I can’t fully replicate their numbers; tell me where I’m wrong in the comments. Or don’t.

This is a paper by Arman Hovakimian of Baruch, Luc Laeven of the IMF, and Edward Kane of BC that attempts to measure the systemic riskiness of banks. They do two things. First, they compute the riskiness of banks to the financial system by treating bank stocks as options on the assets of the bank – or, equivalently, by assuming that there is a taxpayer put on the liabilities of the banks, i.e. an implicit government guarantee on bank debt. This is a very simplifying assumption! But it is not totally nuts when you remember that most of their sample consists of FDIC-y type deposit banks.

Anyway, using this option method allows them to figure out the equity-market-implied volatility of the assets of the bank. If those assets are worth less than the debt of the bank then, they assume, the bank will go bankrupt and its creditors will be made whole by the government. The expected value of that make-whole is the cost to the government of providing implicit support. This is obviously a bit of a made-up number, and they are quite clear about lots of other simplifying assumptions and stylizations. Their point, though, is not to actually calculate a precise value of the implicit support that the government provides, but rather to see how that value changes over time, to see what it predicts (quickly: if the value of the government support goes up, that usually means things are getting worse) and what predicts it (leverage, bank size, etc.).

But I want to calculate the value of the implicit support that the government provides! Here it is. These numbers are basically the annual yearly cost to the government (value to the banks) of the implicit support maybe provided to them by the US government. Or something!

So … that’s underwhelming. I mean, I kind of like this; it conveys this directional sense that Goldman and JPMorgan stand on their own two (ten) feet while Citi and Morgan Stanley don’t quite so much and BofA is kind of a mess. But … like … $60 million a year for BofA? That is a very low number. BofA is very, very safe, huh?*

The second, more interesting thing that the authors do is calculate the systemic risk of various banks, which is basically (1) the aggregate risk of the banking system calculated as above minus (2) the aggregate risk of the banking system minus each individual bank. This calculation gives pleasing results:

The mean value of systemic risk is small and moves only slightly during most of the sample period, but in 2008-2010 the mean value surges dramatically, reaching -470 basis points in 2009. Attaching a negative sign to these values may seem counterintuitive and surprising at first. Our interpretation of this result is as follows. During a very deep financial crisis, bank asset and equity values become more positively correlated, especially at very large and interconnected banks. This means that the benchmark sectoral portfolios become much less diversified and that adding a large bank to the sectoral portfolio offers little or no diversification or financing benefit. On the other hand, assuming that small banks have very different business plans and risk exposures than large banks, their asset values and survival would not be greatly threatened by the collapse of the securitization and mortgage-lending bubbles. During crisis periods, these banks give more support to the safety net than the safety net gives them in return. … [But] even though the contribution to mean systemic risk becomes negative during the crisis period, the systemic risk of particular sample banks became positive and very large during this period.

So small banks basically went bankrupt on their own, or didn’t, and mostly didn’t, so the more small banks you could add to your portfolio the more you were insulated from … well, from Bank of America, which seems to have provided 770 basis points** of systemic risk premium, or well over $100bn/year of cost, or from State Street, which I guess is not surprisingly the most systemically connected bank in 2009 with 1881 bps of systemic risk premium. But then things went back to normal:

Like I said I’m a sucker for this sort of thing, but not really because it’s true. Using (1) methods (methods!) to turn (2) public data into (3) a big thing like Systemic Risk is good fun and allows you to go build silly spreadsheets and say things like “implicit government support is worth $60mm a year to BofA.” But of course the underlying assumption here is large, which is that public equity market moves tell you something deep about underlying bank risks.

Using public information like stock prices to proxy for information on bank interconnectedness and risk that isn’t disclosed – and that no one person could probably hold in his mind or spreadsheet even if he could know it – is pretty attractive, and their numbers suggest that it kind of worked during the financial crisis. But there’s some limit to how well it could have worked; after all, the debt markets … well, let’s say at a minimum that they didn’t consistently predict a government bailout of all bank creditors. At a maximum let’s say they were often more pessimistic than the equity markets. The benign numbers above may say something encouraging about the decline of systemic risk among US banks – or they may just say something discouraging about equity investors’ interest in that risk.

Variation in Systemic Risk at US Banks During 1974-2010 [NBER, earlier free version here]
Here is a spreadsheet that lets you sort of manually goal-seek yourself [Google Docs]

* You can have more fun plugging in scarier numbers. So for Citi at its nadir in March 2009, with a 265% implied volatility and ~$1 price, I get $7.5 billion dollars of annual TBTF-iness cost. Btw I’m using implied vol of course. Also they seem to get much bigger numbers across the board; not sure if that’s a data issue or my spreadsheet is screwy.

** A basis point is 1/100th of a percentage point. NO JUST KIDDING! I meant, the authors are sort of calculating an implied “correct” insurance premium for the implicit government support, so “basis points” refers to “of bank liabilities” (including deposits and, weirdly, preferred stock).

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Comments (12)

  1. Posted by guesticles | May 7, 2012 at 6:12 PM

    TL;DR

    – Arman Hovakimian, Luc Laeven and Edward Kane

  2. Posted by Fan | May 7, 2012 at 8:02 PM

    +1 Matty

  3. Posted by Guest | May 7, 2012 at 10:21 PM

    Come on Matt, you couldn't build the black scholes into the spreadsheet? get out of here.. just go.

  4. Posted by Guest | May 7, 2012 at 10:31 PM

    Where are my teeth?

    – B. Moynihan

  5. Posted by iPad User | May 8, 2012 at 1:02 AM

    You seem to have fixed the iPad issue – thanks!

  6. Posted by Guest | May 8, 2012 at 1:16 AM

    I've been trying to refinance my mortgage with BoA for six months. The droids on the other end of the phone don"t know what a K-1 is… Matt, can you do some analysis of how many monkeys with a phone and computer it would take to underwrite a simple mortgage in less than a year?

  7. Posted by mitchell | May 8, 2012 at 7:16 AM

    Just as we discovered with 'portfolio insurance' in 1987, implied volatility tells us almost nothing about
    future actual volatility, especially for brief periods of time when a business model can collapse under
    the weight of leverage or margin rule changes (for two examples). The conceptual error in most models,
    simply put, is: reverse engineering real-world risk to assume that market prices of puts, calls, CDS's, will
    somehow predict an outcome. This is almost exactly the equivalent of assuming the outcome of a horse race will be predetermined by the parimutuel odds on the board. A much closer — but still clunky –
    model would use the same approach that reinsurance companies use to estimate the costs of severe hurricanes, earthquakes, or other natural disasters if they should take place in certain places. That is, start with the assumption that an unlikely event will take place, and then estimate the cost — the severity of loss — separate from estimating the frequency with which such events will occur. In the case of banks'
    systemic risk, you also need to factor in the underlying risk that insurance-selling counter-parties may fail to pay the claims the are on the hook for via puts, calls, CDS's, etc.. At that point, you can base a
    theoretical model on a reasonable estimate of a real-world worst-case severity event, and then back into the pricing of the insurance that a bona fide insurer of reinsurer would charge for the odds the event will occur in 1, 3, or 100 years.

  8. Posted by Guest | May 8, 2012 at 9:18 AM

    > and then back into the pricing of the insurance that a bona fide insurer of reinsurer would charge

    What exactly do you think a CDS is?

  9. Posted by Guest | May 8, 2012 at 11:09 AM

    They were the industry standard before iTunes / otherwise downloadable music changed the landscape.

    –UBS Entertainment Quant

  10. Posted by Julian, with drink | May 8, 2012 at 12:07 PM

    Markets don't know the value of banks equity, or debt, or any kind of implied TBTF premia. But keep on looking for that perfect model anyways …

  11. Posted by sohbet | May 12, 2013 at 8:20 PM

    Relative game comment sounds like pr straight from ir talking points to me written by an underpaid res associate rather than an honest opinion of what matters: will financing costs for banks rise and will corporates that have stronger ratings than the banks wake up and disintermediation

  12. Posted by reseller tanpa modal | August 17, 2013 at 11:54 PM

    so what we gonna do when the market fall? reseller tanpa modal