Wednesday, March 10, 2010

On Asymmetry, Reflexivity and Sovereign Default

One of the most rewarding aspects of blogging is that it gives me the opportunity learn from those who read and comment on the ideas expressed here. I have had the good fortune of being visited by a number of informed and thoughtful readers, whose remarks have often been of greater quality than the posts to which they were responding. Among those for whom I have developed the greatest respect is the anonymous author of Macroeconomic Resilience, who left a couple of very helpful comments in response to my recent post on credit default swaps.

MR pointed out that the idea of multiple self-fulfilling default probabilities plays a key role in George Soros' theory of reflexivity, and linked to an article in which Soros interpreted the Lehman bankruptcy in precisely these terms. In fact, it is a combination of reflexivity and a particular kind of risk/reward asymmetry that gives rise to what Soros calls self-validating bear raids:
First, there is an asymmetry in the risk/reward ratio between being long or short in the stock market... Being long has unlimited potential on the upside but limited exposure on the downside. Being short is the reverse. The asymmetry manifests itself in the following way: losing on a long position reduces one’s risk exposure while losing on a short position increases it. As a result, one can be more patient being long and wrong than being short and wrong. The asymmetry serves to discourage the short-selling of stocks.

The second step is to understand credit default swaps and to recognise that the CDS market offers a convenient way of shorting bonds. In that market the asymmetry in risk/reward works in the opposite way to stocks. Going short on bonds by buying a CDS contract carries limited risk but unlimited profit potential; by contrast, selling credit default swaps offers limited profits but practically unlimited risks.

The asymmetry encourages speculating on the short side, which in turn exerts a downward pressure on the underlying bonds. When an adverse development is expected, the negative effect can become overwhelming because CDS tend to be priced as warrants, not as options: people buy them not because they expect an eventual default but because they expect the CDS to appreciate during the lifetime of the contract...

The third step is to recognise reflexivity – that is to say, the mispricing of financial instruments can affect the fundamentals that market prices are supposed to reflect. Nowhere is this phenomenon more pronounced than in the case of financial institutions, whose ability to do business is dependent on confidence and trust. That means that “bear raids” to drive down the share prices of these institutions can be self-validating. That is in direct contradiction to the efficient market hypothesis.

Putting these three considerations together leads to the conclusion that Lehman, AIG and other financial institutions were destroyed by bear raids in which the shorting of stocks and buying of CDS amplified and reinforced each other. Unlimited shorting was made possible by the 2007 abolition of the uptick rule (which hindered bear raids by allowing short-selling only when prices were rising). The unlimited selling of bonds was facilitated by the CDS market. Together, the two made a lethal combination.
Soros' point about risk/reward asymmetry directly answers one objection to curtailing purchases of naked credit default swaps, namely that such contracts "provide identical leverage both to the optimistic and the pessimistic side of the transaction." Leverage may be considerable on both sides of the contract but this does not mean that market clearing prices reflect optimistic and pessimistic beliefs in equal measure, because the spreads at which sellers are willing to enter the contract must offer them adequate compensation for the significant downside risk that they face.
MR does not consider reflexivity to be a routine problem in credit markets, arguing that "only when the entity is in a state of low resilience that markets are sufficiently reflexive to push it over the edge." This is also David Merkel's view of the matter:
... if a company or government has a strong balance sheet, and has a lot of cash or borrowing power, there is nothing that speculators can do to harm you.  You have the upper hand.  But, if you have a weak balance sheet, I am sorry, you are subject to the whims of the market, including those that like to prey on weak entities.  Even without derivatives, that is a tough place to be.
But what causes a balance sheet to become weak? In the case of sovereign states, it could be widespread tax avoidance and excessive spending relative to revenues, as has been alleged in the case of Greece. But it could also be a significant decline in economic activity that reduces the tax base and triggers automatic stabilizers. This is how Paul Krugman interprets the experience of Spain, which had a budget surplus three years ago, but "is running huge deficits now [as] a consequence, not a cause, of the crisis: revenue has plunged, and the government has spent some money trying to alleviate unemployment."

Any attempt to raise taxes or cut spending in this environment could make it even harder for the country to meet its near term debt obligations. For this reason, Felix Salmon's claim that countries "have essentially no limit on how much they can tax or cut spending in order to make their debt repayments" cannot possibly be correct as a general principle. A government can change expenditure policies and tax rates, but has no direct control over realized revenues and outlays. As a result, raising tax rates or trimming expenditures (such as unemployment benefits) in the face of severe deficiencies in aggregate demand can worsen rather than improve its balance sheet position.

Under such circumstances, it is terribly important to determine whether the looming threat of default is simply one of several possible equilibrium paths. As Felix acknowledged in his response to my post, it is true in principle that "a company or country can find it easy to repay debt when spreads are low, thereby justifying the low spreads, while finding it hard to repay debt when spreads are high, justifying the high spreads." Default under these conditions would be terribly wasteful, and I can see no reason why attempts to avoid it should not be pursued vigorously.


Update (3/11). Paul Krugman also seems to think that it's worth considering the possibility of multiple self-fulfilling default probabilities in the context of sovereign defaults (h/t Mark Thoma):
Markets are getting slightly more bullish on Greek debt — and Peter Boone and Simon Johnson are crying bubble. I’m not so sure, but I think their argument highlights something else: the possibility of multiple equilibria in sovereign solvency...
Suppose that Greece had as much credibility as Germany, and could borrow at a real interest rate of 2 percent. Then stabilizing the real value of its debt, even with a debt ratio of 150 percent, would require a primary surplus of only 3 percent of GDP. That’s certainly possible for some countries, although maybe not for Greece.
Boone and Johnson assume, however, that Greece would have to pay 10 percent nominal, say 8 percent real. Servicing that would require a primary surplus of 12 percent of GDP, probably impossible for almost anyone.
So this suggests that optimism or pessimism about future default can, to at least some degree, be a self-fulfilling prophecy. Not a new insight, I know, but it looks increasingly important for thinking about where we are now.

Update (3/19). And here's Richard Portes arguing for the importance and empirical relevance of multiple self-fulfilling default probabilities, based on his work with Daniel Cohen (h/t Mark Thoma):
Naked CDS, as a speculative instrument, may be a key link in a vicious chain. Buy CDS low, push down the underlying (e.g., short it), and take a profit from both. Meanwhile, the rise in CDS prices will raise the cost of funding of the reference entity – it normally cannot issue at a rate that won’t cover the cost of insuring the exposure. That will harm its fiscal or cash flow position. Then there will be more bets on default, or at least on a further rise in the CDS price. If market participants believe that others will bet similarly, then we have the equivalent of a ‘run’. And the downward spiral is amplified by the credit rating agencies, which follow rather than lead. There is clearly an incentive for coordinated manipulation, and anyone familiar with the markets can cite examples which look very much like this. The probability of default is not independent of the cost of borrowing – hence there may be multiple equilibria, with self-fulfilling expectations, as Daniel Cohen and I have argued.


  1. Rajiv,
    this is so interesting that I have added a post on my blog:

  2. Thanks... I see your point about puts. But this is a good debate to have; the issues are important and the mechanisms far from obvious.

  3. Good article, Rajiv, keep up the good work.

  4. Thanks David... it's great to hear from you, I'm a big fan of your blog.

  5. This reminds me of another asymmetry I've been wondering about. Does the large difference in tax rates on capital gains and income lead to asset market bubbles? Investors pay a lower tax on capital gains when the market is rising but write off their losses at a higher rate when the market falls, so there is extra incentive to hold assets when asset prices are rising. Taking the argument further, there could be tacit collusion among investors to justify bubbles to take advantage of the difference in rates. Has someone discussed this idea somewhere already?


  6. “Going short on bonds by buying a CDS contract carries limited risk but unlimited profit potential; by contrast, selling credit default swaps offers limited profits but practically unlimited risks.”

    I don’t get this. I know its George Soros, but what’s he talking about? It’s not “unlimited” either way. Bonds can only go to zero and no further.

    The point on the reversal of asymmetry is correct, but the language describing it is sloppy at best. The asymmetry of stock prices is that of limited downside price risk and unlimited upside price reward. The asymmetry of bond prices is that of limited downside price risk but typically more limited upside price opportunity (although this asymmetry can again be reversed in theory if bond coupons are high enough, duration is long enough, and interest rates are low enough - in fact, the only way a short bond position can create “unlimited” risk is if interest rates go negative).

    Shorting stocks is generally riskier than shorting bonds due to the embedded long call option contained in the stock price. Therefore, buying CDS (equivalent to shorting bonds) is generally safer than shorting stocks. And while the opposing sides of the asymmetry are in reverse proportion to the case of stocks, “unlimited risk” or “unlimited return” does not come into play in the case of a bond or CDS.

  7. Rajiv:

    These are important strands you are trying to integrate. Keep going.

    This one in particular:

    "As a result, raising tax rates or trimming expenditures (such as unemployment benefits) in the face of severe deficiencies in aggregate demand can worsen rather than improve its balance sheet position."

    There is a paradox of public thrift here, isn't there? We saw it in Argentina just less than a decade ago, we have seen it in Latvia, and Ireland more recently. And it will no doubt begin to show up in Greece, and there will be demands for further tax hikes and government expenditure cuts as they miss their fiscal targets.

    What is missing - and I believe you must be able to see this, since you have studied Minsky - is a recognition that the financial balances of one sector (the difference between sector saving and investment, or altenatively, sector income and expenditures) do not exist in a vacuum. Change the financial balance of one sector, say government, and the private and foreign sector financial balances are likely to be influenced.

    Tax hikes suck cash flow out of the domestic private sector. Expenditure cuts restrict cash inflows into the domestic private sector. Should it be any wonder then, if we get private income deflations, like Latvia's Great Depression sized collapse, when fiscal retrenchment is forced on nations already facing insufficient private aggregate demand?

    I think we need to recognize the insanity of what is being proposed here...and it is a dangerous insanity that will lead to precisely the opposite of the intent of the original eurozone project, which was to reduce the odds for divisive, political extremist movements to gain traction in the region ever again.

    I have written about the interconnected nature of the sector financial balances here:

    Would be interested if you have any response on the perspective I lay out, because I think it is essential that people see these relationships clearly before more damage is done.



  8. Bruce, JKH, Rob - thanks for your comments... I'm traveling at the moment but will respond later in the day. And JKH, welcome back....

  9. Rajiv - I don't want to be too harsh here as I am new to the blog, however, you make same huge contradictions in your article which essentially completely negates your own argument. There are also quite a number of factual inaccuracies.

    - You destroy your chief argument in the asymmetry of the payoff diagram between a bought or sold CDS position yourself, by simply stating that "oh the holders of these CDS mark to market so in reality they are not trading the asymmetry, but trading the market".

    The asymmetry argument only holds, as you state, for pure buy and hold investors - I have previously traded a CDS for a global IB - let me tell you there are NO buy and hold investors - they all mark to market.

    The chief problem you need to grapple with, in my opinion, is whether a CDS contract is actually an "insurance agreement" which entails different regulation, capital and also importantly accounting treatment (potentially).

    Your argument is why Academics get steamrolled in markets, a la LTCM

    A CDS is a levered (unfunded) view on credit spreads in a pure mark to market world - the one we live in.


  10. Bruce, it's an interesting idea but I'm skeptical. In order for bubbles to get going there usually has to be some serious disagreement about fundamentals and the prospect of rapid capital gains, these are episodic events while the tax code is a constant in the background. It could be that the different tax treatment affects the frequency and character of bubbles but I haven't seen any literature on this.

    JKH, you're right of course that gains and losses are not unlimited, so this was sloppy language on the part of Soros, but his point is basically correct. Buying naked CDS when spreads are low has the potential for huge gains if a low probability default event occurs, just as buying deep out-of-the-money puts on a stock does.

    Rob, I enjoyed your article (as well as Edward Harrison's recent post on Spain and Germany on naked capitalism). A paradox of public thrift is a good way to put it. You're absolutely right that people need to see these relationships before further damage is done. They also need to recognize that the likelihood of default is not independent of market expectations of default (as reflected in CDS spreads and risk premia).

    Gary, I'm sorry, but I really don't understand your comment. Are your referring to the Soros quote about CDS being priced as warrants rather than options? If so, then I think you're missing the point. The asymmetry refers to the payoff structure of the contract, not to the kind of investor holding it. Of course you can exit (or be forced to exit) a position at any time and your losses are constrained by your margin, but this does not alter the risk-reward asymmetry on the two sides of the contract.

    Just to be clear, I'm not giving investment advice here so there's no possibility of anyone getting "steamrolled". I'm trying to understand the effects on system stability of widespread naked CDS trading. The "insurable interest" argument is relevant to the debate but it's not the only relevant argument. And Soros, of course, is not an academic.

  11. Rajiv,

    What little I've read of Soros' theory of reflexivity leads me to believe that he's frustrated by a lack of reception to it.

    Do you have your own interpretation of what he's saying, and whether/how it intersects with other theory? Doesn't it have something in common with Minsky?

  12. JKH, you're absolutely right, Soros does feel that reflexivity should be taken much more seriously by economists. Part of the problem is communication. There is a literature on coordination games with incomplete information that deals with the reflexivity problem (but without using the term or referring to Soros). Most of this literature uses the global games framework introduced by Carlsson and van Damme:

    Morris and Shin have applied this framework to study self-fulfilling currency attacks:

    But what makes Soros' ideas more interesting to me is not just reflexivity but the manner in which this interacts with other features of financial markets such as risk-reward asymmetry. This I have not seen in the economics literature.

    Minsky did not consider reflexivity as far as I recall, but he did something that is very relevant to this debate. He provided a theory of changes over time in the degree of maturity transformation (which he called a shift from hedge to speculative financing). I want to write a post on this at some point because I think it explains very well the behavior of AIG over a strech of time when CDS spreads were relatively stable.

  13. Rajiv - Thank you! I would just add that the view of reflexivity as an intermittent problem is one Soros himself has come around to. Quoting from his MIT speech: "In normal conditions, there is a tendency for the participants’ views and the actual state of affairs to converge or, at least, there are mechanisms at work to prevent them from drifting too far apart. I call these conditions “normal,” because that is what our intellectual traditions—including philosophy and scientific method —have prepared us for. I contrast them with far-from- equilibrium conditions, where the participants’ views are far removed from the actual state of affairs and there is no tendency for the two of them to come together."

    JKH - This is how Soros writes! Precision has never been his strength but he's usually worth reading. Having said that, this article is not his finest moment. Your point is spot on - the correct phrase would be that the buying of credit protection has a severely positively skewed payoff profile.

    Also, the Lehman report yesterday atleast proves that Lehman didn't die just due to a bear raid, it was already in a fragile state. I completely agree with Barry Ritholz's post on the proximate vs ultimate causes of Lehman's failure and the same argument could be used against blaming reflexive markets for Lehman's demise.


  14. Macro,

    It was that MIT speech I was thinking of when I suggested that Soros was at least mildly bitter about lack of attention to his reflexivity theory. The theory reminds one immediately of Heisenberg’s uncertainty principle, although I don’t know much physics, and could never quite grasp the intuition of that one. I’m not a fan of economics/physics analogies generally, given the more straightforward weakness of much of the economics profession to grasp the importance of the mathematical logic of double entry book keeping, especially at the macro level.

    I relate the rough shod option analysis in the article here to his more general weakness in communicating reflexivity theory. Re-reading the MIT speech, I’m not too bowled over by the mystery of simulating the macro behaviour of leverage when there are other similarly behaving “participants” in the same market. I think it’s more a matter of macro simulation, scenario analysis, and risk management than some mystery called reflexivity. Reflexivity seems interesting as an idea, but his description of it in the MIT speech like his description of option risk here is unsatisfying.

    As far as efficient market theory is concerned, I never believed nor disbelieved in it so much as believing that it was intellectually useless in any event. Volatility exists. That results at least from changing information. Why does anybody really care so much about the degree to which current information is impounded in prices?

  15. JKH - Yes, Reflexivity is often compared to the Heisenberg uncertainty principle but I really don't think it's that complex.

    I can't really defend Soros' sloppy theorising. But let me try and distill what I find most useful in the notion of reflexivity:

    For the most part, markets are dominated by equilibriating negative feedback forces. However, occasionally, some markets can lose resilience to the extent that a concerted move in the market can generate a self-fulfilling prophecy i.e. the market move affects "reality" and both get locked into a positive feedback cycle.

    For practitioners like Soros, such a situation represents an opportunity with superior risk-reward. Black Wednesday of course was the best example of this.