Some two decades ago, we thought that financial repression had been more or less eliminated in the developed world, and was being gradually eliminated in the developing world as well. Post crisis, as much of the developed world deals with the sustainability of sovereign debt, financial repression is back in fashion, and macroprudential regulation provides a wonderful figleaf.

• All government rescue packages around the world were structured like CDOs. The typical recipe was as follows: all problem assets were pooled into a CDO like structure (for example, Maiden Lane); the pool was tranched; the beneficiary institution held the equity tranche (first dollar of loss subject to a modest limit); and the central bank or government held the senior piece. The toxic assets disappeared from the balance sheet of the tottering TBTF institution which therefore became solvent (or a little less insolvent). The central bank then embarked on unconventional monetary policy actions that boosted asset prices and ensured that the senior piece became worth par.
• The same strategy was adopted for dealing with sovereign debt crisis in the eurozone. The European Stability Mechanism (ESM) like its predecessor the EFSF, was a CDO like structure that received a AAA rating because of over collateralization though its sponsors included a number of beleaguered nations whose creditworthiness was hardly pristine.
• Of late, the strategy has been adopted retrospectively to failing institutions in Europe. Post facto, banks have become CDOs with lower tranches being written off in typical CDO style without a formal bankruptcy process. The Dutch bank SNS Bank (and SNS Reaal) were turned into CDOs by government decree overnight. On January 31, 2013, you might have thought that you had lent money to SNS Bank; on February 1, you were told that you were actually holding a tranche of a CDO, and that this tranche has now been written down to zero (The decree actually called it expropriation). Meanwhile, the bank continued to operate normally and the depositors were fine because they were holding a senior tranche that was still unimpaired.
• The strategy has been pushed even further in the Cyprus package. In this case, the depositors were told that their tranche was also impaired.
• The clearing corporations that were the oases of stability during 2008 have also joined the game. They are now openly saying that their obligation to guarantee all trades is not really a guarantee anymore. If your trade has been novated by the clearing corporation, then you actually hold a highly senior tranche of a CDO: if the losses eat through all junior tranches, then first your mark to market gain will be haircut, and if that is not enough then your contracts will simply be torn up at some settlement price that ensures the continued solvency of the clearing corporation. After that, the clearing corporation will continue to operate normally. The Bank of England recently published a Financial Stability Paper entitled “Central counterparty loss-allocation rules” by David Elliott which describes in gory detail how far this process has progressed around the world.

The biggest innovation in the CDO was actually a contractual bankruptcy process that is lightning fast and extremely low cost (see my blog posts on the Gorton-Metrick and Squire papers that argue this in detail). The world is gradually coming around to realizing that normal bankruptcy does not work for the financial sector and the contractual CDO alternative is far better. In 2006, I wrote that the invention of CDOs has made banks and other legacy financial institutions unnecessary. The crisis seems to be turning that speculation into reality.

Of course, despite the deeply (biologically) ingrained love of symmetry, central banks can decide to abandon symmetry and move the central and upper rates independently. In fact, the historical data shows that in the first three months of the ECB’s existence, the corridor was not symmetric around the central rate, but since April 1999, the symmetry has been maintained.

Modelling short term rates in a symmetric corridor floored at zero is problematic. The log normal model has problems because it does not allow rates to be zero. Yet it is the natural way to model the proportionate changes in the central and upper rates.

1. In the early years of Bitcoin, computing power allows the mining of new bitcoins. This is pure seigniorage.
2. When most of the coins have been mined, computing power can be used to charge transaction fees on every bitcoin transaction. This is also seigniorage income in the form of an all encompassing Tobin tax beyond the wildest dreams of the proponents of that tax.

Is this a design flaw or is it a necessary feature? After careful consideration, I think it is necessary. A monetary system can be sustained only if there are people with the incentive to invest in the maintenance of the system. In the case of fiat money, the sovereign expends considerable effort in preventing counterfeiting. One might think that commodity money like gold does not require such effort. But the historical evidence suggests otherwise:

1. After the collapse of the Roman empire, “within a generation, by about A.D. 435, coin ceased to be used [in Britain] as a medium of exchange … although many survived as jewellery, or were used for gifts or for compensation.” (Christine Desan, “Coin Reconsidered: The Political Alchemy of Commodity Money”, quoting Peter Spufford.) With nobody having enough seigniorage income to try and maintain the system, commodity money was simply re-purposed to non monetary uses, and Britain relapsed into a barter economy.
2. Christine Desan also points out that a monetary system based on silver was reestablished centuries later by sovereigns who extracted seignorage income by charging a 5-10% spread between the mint and melting points of the metal.
3. On the other hand, Luther and White have several papers showing that after the collapse of the Somalian government, the old currency continued to circulate and local warlords maintained the money supply by counterfeiting the old currency notes to earn seigniorage income.

All this suggests that any form of money (whether fiat, commodity or a decentralized open source money like Bitcoin) needs some form of seigniorage to sustain it.

It was also possible to take a middle ground – the celebrated square root model related the fluctuations to the square root of the level. A doubling of the level from 3% to 6% would cause the fluctuation to rise by a factor of √2 from 0.5% to 0.71%. People generalized this even further by assuming that the fluctuations scaled as (level)^λ where λ=0 gives the normal model, λ=1 leads to the log-normal, and λ=0.5 yields the square root model. Of course, there is no need to restrict oneself to just one of these three magic values. The natural thing for any statistician to do is to estimate λ from the data using standard maximum likelihood or other methods. Long ago, I did do such estimations for Indian interest rates.

The Libor Market Model killed this cottage industry. It was most natural to assume log normal distributions for the interest rates and then let the option implied volatility smile deal with departures from this distributional assumption. And there matters rested until the problem resurfaced when interest rates were driven down to zero after the global financial crisis. The difficulty is that zero is an inaccessible boundary point for a log normal process. A log normal process (geometric Brownian motion) can not reach zero (in any finite time) starting from any positive rate, and if you somehow started it out from zero, it could never leave zero (because the volatility becomes zero).

The regulatory push to mandate central clearing for OTC derivatives has turned this esoteric modelling issue into an important policy concern because central clearing counterparties (CCPs) have to set margins for a variety of interest rate derivatives where the modelling of volatility becomes a first order issue. A variety of different approaches are being taken. The OTCSpace blog links to a couple of practitioner oriented discussions on this subject (here and here). Among the solutions being proposed are the following:

Shift to a normal model

This would eliminate under margining at zero interest rates, but potentially create severe under margining at high rates.

Combine normal and log-normal fluctuations

The idea is that there are two sources of fluctuations in interest rates – one behaves in a “normal” and the other in a “log-normal” manner. This may be intractable for valuation purposes, but might be acceptable for risk modelling since it solves the under margining problem at both ends of the interest rate spectrum.

Interest rate plus a small constant is log normal

For example, assume that the fluctuations in interest are proportional to the level of rates +1%.

As an aside, I believe that the zero lower bound is actually a bound not on the interest rate, but on the contango on money. In other words, the zero lower bound is simply the proposition that money (being the unit of account itself) can neither be in contango nor in backwardation. The standard cost of carry model for futures pricing tells us that the contango on money is equal to the risk free interest rate PLUS the storage cost of money MINUS the convenience yield. It is this contango that is constrained to be zero.

If the convenience yield of money is larger than the storage costs (as it usually is in normal times), the contango is zero when the interest rate is positive. In an era of unlimited monetary easing, the convenience yield of money can become very small and the zero contango implies a slightly negative interest rate since the storage cost is not zero. For physical currency, the storage cost is high because of the need to guard against theft. For insured bank deposits, the bank needs to recoup deposit insurance in some form through various fees. Of course, uninsured bank deposits are not money – they are simply a form of haircut prone debt (think Cyprus). Actually, Cyprus makes one sceptical about whether even insured bank deposits are money.

1. China’s experiments with paper money ended in inflationary disaster (as almost all fiat money appear to do), but it succeeded in replacing China’s long standing bronze coin standard with a silver unit of account (see for example, Richard von Glahn (2010), “Monies of Account and Monetary Transition in China, Twelfth to Fourteenth Centuries”, Journal of the Economic and Social History of the Orient, 53(3), 463-505)
2. Johan Palmstruch who brought paper money to Europe and founded the world’s first central bank (the Sveriges Riksbank of Sweden) was sentenced to death. Though he was reprieved, he still lost everything and ended up in jail.

There is little doubt in my mind that digital currencies represent a vast technical and conceptual advance over the currencies in existence today. This would remain true even if Bitcoin implodes in a collapsing bubble or is destroyed by technical flaws in its design or implementation.

Nemo at self-evident.org has an excellent ten part series providing a gentle introduction to all the mathematics that one needs to understand how Bitcoin works. This is a good starting point for somebody wanting to go on to Satoshi Nakamoto’s seminal paper introducing the idea of Bitcoin.

From a finance point of view, what is most interesting about Bitcoin is that it is perhaps the first currency to be designed with a strong deflationary bias. There is an upper limit on the number of bitcoins that can ever be created – even lost bitcoins cannot be replaced unlike normal central banks that replace worn out notes with newly printed ones. In paper currencies, if I lose a currency note, somebody else probably finds it, and so the note remains in circulation. By contrast, Bitcoin is so designed that if the owner loses a bitcoin, the “finder” cannot use it, and so the lost bitcoin ceases to exist for all practical purposes. (If you are puzzled by the apparently inconsistent capitalization of bitcoin/Bitcoin in this paragraph, you may want to read this).

While most fiat currencies end up printing notes in higher and higher denominations to combat inflation, Bitcoin is designed to combat deflation by using smaller and smaller denominations like milli bitcoins and micro bitcoins all the way down to the smallest unit named the Satoshi which is equivalent to 10 nano bitcoins. As a result, the zero interest rate lower bound could be an even more serious problem for Bitcoin than for existing currencies.

One theoretical possibility is that the deflation overshoots significantly so that the currency can experience a mild inflation from that point onward somewhat on the lines of the Dornbusch overshooting model. But for that to work on a sustained basis, there would need to be periodic bouts of intense episodic deflation. The sharp appreciation of the bitcoin in the last few weeks in response to the Cyprus crisis suggests one way in which this could happen, but that would be a nightmare to model.

At first reading, I thought that Mai was simply talking about fat tails and the true volatility being higher than the option implied volatility. But on closer reading, this does not appear to be the case. In another section of the interview, Mai talks about the market under estimating the volatility of the distribution, while at another point, he describes the market making mistakes in the mean of the option implied distribution. So it does appear that Mai is distinguishing between errors in the mean, the volatility and the shape of the distribution.

This set me thinking about whether the bimodality of the distribution would make a big difference if the market assumes a (log) normal distribution with the correct mean and variance. Bimodality is very different from fat tails. In fact, if the distribution around each of the two modes is tight, then the tails are actually very thin. The departure from normality is actually a hollowing out of the middle of the distribution. For example, one may believe that a stock would either go to near zero (bankruptcy) or would double (if the risk of bankruptcy is eliminated) – the probability that the stock would remain close to the current level may be thought to be quite small. Mai himself discusses such an example.

To understand the phenomenon, let us take an extreme case of bimodality where there are actually only two outcomes. For simplicity, I assume that the risk free rate is zero. To facilitate comparison with the log normal distribution, I assume that the distribution of log asset prices is symmetric. If the current asset price is equal to 1, then by log symmetry, the two outcomes must be H and ¹⁄_H. Since the two possible outcomes of the log price are ± ln H, the volatility is ln H assuming that the option maturity is 1. The risk neutral probabilities of the two outcomes (p and 1 − p) are easy to compute. Since the risk free rate is zero, p H + (1 − p) ¹⁄_H = 1 implying that p = 1 ⁄ (1 + H) and 1 − p = H ⁄ (1 + H). (Unless H is quite large, these probabilities are not very far from ¹⁄₂).

With all these computations in place, it is straightforward to compare the true bimodal option price with that obtained by the Black Scholes formula using the correct volatility. The plot below is for H = 1.2.

It might appear that the impact of the bimodal distribution is quite small. However, the important question is what is the expected return from buying an option at the wrong (Black Scholes) price in the market and holding it to maturity. The plot below shows that the best strategy is to buy an option with a strike about 6% out of the money. This earns a return of almost 31% (there is a 45% chance of earning a return of 188% and a 55% chance of losing 100%).

The bimodal example tells us that even with thin tails and no under estimation of volatility (no Black Swan events), there can be significant opportunities in the option market arising purely from the shape of the distribution. How would one detect whether the market is already implying a bimodal outcome? This is easily done by looking at the volatility smile. If the market is using a bimodal distribution, the volatility smile would be an inverted U shape which is very different from that normally observed in most asset markets.

Last week, Commissioner Scott D. O’Malia of the US Commodities and Futures Trading Commission delivered a speech in which he admitted that “Big Data Is the Commission’s Biggest Problem ”. This is what he had to say (emphasis added):

This brings me to the biggest issue with regard to data: the Commission’s ability to receive and use it. One of the foundational policy reforms of Dodd­Frank is the mandatory reporting of all OTC trades to a Swap Data Repository (SDR). The goal of data reporting is to provide the Commission with the ability to look into the market and identify large swap positions that could have a destabilizing effect on our markets. Since the beginning of 2013, certain market participants have been required to report their interest rate and credit index swap trades to an SDR.

Unfortunately, I must report that the Commission’s progress in understanding and utilizing the data in its current form and with its current technology is not going well. Specifically, the data submitted to SDRs and, in turn, to the Commission is not usable in its current form. The problem is so bad that staff have indicated that they currently cannot find the London Whale in the current data files. Why is that? In a rush to promulgate the reporting rules, the Commission failed to specify the data format reporting parties must use when sending their swaps to SDRs. In other words, the Commission told the industry what information to report, but didn’t specify which language to use. This has become a serious problem. As it turned out, each reporting party has its own internal nomenclature that is used to compile its swap data.

The end result is that even when market participants submit the correct data to SDRs, the language received from each reporting party is different. In addition, data is being recorded inconsistently from one dealer to another. It means that for each category of swap identified by the 70+ reporting swap dealers, those swaps will be reported in 70+ different data formats because each swap dealer has its own proprietary data format it uses in its internal systems. Now multiply that number by the number of different fields the rules require market participants to report.

To make matters worse, that’s just the swap dealers; the same thing is going to happen when the Commission has major swap participants and end­users reporting. The permutations of data language are staggering. Doesn’t that sound like a reporting nightmare? Aside from the need to receive more uniform data, the Commission must significantly improve its own IT capability. The Commission now receives data on thousands of swaps each day. So far, however, none of our computer programs load this data without crashing. This would seem odd with such a seemingly small number of trades. The problem is that for each swap, the reporting rules require over one thousand data fields of information. This would be bad enough if we actually needed all of this data. We don’t. Many of the data fields we currently receive are not even populated.

Solving our data dilemma must be our priority and we must focus our attention to both better protect the data we have collected and develop a strategy to understand it. Until such time, nobody should be under the illusion that promulgation of the reporting rules will enhance the Commission’s surveillance capabilities. As Chairman of the Technology Advisory Committee, I am more than willing to leverage the expertise of this group to assist in any way I can.

The regulators have only themselves to blame for this predicament. As I pointed out in a blog post nearly two years ago, the SEC and the CFTC openly flouted the express provision in the Dodd Frank Act to move towards algorithmic descriptions of derivatives. I would simply repeat what I wrote then:

Clearly, the financial services industry does not like this kind of transparency and the regulators are so completely captured by the industry that they will openly flout the law to protect the regulatees.

Unsurprisingly, the Senate staff report takes a very critical view of the JPMorgan trades which the bank’s chairman described in a conference call last May as a “bad strategy … badly executed … poorly monitored.” Where I think the staff report goes overboard is in describing even the original relatively simple hedging strategy that JPMorgan adopted during the global financial crisis (well before the complete corruption of the strategy in late 2011 and early 2012).

The staff report says:

A number of bank representatives told the Subcommittee that the SCP was intended to provide, not a dedicated hedge, but a macro-level hedge to offset the CIO’s $350 billion investment portfolio against credit risks during a stress event. In a letter to the OCC and other agencies, JPMorgan Chase even contended that taking away the bank’s ability to establish that type of hedge would undermine the bank’s ability to ride out a financial crisis as it did in 2009. The bank also contended that regulators should not require a macro or portfolio hedge to have even a “reasonable correlation” with the risks associated with the portfolio of assets being hedged. The counter to this argument is that the investment being described would not function as a hedge at all, since all hedges, by their nature, must offset a specified risk associated with a specified position. Without that type of specificity and a reasonable correlation between the hedge and the position being offset, the hedge could not be sized or tested for effectiveness. Rather than act as a hedge, it would simply function as an investment designed to take advantage of a negative credit environment. That the OCC was unable to identify any other bank engaging in this type of general, unanchored “hedge” suggests that this approach is neither commonplace nor useful

I think everything about this paragraph is wrong and indeed perverse.

1. What the crisis taught us is that tail risks are more important than any other risks and far from criticising tail hedges, policy makers should be doing everything possible to encourage them. That the US regulators could not find any other bank that implemented such tail hedges speaks volumes about the complacency of most bank managements. It is those banks that deserve to be criticized.
2. We do not need correlations to size or test the effectiveness of macro hedges. Consider for example hedging a diversified equity portfolio with deep out of the money puts. For a complete tail hedge, the notional value of the put would be equal to the value of the portfolio itself. A beta equal to one might be a perfectly reasonable assumption for a diversified portfolio since a precise estimate of the tail beta might not be very easy. There is no need to compute a correlation between the put value and the portfolio value to determine the effectiveness of the hedge. Even the correlation between the index and the equity portfolio is not too critical because in a crisis, correlations can be expected to go to one.
3. A put option of the kind described above is not an investment designed to take advantage of a stock market crash. Viewed as an investment, the most likely return on a deep out of the money put option is -100% (the put option expires worthless), just as the most likely return on a fire insurance policy is -100% because there are no fires and no insurance claims.

I think the problem with the JPMorgan hedges as they metamorphosed during 2011 was something totally different. The key is a statement that the JPMorgan Chairman made in the May 2012 conference call after the losses became clear:

It was there to deliver a positive result in a quite stressed environment and we feel we can do that and make some net income.

Sorry, tail hedges do not produce income, they cost money. Any alleged tail hedge that is expected to earn income under normal conditions is neither a hedge nor a speculative investment – it is just a disaster waiting to happen.