Prof. Jayanth R. Varma’s Financial Markets Blog

A blog on financial markets and their regulation

Does better mathematics win in the markets?

Last week, the US District Court Southern District of New York issued a judgement dismissing the US CFTC’s complaint of market manipulation against Donald R. Wilson and DRW Investments (h/t Matt Levine). Describing the CFTC’s theories as little more than an “earth is flat” style conviction, the court wrote:

It is not illegal to be smarter than your counterparties in a swap transaction, nor is it improper to understand a financial product better than the people who invented that product. In the summer and fall of 2010, Don Wilson believed that he comprehended the true value of the Three-Month Contract better than anyone else, including IDCH, MF Global, and Jeffries. He developed a trading strategy based on that conviction, and put his firm’s money at risk to test it. He didn’t need to manipulate the market to capitalize on that superior knowledge, and there is absolutely no evidence to suggest that he ever did so in the months that followed.

In August 2011, DRW unwound its swap futures trade at a profit of $20 million, and the CEO of the biggest firm on the other side Jeffries emailed Wilson: “You won big. We lost big.”. The mathematics behind this trade is well described in a paper by a well known academic quant and two quants who worked for DRW:

Rama Cont, Radu Mondescu and Yuhua Yu “Central Clearing of Interest Rate Swaps: A Comparison of Offerings” available on SSRN.

The purpose of this blog post is to ask a different question: how common is it for traders make money simply by better knowledge of the mathematics than other participants. My sense is that this is relatively rare; traders usually make money by having a better understanding of the facts.

Perhaps the best known mathematical formula in the financial markets is the Black-Scholes option pricing formula, and Black has described his attempts to make money using this formula:

The best buy of all seemed to be National General new warrants. Scholes, Merton, and I and others jumped right in and bought a bunch of these warrants. For a while, it looked as if we had done just the right thing. Then a company called American Financial announced a tender offer for National General shares. The original terms of the tender offer had the effect of sharply reducing the value of the warrants. In other words, the market knew something that our formula didn’t know.

Black, F., 1989. “How we came up with the option formula”. Journal of Portfolio Management, 15(2), pp.4-8.

Many years later, Black did make money with superior knowledge of the mathematics of option pricing. A well known finance academic Jay Ritter has described the sad story of being on the losing side of this trade:

I lost more in the futures market than I made from my academic salary. … Years later, I found out who was on the other side of the trades in the summer of 1986. It was Goldman Sachs, with Fischer Black advising the traders, that took me to the cleaners as the market moved from one pricing regime to another. In the first four years of the Value Line futures contract, the market priced the futures using the wrong formula. After the summer of 1986, the market priced the Value Line futures using the right formula. The September 1986 issue of the Journal of Finance published an article (Eytan and Harpaz, 1986) giving the correct formula for the pricing of the Value Line futures. In the transition from one pricing regime to the other, I was nearly wiped out.

Ritter, J.R., 1996. “How I helped to make Fischer Black wealthier”. Financial Management, 25(4), pp.104-107.

One person who did make money by understanding the mathematics of option pricing was Ed Thorp who kept his knowledge secret till Black and Scholes discovered their formula and published it. Decades later Thorp said in an interview:

… with blackjack, … I thought it was mathematically very interesting, so as an academic, I felt an obligation to publicize my findings so that people would begin to think differently about some of these games. … Moving on to the investment world, when I began Princeton/Newport Partners in 1969, I had this options formula, this tool that nobody else had, and I felt an obligation to the investors to basically be quiet about it. … I spent a lot of time and energy trying to stay ahead of the published academic frontier.

Consulting Submitter, Journal of Investment, “Putting the Cards on the Table: A Talk with Edward O. Thorp”, PhD (July 1, 2011). Journal of Investment Consulting, Vol. 12, No. 1, pp. 5-14, 2011. Available at SSRN

Academics in general have been content to publish their results even when they think it is worth a billion dollars:

Longstaff, F.A., Santa-Clara, P. and Schwartz, E.S., 2001. “Throwing away a billion dollars: The cost of suboptimal exercise strategies in the swaptions market”. Journal of Financial Economics, 62(1), pp.39-66.

Using unpublished mathematical results to make money often has the effect of destroying the underlying market. Nasdaq (which owned IDCH) delisted the swap futures contract within months of DRW unwinding its profitable trade. Similarly, Fischer Black effectively destroyed the Value Line index contract through his activities. Markets work best when the underlying mathematical knowledge is widely shared. It is very unlikely that the option markets would have grown to their current size and complexity if the option pricing formulas had remained the secret preserve of Ed Thorp. Mathematics is at its best when it is the market that wins and not individual traders.

PS: One of the things that has puzzled me about the DRW case is that DRW was a founding member of Eris which offered a competing Swap Futures product. Why didn’t anybody raise a concern that DRW and Eris were conspiring to destroy IDCH? Of course, DRW would have the compelling defence that with $20 million of profits to be made from the arbitrage, they did not need any other motive to do the trade. But still it bothers me that the matter does not seem to have come up at all.

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Earnings related trading: Futures or Options

There is a large body of literature (mainly in the US) that a lot of the trading activity in response to earnings information happens in the options market. (The seminal paper in this field is Roll, R., Schwartz, E., & Subrahmanyam, A. (2010). O/S: The relative trading activity in options and stock. Journal of Financial Economics, 96(1), 1–17.) Unfortunately, the US and most other countries do not have a liquid single stock futures market, and so we do not know whether the options market was the preferred choice of the informed traders or it was the second best choice substituting for the missing first choice (the futures market). If what the informed trader wanted was leverage and short selling ability, the futures are a much better vehicle because there is no option premium and no delta rebalancing cost. On the other hand, if the trader believed for example that there was a high probability of a large upside surprise in the earnings, counterbalanced by a more modest risk of downside surprise, then the sensible way to express that view would be with a bull-biased strangle (buy a substantial number of out-of-the-money calls and a somewhat smaller number of out-of-the-money puts). It would be too risky to trade this view in the futures market without the downside protection provided by options.

India provides the perfect setting to resolve this issue because it has liquid single stock futures and single stock options markets (both of these markets are among the largest such markets in the world). In a recent paper, my doctoral student, Sonali Jain, my colleagues, Prof. Sobhesh Agarwalla and Prof. Ajay Pandey and I investigate this (Jain S, Agarwalla SK, Varma JR, Pandey A. Informed trading around earnings announcements – Spot, futures, or options?. J Futures Markets. 2018. https://doi.org/10.1002/fut.21983) We find that in India single stock futures play the role that the options market plays in the US implying that the informed traders are seeking leverage benefits of derivatives rather than the nonlinear payoffs of options. We also find patterns in the data that are best explained by information leakage. Though, Indian derivative markets are often disparaged as being gambling dens dominated by noise traders, our results suggest that the futures markets are also venues of trading based on fundamentals.

Spreads price constraints

Craig Pirrong writes on his Streetwise Professor blog that “Spreads price constraints.” Though Pirrong is talking about natural gas calendar spreads, I think this is an excellent way of thinking about many other spreads even for financial assets. In commodities, the constraints are obvious: for calendar spreads, the constraint is that you cannot move supply from the future to the present, for location spreads, the constraints are transportation bottlenecks, for quality spreads, technological constraints limit the elasticity of substitution between different grades (in case of intermediate goods), while inflexible tastes constrain the elasticity in case of final goods.

But the idea that “spreads price constraints” is also true for financial assets where the physical constraints of commodities are not applicable. The constraints here are more about limits to arbitrage — capital, funding, leverage and short-sale constraints, regulatory constraints on permissible investments, and constraints on the skilled human resources required to implement certain kinds of arbitrage.

Thinking of the spread as the shadow price of a constraint makes it much easier to understand the otherwise intractable statistical properties of the spread. Forget about normal distributions, even the popular fat tailed distributions (like the Student-t with 3-10 degrees of freedom) are completely inadequate to model these spreads. Modelling the two prices and computing the spread as their difference does not help because modelling the dependence relationship (the copula) is fiendishly difficult (see my blog post about Nordic power spreads). But thinking about the spread as the shadow price of a constraint, allows us to frame the problem in terms of standard optimization theory. Shadow prices can be highly non linear (even discontinuous) functions of the parameters of an optimization problem. For example, if the constraint is not binding, then the shadow price is zero, and changing the parameters makes no difference to the shadow price until the constraint becomes binding, at which point, the shadow price might jump to a large value and might also become very sensitive to changes in various parameters.

This is in fact quite often observed in derivative markets — a spread may be very small and stable for years, and then it can suddenly shoot up to very high levels (orders of magnitude greater than its normal value), and can also then become very volatile. If the risk managers had succumbed to the temptation to treat the spread as a very low risk position, they would now be staring at a catastrophic failure of the risk management system. Risk managers would do well to refresh their understanding about duality theory in linear (and non linear) programming.

Aadhaar and signing a blank sheet of paper redux

The Aadhaar abuse that I described a year ago as a hypothetical possibility a year ago has indeed happened in reality. In July 2017, I described the scenario in a blog post as follows:

That is when I realized that the error message that I saw on the employee’s screen was not coming from the Aadhaar system, but from the telecom company’s software. … Let us think about why this is a HUGE problem. Very few people would bother to go through the bodily contortion required to read a screen whose back is turned towards them. An unscrupulous employee could simply get me to authenticate the finger print once again though there was no error and use the second authentication to allot a second SIM card in my name. He could then give me the first SIM card and hand over the second SIM to a terrorist. When that terrorist is finally caught, the SIM that he was using would be traced back to me and my life would be utterly and completely ruined.

Last week, the newspapers carried a PTI report about a case going on in the Delhi High Court about exactly this vulnerability:

The Delhi High Court on Thursday suggested incorporating recommendations, like using OTP authentication instead of biometric, given by two amicus curiae to plug a ‘loophole’ in the Aadhaar verification system that had been misused by a mobile shop owner to issue fresh SIM cards in the name of unwary customers for use in fraudulent activities. The shop owner, during Aadhaar verification of a SIM, used to make the customer give his thumb impression twice by saying it was not properly obtained the first time and the second round of authentication was then used to issue a fresh connection which was handed over to some third party, the high court had earlier noted while initiating a PIL on the issue.

This vindicates what I wrote last year:

Using Aadhaar (India’s biometric authentication system) to verify a person’s identity is relatively secure, but using it to authenticate a transaction is extremely problematic. Every other form of authentication is bound to a specific transaction: I sign a document, I put my thumb impression to a document, I digitally sign a document (or message as the cryptographers prefer to call it). In Aadhaar, I put my thumb (or other finger) on a finger print reading device, and not on the document that I am authenticating. How can anybody establish what I intended to authenticate, and what the service provider intended me to authenticate? Aadhaar authentication ignores the fundamental tenet of authentication that a transaction authentication must be inseparably bound to the document or transaction that it is authenticating. Therefore using Aadhaar to authenticate a transaction is like signing a blank sheet of paper on which the other party can write whatever it wants.

Indian Single Stock Option Pricing

A recent paper by my doctoral student, Sonali Jain, my colleague, Prof. Sobhesh Agarwalla and myself (Jain S, Varma JR, Agarwalla SK. Indian equity options: Smile, risk premiums, and efficiency. J Futures Markets. 2018;1–14. https://doi.org/10.1002/fut.21971) studies the pricing of single stock options in India which is one of the world’s largest options markets.

Our findings are supportive of market efficiency: A parsimonious smile-adjusted Black model fits option prices well, and the implied volatility (IV) has incremental predictive power for future volatility. However, the risk premium embedded in IV for Single Stock Options appears to be higher than in other markets. The study suggests that even a very liquid market with substantial participation of global institutional investors can have structural features that lead to systematic departures from the behavior of a fully rational market while being “microefficient.”

The good news here is that (a) options with different strikes on the same stock are nicely consistent with each other (parsimonious smile), and (b) the option market predicts future volatility instead of blindly extrapolating past volatility. The troubling part is that the implied volatility of Indian single stock options consistently exceeds realized volatility by too large an amount to be easily explained as a rational risk premium. Globally, there is a substantial risk premium in index options but not so much in single stock options in accordance with the intuition that changes in index volatility are a non diversifiable risk, while fluctuations in the idiosyncratic volatility of individual stocks are probably diversifiable. The large gap between Indian implied and realized volatility is therefore problematic. However, the phenomenon cannot be attributed entirely to an irrational market: we find that the single stock implied volatility has a strong systematic component responding to changes in market wide risk aversion (the index option smile).

There is a puzzle here that demands further research. There is some anecdotal evidence that option writers demand a risk premium for expiry day manipulation by the promoters of the company. I also think that there is a shortage of capital devoted to option writing despite the emergence of a few alternative investment funds in this area. Perhaps there are other less well understood barriers to implementing a diversified option writing strategy in India.

Markets versus Institutions

I had the opportunity to engage in a conversation with Nobel Laureate Robert Merton after he delivered the R H Patil Memorial Lecture as part of the Silver Jubilee celebrations of the National Stock Exchange last week. The video is available here, and a large part of the conversation is about whether financial markets can be trusted more than financial institutions particularly in the Indian context.

Lessons from the Nasdaq Clearing Default

Last month, the loss caused by the default of a single trader in a Nordic power spread contract cleared by Nasdaq Clearing consumed the entire €7 million contribution of Nasdaq to the default waterfall and then wiped out more than two thirds of the €168 million default fund of the Commodities Market segment of Nasdaq (the diagram on page 7 of this document shows the entire default waterfall for this episode).

Nasdaq explained its margin methodology as follows:

The margin model is set to cover stressed market conditions, covering at least 99.2% of all 2-day market movements over the recent 12 month period. In the final step of the margin curve estimation a pro-cyclicality buffer of 25% is applied.

The MPOR (Margin Period of Risk) for the relevant products is two days.

It also provided the following historical data:

  • Prior to the default, the largest daily change in spread since 2011 was €1.6.
  • 99% of all observations during this period were below €1.
  • Nasdaq Clearing’s margin model for this particular spread was calibrated to cover changes in margin spread up to approximately €4
  • The change in the spread on the default date was €5.56.

There has been a lot of excellent commentary on this episode:

The episode highlights a number of important lessons about risk management that we knew even before this default happened:

  • Electricity is a nasty asset both for traders and for risk managers. Equities are of course the nicest asset class in terms of return distributions, but electricity is really messy compared to even quite ill behaved commodities like natural gas.
  • Spreads are a lot worse than the underlying assets from a risk modelling point of view. Over the last few decades, finance has figured out a lot about volatility, but we still do not know much about modelling correlation and dependence. (Ability to utter the magic word “copula” does not amount to knowledge).
  • It is very hard to get much beyond 99.9% risk coverage using margins alone — not even in equities. A decade ago, I computed that margins set at eight standard deviations would cover only 99.95% risk (in terms of expected shortfall) in the Indian index futures market.
  • To get to a AAA equivalent 99.99x% risk coverage would need other elements of the default waterfall like member and clearing house capital. Member contributions to CCP default funds are therefore at significant risk of loss.
  • There is always a risk that all this waterfall would not be enough. If one trader can blow away two-thirds of the default fund of one CCP, some day somebody is bound to blow away the entire default fund of some CCP somewhere. With the increasing clearing of toxic asset classes like credit and power, I think it is only a matter of time before that happens.
  • It is important to isolate different market segments with separate waterfalls and segregated default funds. In the Nordic power episode, even if there had been a delay or failure to replenish the default funds, it would have affected only the commodities segment, and Nasdaq would have continued to clear all other products. In India, I have always argued that this is extremely important since cash equities and derivatives trade on the same exchange: even if the derivatives clearing segment goes bust, cash equities must continue to trade.
  • Fire sale liquidation of defaulted positions appears to be a growing problem at the clearing houses. I remember when Nick Leeson almost brought down Symex, they chose to wind down the position over several days to reduce losses. The US exchanges seem to prefer a quick auction. When Lehman failed, CME did an immediate auction of the entire Lehman portfolio of positions at that exchange, while LCH used its well oiled machinery for trading down defaulted positions. (Lehman’s bankruptcy examiner complained bitterly about the losses suffered by the Lehman estate due to this auction, but ultimately concluded that the exchange action is protected by law and could not be challenged). In the Nordic episode also, Nasdaq has displayed the American penchant for quick auctions.The Streetwise Professor discusses another power spread related default in the United States where the clearing house abandoned the auction when it “resulted in liquidation prices that were more than six times higher than the actual portfolio losses“. I have long argued that Indian exchanges should build up the operational and technical capabilities to trade down large defaulted positions, but I fear that these capabilities are quite deficient. Regulators also seem to be insufficiently concerned about this problem.

Mutual fund redemptions redux

Debt mutual funds are not banks: when mutual fund investors redeem their units at an inflated Net Asset Value (NAV) they simply steal money from their co-investors. This adjacency risk or co-investor risk comes to the fore every now and then, when heightened default risk makes bond prices volatile and unreliable. This happened in India in 2008 during the global financial crisis and is happening again today. Providing liquidity to solvent banks in a crisis makes sense, but providing liquidity to debt mutual funds is a bad idea because it simply allows rich, better informed investors to steal from less informed co-investors. The correct way to provide liquidity is to lend not to the mutual fund but to the unit holder (against units of debt mutual funds).

Unfortunately, I appear to be in a minority on this issue. Even the best analysts appear to support liquidity lines for the mutual fund; for example, the highly knowledgeable and respected Akash Prakash writes in today’s Business Standard (paywall):

Liquidity lines and repo facilities have to be set up for the debt mutual funds. We cannot allow forced selling at panic prices. Panic selling will force other funds to also mark down their bonds, showing paper losses, creating more redemptions, more selling and we will spiral into a negative feedback loop.

My position is the opposite: we must force mutual funds to mark down their bonds so that their NAVs are fair and correct. The way to stop panic selling is side pockets and gates as I have been saying for the last ten years: during the 2008 crisis in India (borrowing and gating), during the Amtek Auto episode, and in response to US money market mutual fund reforms (minimum balance at risk and gates).

Liquidity lines to the mutual funds are a bail out of rich corporations and high net worth individuals at the cost of the ordinary investor. Liquidity lines to unit holders (against the security of units of debt mutual funds) do not have this problem because then the bond price risk remains with the borrower and is not transferred to other co-investors.

Indian banks: quiescent shareholders and activist regulators

The Indian central bank or other government agencies have been instrumental in effecting a change of management in three under-performing private sector banks (ICICI Bank, Axis Bank and Yes Bank) in recent months. While much has been written about the functioning of the boards and of the central bank, the more fascinating question is about the dog that did not bark: the quiescent shareholders of these banks. They have suffered in silence as these banks have surrendered the enviable position that they once had in India’s financial system. The void created by the wounded banking system in India is being filled by non bank finance companies. So much so that one of these non banks (Bajaj Finance) trades at a Price/Book ratio 3-4 times that of the above mentioned three banks and now boasts of a market capitalization roughly equal to the average of these three banks.

The question is why has this not attracted the attention of activist investors. One looks in vain for a Third Point, Elliott or TCI writing acerbic letters to the management seeking change. The Indian regulatory regime of voting right caps and fit and proper criteria has ensured that such players can never threaten the career of non performing incumbent management in Indian banks. The regulators have entrenched incumbent managements and so the regulators have to step in to remove them.

Incidentally, the securities regulator in India has been no better. It too has ensured that the big exchanges and other financial market infrastructure in India are immune to shareholder discipline, and over the last several years many of these too have performed far below their potential.

Indian regulators do not seem to understand that capitalism requires brutal investors and not just nice investors talking pleasantly to the management. Capitalism at its best is red in the tooth and claw.

The FED’s bite is worse than its bark

If any emerging market thought that the US Federal Reserve is a paper tiger whose bark is worse than its bite, the last few months have shattered that illusion. Already, the bite is hurting a lot more and the tiger still appears to be hungry and on the prowl.

The comparison below is actually biased in favour of a bigger effect for the bark because it focuses on the Fragile Five who were the worst sufferers during the barking phase. I have left out Argentina and China who have suffered only or mainly in the biting phase.

The FED’s bark (Taper Tantrum: April-July 2013)

The data is from Barry Eichengreen and Poonam Gupta, Tapering Talk: The Impact of Expectations of Reduced Federal Reserve Security Purchases on Emerging Markets. Following Eichengreen and Gupta, I have measured the exchange rate pressure by the percentage increase in the nominal exchange rate (units of domestic currency per US dollar), though ideally it should be the decline in the inverse of this number. Unlike Eichengreen and Gupta, I have simply added the percentage exchange rate change and the percentage reserve loss for a crude measure of the total effect. For a blog post, I am too lazy to weight the two measures by the inverse of their respective standard deviations (and I am also quite happy with improper linear models).

Depreciation Reserve Loss Total
Brazil 12.52 1.69 14.21
India 9.98 4.77 14.75
Indonesia 3.58 13.61 17.19
South Africa 8.96 5.42 14.38
Turkey 7.61 8.20 15.81

The FED’s bite (Ongoing since April 2018)

The following data is what I have been able to put together from easily available sources on the internet. The currency depreciation is from Yahoo Finance and covers the period from April 16, 2018 to September 13, 2018. The reserve loss is from end March (or mid April where available) to the latest date for which I could get data clicking through to the data links on the National Summary Data Pages (NSDPs) of the IMF’s Dissemination Standards Bulletin Board (DSBB). Except for Turkey, the data for the rest of the countries is not hopelessly out of date, and for Turkey, the reserve loss is totally swamped by its currency depreciation.

If you have better data, please free to provide that in the comments section.

Depreciation Reserve Loss Total
Brazil 22.22 0.26 22.48
India 10.46 5.90 16.36
Indonesia 8.02 6.35 14.37
South Africa 21.36 -0.00 21.36
Turkey 50.86 8.15 59.01