It is not illegal to be smarter than your counterparties in a swap transaction

"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."

Richard J. Sullivan
United States Circuit Judge
30 November 2018

This is an interesting statement from the judgement in the United States in the case "CFTC versus Wilson and DRW" (full text available here).

The text of the judgement provide a (surprisingly?) good explanation of derivatives market, including convexity effect on futures. The judgement relates to IDEX 3-month futures. Those futures are not traded anymore since 2011. The text includes consideration about variation margin, basis risk, PAI, convexity adjustments, and futures design.

The background is a badly designed swap futures where some participants notice the bad design and its implications while others didn't. The marketing of the futures claimed that "IDEX IRS futures are designed to be economically equivalent in every material respect to plain vanilla interest rate swap contracts currently traded in the OTC derivatives market" (see marketing flyer here). The "economically equivalent" had to be taken with a poetic license, some market participants (and the clearing house) took it at face value to some extend.

CFTC was suing DRW for biding in this very illiquid market at a price closer to the DRW estimated fair value than the unadjusted OTC swap price. As DRW was the only bidder in this illiquid market, DRW was actually the daily settlement price maker.

My comments are not about the manipulation case but about the futures design. Bad designs of swap futures are dangerous in a market with trillions notional underlying. If you are planning to trade those products, don't take marketing and "every body is doing this" at face value, specially in the flow/linear products interest rate market. Analyze all the facets of the product, including cash flows, settlement mechanisms, regulation, margin (variation and initial), convexity adjustment with respect to other flow instruments, comparison with liquid products, hedging strategies, etc. Innocuously looking effects may have a large value in markets with huge notionals. If you are an exchange planning to launch a contract, get independent opinion or advice from experts, don't be seen as someone who don't understand its own products as well as its clients.

I have proposed a swap futures design that is very close to the OTC market in quotation mechanism and convexity adjustments: see my blog post and detailed technical note.

When you deal with new products and related markets, choose your experts well. Make sure he understands the market your are trading in from inside and all the details of its functioning. Do not choose one of which your shareholders (or a judge in the case described above) could say that his "assertions [are] absurd", as the CFTC did.


Has value transfer in LIBOR fallback started?

In my previous blog, I indicated that I was surprised by ISDA decision to use ‘historical mean/median approach’ for the spread adjustment. I also indicated that this fallback method will create some value transfer between the different sides of the existing trades. To my opinion, that value transfer will not take place at the discontinuation announcement date but at the fallback methodology announcement date, which is now.

The full details of the exact spread computation methodology have not been announced yet, but we can already check some ballpark figures. I have looked at the GBP figures. The reason is that in USD there is no historical data for SOFR (not the multi-year history required by the methodology) and no liquid SOFR-OIS trading and in EUR, the new benchmark is not even published yet.

I start with the LIBOR-3M/SONIA spread has this is the most liquid SONIA spread in trading. My analysis start from the hypothesis that the LIBOR will be discontinued on 1-Jan-2022. The analysis could be adapted for other discontinuation dates. I have computed the historical spread for LIBOR-3M v SONIA-compounded-in-arrears-over-3M (using historical data for the benchmarks, all correct market conventions, holidays, dates, etc.). Which history should be used? The proposed periods in the consultations were 5 and 10 years. Let's take 10 years to start. The 10-year period is from the discontinuation announcement. For simplicity, I take 1-Jul-2021 for that date, which leave a 6-month period between announcement and actual discontinuation. I don't know yet what will happen between now and Jul-2021, but I have already a good view of the mean as I have almost 7 years of the 10 years. And the mean number I get is 17.40bps.

Figure 1: GBP-LIBOR-3M and SONIA compounded-in-arrears over a 3-month period. Spread and historical mean.

Where is the LIBOR-3M v SONIA basis trading today for a 30Y tenor? It is at 19.5 bps. And where was it before the methodology announcement? It was at 22.5 bps. Out of the 5 bps decrease forecast by my simple analysis, 3 bps have been gained in a week.

Luck or skills? Let's see other spreads. Another liquid spread is the LIBOR-6M v LIBOR-3M. The average historical spread (using the same method as above): 15.40 bps. The market 30Y basis spread is at 7.7 up from 6.0 before the announcement. Note that the level 7.7bps is the highest level over the past 3 years. That is two out of two.

For the LIBOR-6M v LIBOR-1M, the average historical spread (using the same method as above): 25.00 bps. The market 30Y basis spread is at 13.8 up from 12.1 before the announcement. Note that the highest level over the past 3 years was 14.2. That is three out of three.

I don't know yet the exact technical details that will be proposed for the spread computation: appropriate length of the look-back period (5 or 10 years), look-back period based on IBOR fixing date or maturity date (due to in-arrears), mean or median, holidays (the overnight benchmarks may not have the same good business days than the IBORs), rounding, cut-off days, etc. So there is still some range for the known part of the spread and there is certainly also some uncertainty about the future values of the fixings (between now and discontinuation announcement).

I have run several scenarios for historical data. For the LIBOR-3M v SONIA, I have a range of spreads from 9 to 18 bps; for the LIBOR-6M v LIBOR-3M, from 8 to 16 bps and for LIBOR-6M v LIBOR-1M, from 14 to 25 bps. All the scenarios are in the same direction with respect to the current basis spread market for long tenors. In all cases, in the last week, the market has moved in the direction indicated by the above analysis. In all cases the market has moved to the be very close to one of the bound of the ranges indicated above. In two cases out of three, the basis spread is near its maximum over the last 3 years.

The question in the title was: Has value transfer in LIBOR fallback started? It looks like the answer is: Yes.

Can we still make money out of it? That is more difficult to say at this stage. But I will take a (paper) position based on the above analysis: I enter into a basis swap where I pay LIBOR-1M v receive SONIA + spread on a 30-year tenor for a notional of 1m. The current spread is at 13.4 bps. My analysis give me a 4 to 8 basis points range for the fallback spread. I expect that the market will settle on an estimate of the fallback spread within one year. The horizon for my position is 29-Nov-2019. Target profit is 5bps x ~2000 GBP/bps = ~10,000 GBP. I cut the position on the earliest of when the market has reached 8.5 bps or on 29-Nov-2019. I'm also expecting a little bit of carry as the current level of realized spread (1 to 3 bps) is below the market basis spread.

See you on 29-Nov-2019 for the result!

Feel free to contact me for analysis in other currencies or to discuss positions to could take advantage of the fallback.

Edit 2-Dec-2018: I have started to add the code used for this blog in my open sources muRisQ Libraries. The computation of the composition is available at https://github.com/marc-henrard/muRisQ-ir-models/blob/master/src/main/java/marc/henrard/murisq/pricer/generic/FallbackUtils.java. I will add the code that I used for the graphs and average computations at a later stage.


ISDA published Preliminary Results of Benchmark Consultation

ISDA has published Preliminary Results of Benchmark Consultation.

As expected, the majority of respondents preferred the ‘compounded setting in arrears rate’ for the adjusted risk-free rate (RFR). This is to my opinion an error, as detailed in my Quant Perspective. The proponent of the method have not yet detailed how it would work in practice for instruments that require an immediate settlement (FRA, IBOR in arrears, range accrual, etc.; a minority of trades but not a small amount) and vanilla instruments with non-good business day adjustments (the majority of trades).

The ISDA statement indicates that "as part of that decision, the ISDA Board Benchmark Committee will set out the details related to the adjusted RFR and spread adjustment that remain outstanding". Hopefully, the details related to the dates question I have mentioned in my answer to the consultation will be provided.

The second part of the consultation provided an answer that I was not expecting. The spread adjustment option selected by the majority is the ‘historical mean/median approach’. The big advantage of the methodology is that it is simple, with little possibility to manipulate (would require to manipulate the past 5 or 10 years) but its big disadvantage was that it would create a value transfer at discontinuation. The value would have changed from the expected economic difference between the future value of LIBOR to the average of the past. I used the past and conditional in the above sentence for the following reason.

By deciding the use an historical average, the transfer of value is still present but at a different moment. The value transfer is not anymore at the discontinuation announcement date but at the fallback methodology announcement date. We expect the discontinuation for LIBOR to happen in 2021, in 3 years time. We don't need to look at the economic reality of LIBOR-OIS spread (bank credit risk) anymore to price a LIBOR-OIS spread for any fixing beyond 2021. The only thing that is important is the past 7 years and the next 3 years (to obtain a 10 year history), not the reality at the fixing date. The value transfer took place when the fallback option was decided. The value transfer will not be seen immediately as the market has to absorb the information and the different participants have to incorporate it in their anticipations.

Unfortunately I don't have access to detailed market data about basis in the different currencies to do an in depth analysis. But it would be interesting to see how much the long term forward basis (beyond 2021) in the LIBOR related currencies have changed to be close to the historical mean over the last months, since the publication of the consultation and the reception of its answers.


A two cent arbitrage - free options

Mandatory arbitrage

Belgium is now imposing mandatory arbitrage in retail. I concede that this is a 2 cents (0.02 EUR) maximum arbitrage by transaction, but an arbitrage nevertheless. The arbitrage is imposed on retailer by forcing them to issue free option with each retail transaction. There is no limit to the number of transactions by customer and retailers cannot refuse the transaction (and the arbitrage).

The mandatory free option was proposed by a Belgium vice-premier and minister of Economy (Kris Peeters; one of the top 5 minister in Belgium) and approved by the Council of Ministers.

Obviously the minister press release does not describe his decision like I did. It is presented as a simplification measure without impact. The press release even indicate that "on average the consumer will pay the same amount". According to the press release, the ECB shares the analysis (I would like to see the analysis). The press release (in French) can be found here:
http://www.krispeeters.be/sites/default/files/20181123_CP_Arrondissement_paiements_cash.pdf (I'm still looking for an official document, not only a press release on the personal website of the minister).

Arbitrage origin

Now I need to explain where this issue is coming from. The official smallest currency amount in Euro-land is one cent (0.01 EUR). This is a very small amount. The production and handling of the 1 cent and 2 cents coins have a large cost. The idea is then to leave the official smallest amount to 1 cent but change it in practice for actual payments to 5 cents (the third smallest coin) by a rounding mechanism. The rounding is not apply on the price for each item but on the price for each purchase of multiple items. Currently the rounding is not mandatory but can be decided by the retailer. To my knowledge, there is no obligation for the retailer to indicate to the customers if they apply the rounding option before the total price is indicated to the customer. It seems that the retailers have today the free option to chose the rounding or not and that they can do so for each purchase. In practice, very few retailers use the rounding free option, because they are afraid to be seen taking advantage of the system and somehow getting a bad reputation.

The proposal by the minister is to impose a mandatory rounding, but only for the cash payments, not the card payments. Now the option is inverted and there is no need of the customer to loose face or reputation by indicating explicitly his rounding choice. If the total price of his purchases is ending by 1, 2, 6 or 7 cents, pay by cash and get a 1 or 2 cents discount. If the total price ends by 3, 4, 7 or 9 cents, pay by card and pay the exact price. In case of 0 or 5, do whatever is most convenient. So exercise your free rounding option, not by saying explicitly that you do it, but by exercising your cash/card option (which would be value neutral otherwise). You can be greedy without saying it.

On the other side, you have to weight the 1 or 2 cents arbitrage with the potential inconvenience of checking the final price and having enough cash with you to exercise the option.

Exercising your free option

On my side, I plan to use this option (at least once ;)). It would be funny to see a lot of people using that option. The impact would be (small) financial losses for the retailer, probably larger losses in term of operational cost. More cash transactions, less self service teller used (if they don't have cash option).

This is the risk of having a economy minister that is not a quant (he is a lawyer and accountant by background). He is also in charge of "financial products" and financial regulators (FSMA), two good reasons to have a quant or at least a quant aware person at that position or in last resort having a quant advisor (in the list of his many advisors, I don't see any "financial products" or "financial regulation" advisor). He can create, probably out of good will, unintended quantitative finance consequences from qualitatively looking innocuous decisions. Like for all regulatory proposal related to finance and economy, I would encourage regulators and law makers to consult with quants on the quantitative impacts. Some conséquences may be unintended but most of them are certainly not un-forecastable. (I'm available for consulting engagements if needed).

Having fun

The new law related to the rounding will take effect only on 1 December 2019. So I will need to wait another year before being able to test my arbitrage. It would be fun (at least for some meaning of fun) if on that date everybody was exercising its free option and take advantage of the possibility. We could call it the "quant awareness day". Nowadays, there are "awareness day" for almost everything (see for example https://www.awarenessdays.com/) why not for quantitative analysis. This is not only a reverie for recognition, but also a hope for better regulation and laws.


Fallback, cash flows and OIS discounting

In the IBOR fallback issue, there are different criteria we would like to impose in order to obtain a clean fallback. Among those criteria are the absence of value transfer and the coherence (IBOR is IBOR).

The fallback procedures proposed in ISDA consultation rely on the replacement of each IBOR fixing by an RFR-linked rate plus an adjustment spread.

The existence of CCP basis (and bilateral to CCP basis) which is potentially different between LIBOR products and OIS products leads to the following paradox: if we want to achieve the absence of value transfer, we need to select an adjustment spread that is different for the same IBOR and RFR depending on the clearing location, which is a violation of the coherence criterion. If we keep coherence, we have the same spread and consequently there is a value transfer.

Where is the paradox coming from? I would say that it is coming from a misunderstanding of the OIS discounting formula. The formula is written as (see Formula 8.6, based on Formula 8.3, Theorem 8.1 in my multi-curve book)

The formula looks like the valuation is obtained by discounting a cash flow. This is also what the popular name of the formula seems to imply; and this is also why I don't like the name. It gives the wrong intuition. The formula is correct but should not be interpreted as discounting a single cash flow. The reality is many cash flows (daily variation margin); the actual theoretical IBOR fixing is never paid as a single amount. The summary of all those daily cash flows into a single expectation is a very simple formula for a complex process. The formula is based on hypothesis, including perfect replication hypothesis by IBOR related instruments and OIS (hence the OIS discounting formula). But that replication is dynamic, with the hedging changing on a continuous basis, depending on the VM paid and the evolution of the market.

This approach is valid only where there is availability of the hedging instruments. In practice, it means that there is one formula coming from one pool of liquidity and one set of rules at each CCP (and at each bilateral agreement). Each CCP is its own world in term of hedging and price. Of course in practice it is possible to transfer risk (and thus price) from one CCP to another, but at a cost (the posting of IM, summarised in MVA figures). Between CCP prices there is not unique transformation of price but a price range, with the range depending of the IM rules and the cost of funding of potential arbitrageurs.

But this does not answer to the question: where is the paradox coming from. Based on the above analysis, my answer would be that there is no paradox in our criteria of asking for an absence of value transfer and a coherence on IBOR fixing. The problem/paradox/error comes from trying to solve the dynamic hedging problem with a static solution. The ISDA proposed solution (adjusted RFR + adjustment spread) is decided on the announcement date and is fixed from then on. Imposing a static solution to a dynamic problem leads to impossibility to obtain the price based on a dynamic world with segregated pools of liquidity.

The problem is not coming from our criteria, those are, to my opinion, fair requests, but from the constraints imposed on the solution which are not in line with the valuation framework where we want to apply them.