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.