Similar issues have been discussed in the past: Tax questions cloud prospects for CME swap future and MAC swaps.

### MAC what?

MAC stands for

*Market Agreed Coupon*. “Market Agreed” is probably a misnomer as nobody other than the trade participants has to agree with the coupon. The real meaning is a swap with a fixed coupon at a rounded figure, usually every 25 bps, and the trade is not done on the fixed rate but on the price. For example a quote can be “a 10Y receiver, 2.25% coupon swap at a price of 97bps” or something similar. The price is paid as a one-off fee at the settlement or effective date of the swap. In the sequel I will call “

*continuous coupon swap*”, the swaps where the coupon is not necessarily one of the discrete coupons, the swap is traded in term of the fixed rate paid and no up-front fee is paid.

### Problems

The concerns related to those instruments are from a tax perspective and also from a risk perspective. Those two very different types of concerns have their roots in the same feature of the swaps, which is the up-front (non-periodic) payment of a ‘fee’.

*Tax*: One of the issues with this type of swaps is its accounting treatment. Under the accounting rules of some countries the fact that there is an up-front payment may lead to the classification of the transaction as a loan instead of a derivative for tax purposes.

*Risk*: The hedging of interest rate risk with this type of swaps is quite different of the one with continuous coupon swaps. If you use a standard curve calibration mechanism with the MAC swaps quoted on price, you obtain a delta risk figure which is fundamentally different from the one of a continuous coupon swaps. Roughly speaking the risk figure for a 10Y swap will be 10 times smaller. The price has roughly a sensitivity of 10 with respect to the rate. It is similar to a view of a bond world in term of price change by opposition to yield change. For example a “parallel” movement of the rate curve becomes a movement of the price curve roughly proportional to the maturity.

### Why introducing those problems?

Before trying to solve those problems in a way or another, maybe we can try to understand why the feature was introduced in the first place. A fixed coupon is attractive to people as different trades can be compressed in a unique trade. The standard MAC swaps trade often come not only with standard coupons but also with standard effective dates, usually the quarterly IMM dates. The swaps can be traded over a quarter and accumulated into a single position with full offset between payers and receivers.

With the standard (and soon mandatory) collateral (variation margin), the upfront payment is not really a payment anymore. The amount paid is immediately received back as a VM (see my previous post Continous dividend v discrete cash flows for a discussion on the “immediately”). It is not a cash play but a curve play. The difference between a MAC swap and a standard swap is a little bit of curve play between the overnight amount (upfront payment) and the regular payments on the coupons.

### Is this the best solution?

Before proceeding further in the analysis, we have to note that when we say “fixed” or “standard” (or “agreed”) coupon, it has to be understood as standard for a given period. If the market move enough, the new standard will be different. If the continuous coupon swaps trade a 2.15%, the MAC coupon will be 2.25%; if the continuous coupon swaps trade at 2.10%, the MAC coupon will move to 2.00%. What we described above as a unique coupon portfolio is actually a multiple coupon portfolio with the coupons at discrete values.

It would be possible to achieve the same results while still quoting the swaps in term of coupon and have no up-front fee. One method is to deliver not one swap with the quoted coupon but a portfolio of two swaps with discrete coupons (the MAC-like coupons) and notional of those swaps such that the weighted average of the coupons is the quoted coupon. Suppose that the 10Y swap is quoted at 2.10% for a notional of 100m. The delivery would be two swaps, one with a coupon of 2.00% and a notional of 60m and one with a coupon of 2.25% and a notional of 40m. The cash flows generated by those 2 swaps are identical to the cash flows of the unique swap with coupon 2.10%.

In general the equations to solve for the notional

*n*and

_{0}*n*related to a swap of notional

_{1}*n*with coupon

*c*which is between

*s*and

_{0}*s*, are

_{0}*n*

_{0}+ n_{1}= nand

*n*

_{0}* s_{0}+ n_{1}* s_{1}= n * c*n*

_{1}= n * (c - s_{0}) / (s_{1}- s_{0})and

*n*

_{0}= n * (s_{1}- c) / (s_{1}- s_{0})This process has (almost) all the properties of the original approach and none of the drawbacks. There is no up-front fee and the risk management is done in term of coupon/yield. When several trades with same dates are traded, they can be netted easily. The only draw back is that if you trade only one swap, you will have two swaps in your books. But as soon you trade many of them with the same counterparts, like in the cleared IRS case, the netting comes into play automatically.

We need a name for this new approach. My vote goes to “double MAC”, hence the title of this blog.

### And swap futures?

Swap futures can also be designed with a similar idea in mind. The natural dimension in the swap market is the rate. One can create a swap that is quoted in term of rate and have the daily margin based on the rate multiplied by the notional and multiplied by a fixed amount representing the PVBP. For a true swap, the PVBP is changing with the level of the market. We could design the swap future with a fixed PVBP, let say 10 for a 10Y underlying and work from there. This type of swap futures requires a

*convexity adjustment*, but anyway you already need one due to the daily margin feature of futures. The valuation of this product would require mixture of short term CMS with futures pricing. The quotation mechanism would make it the best instrument for hedges. Suppose that the notional for the swap futures is 100,000. You see a PV01 of 123,400 by basis point on you screen for the 10Y bucket, the hedge ration is 10*100,000/10,000=100. You need 1,234 contract to hedge that risk. Easy, isn't it? At expiry of the futures, two cleared swaps would be delivered, a double MAC with coupons and notionals selected to reproduce the last futures price. Notional can be selected to reproduce the futures theoretical notional or to conserve the total PVBP at delivery. The latter makes sense for those who view the futures as hedges and want to have a smooth risk transition at expiry.

I proposed that type of swap futures some years ago, but it was never quoted on any exchange. Maybe it is the right moment to propose the idea again. This can be viewed as a new episode of my series on “

*financial fiction*” that started some time ago.

Note also that those rate quoted swap futures lead naturally to swaption futures. Swaptions trade in price on an underlying with a given coupon/strike and no upfront payment on the swap. The swaption futures would have a quoted price (and daily margin) and a strike rate which has the same meaning as in the swaption case. At expiry of the swaption futures the parties enter into a (cleared) swap or not at the choice of the party long the swaption futures.

I presented my proposal at the “The 4th Interest Rate Conference” in March 2015. I have also numerous (non public) documents with analysis of the convexity impact, the hedging mechanism, detailed settlement and delivery process and so on.

If you have an interest in those mechanisms, to implement them in the OTC market or in the futures market, don’t hesitate to contact me for more details. You may also be interested by my analysis of the pricing of swap futures quoted in price which is available in a SSRN working paper: Deliverable Interest Rate Swap Futures: Pricing in Gaussian HJM Model.

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