# Hedging Mexico’s Bondes D with CME F-TIIE Futures

Bondes are Federal Government Development Bonds (Bonos de Desarrollo del Gobierno Federal), floating-rate Mexican government securities.

Mexican Bondes D coupons are a function of the Central Bank of Mexico’ s overnight bank funding rate over the four-week coupon period.

Final coupon calculations are made by assigning rates to each day in the coupon period, including weekends and holidays, and then compounding such rates daily to calculate an annualized rate for the coupon period. The rate is then applied over the four-week, or 28-day, period to generate a coupon cash flow. Rates assigned to weekends and holidays are based on the prior published daily rate.

This method of coupon calculation is mirrored in the CME F-TIIE contracts (see whitepaper on settlement calculation). The similarities of both the index and the compounding calculation make CME F-TIIE futures ideal instruments to hedge future Bondes D cash flows or to price the value of outstanding bonds.

This paper examines how CME F-TIIE futures can be used to effectively hedge changing overnight F-TIIE rates and to lock in the value of Bondes coupons, as implied by the purchase price.

# Hedge ratio and equivalent notional

In order to determine the correct number of F-TIIE contracts required to hedge a Bondes position, we first need to calculate hedge ratios. In order to do that, we consider the concept of equivalent notional.

F-TIIE contracts are defined by the value of the IMM index at 20,000 MXN per 1%. This is often expressed in terms of basis points (1/100 of 1%) and is also known as the basis-point value or tick value. For F-TIIE contracts this value is 200 MXN (20,000/100).

Since we now know from this contract specification that for a 1bp move in rates, the value of an F-TIIE contracts changes by 200 MXN, we can calculate the equivalent notional of an OTC contract that would change in value by the same amount and covering the same period.

We need to solve the following equation:

Notional  x  0.01%  x  (no. of days in period / 360)  =  200 MXN

Recalling that 0.01%      =          1/10,000;         we can rearrange the above to:

Notional                       =          200 x 10,000 x 360 / no. of days in month;      or:

Notional (in millions)     =          720 / no. of days in month

The following table details the equivalent notional of one contract for months of varying lengths:

Exhibit 1

Month

Days in month

Notional equivalent (Millions MXN)

January

31

23.23

February

28

25.71

March

31

23.23

April

30

24.00

May

31

23.23

June

30

24.00

July

31

23.23

August

31

23.23

September

30

24.00

October

31

23.23

November

30

24.00

December

31

23.23

Using the information in the above table, we can calculate the required number of futures to hedge a position in Bondes D. Let’s work through an example:

### Worked example

Imagine we are at the beginning of 2021 and own a hypothetical Bondes D security with six months left to maturity.

At the time of purchase of the Bondes D the forward interest rate curve is almost constant at close to 4.25% as shown by the dark blue line below in exhibit 2.

Exhibit 2

If the expectations for interest rates decrease the value of coupons of our Bondes D position would also fall, if interest rates expectations were to rise then the Bondes D would similarly become more valuable.

The lighter blue line represents a scenario where expectations for interest rates do fall and in fact these new expectations are realised by daily funding rates. In this situation our Bondes D value would be lower than previously. We can hedge this with F-TIIE futures.

As interest rates fall the value of F-TIIE future rises and vice versa. Hence in our scenario we need to buy F-TIIE futures to protect against losses on the Bondes D position in the case where interest rate expectations fall.

The Notional of our position in Bondes D is 1bn MXN pesos. In order to hedge we would need to buy futures contracts in each of the next six months until the Bondes maturity date. The number of each contract required can be calculated by taking MXN 1,000 mio and dividing by the notional equivalent for each month per the table in exhibit 1 above. Hence, we get the calculation below:

Exhibit 3

Month

Days in Month

Futures contract Notional Equivalent (Millions MXN)

# of contracts to hedge 1bn MXN Bondes D

Futures price at 02-Jan-2021

January

31

23.23

43.00

95.75

February

28

25.71

39.00

95.74

March

31

23.23

43.00

95.74

April

30

24.00

42.00

95.74

May

31

23.23

43.00

95.74

June

30

24.00

42.00

95.74

The expected coupon interest as at 02-Jan-2021 on the hypothetical MXN 1bn notional of Bondes D can be seen in this table:

Exhibit 4

Coupon Date

Days remaining in Coupon

Coupon implied by daily rates %

Coupon Interest (MXN Peso)

31-Dec-20

14-Jan-21

14

4.25

1,651,126

11-Feb-21

28

4.25

3,307,861

11-Mar-21

28

4.26

3,313,672

08-Apr-21

28

4.26

3,313,170

06-May-21

28

4.26

3,313,170

03-Jun-21

28

4.26

3,313,170

01-Jul-21

28

4.26

3,313,170

Total Coupon Interest

21,525,338

If the revised market expectations are borne out, the coupon interest that would be earned (as depicted by the lighter blue line in the yield curve chart above) would be lower, as demonstrated in this table:

Exhibit 5

Coupon date

Days remaining in coupon

Coupon implied by daily rates %

Coupon interest (MXN peso)

31-Dec-20

14-Jan-21

14

4.24

1,650,152

11-Feb-21

28

4.18

3,254,373

11-Mar-21

28

4.04

3,145,121

08-Apr-21

28

4.03

3,132,290

06-May-21

28

4.01

3,122,748

03-Jun-21

28

4.01

3,116,339

01-Jul-21

28

4.02

3,123,583

Total coupon interest

20,544,606

We see that the total amount of coupon interest earned would be lower by 980,732 MXN in the revised market scenario versus the hypothetical starting point.

Had we hedged the change in rates, we would have seen a profit on the F-TIIE futures hedges similar in magnitude to the losses on expected interest.

When market rate expectations were at 4.25%, the prices of F-TIIE futures would have been those in the column below labelled “Purchase price.”  Similarly, the price of futures implied by the revised market scenario depicted by the light blue line in exhibit 2 is calculated and displayed in the column labelled “Current Market price.”

Note that the quantity of futures that we would have hypothetically purchased is the same as in Exhibit 3 above and is calculated from the notional amount of the Bondes D holding. Let’s see that shown again in a table:

Exhibit 6

Month

# of contracts

Purchase Price

Current Market Price

Price Change since purchase (bp)

Profit

January

43

95.75

95.75

0

-

February

39

95.74

95.94

20

156,000

March

43

95.74

95.97

23

197,800

April

42

95.74

95.98

24

201,600

May

43

95.74

95.99

25

215,000

June

42

95.74

95.98

24

201,600

252

Futures Profit

972,000

Readers will note that the futures profits are very close to the loss of interest income on the Bondes D, which was due to the shift in interest rate expectations. Thus, we have executed an effective hedge.

# Conclusion

CME Group’s MXN F-TIIE rate futures are an excellent hedge for the interest rate risk variability of Bondes D coupons. They allow users to effectively hedge changing overnight F-TIIE rates and to lock in the value of Bondes coupons, as well as potentially speculating on any potential changes in value.