Calculating Term Fixed Rates Using 1mo Ameribor Futures AND Term Rate Applications
Before the applications, calculating a compound fixed rate from Ameribor futures is needed. These compound rates are also an essential piece needed to calculate simple interest. Using the 1-month Ameribor Futures, we can use the Fed’s favorite calculations (as applied to SOFR) to calculate our Term Ameribor rate. Note: we assume 360 annual day count for all calculations below.
1-month Ameribor futures settle to the AVERAGE daily overnight Ameribor rate traded on the spot platform. So a futures price of 9990 implies an average rate of 0.10% on the Ameribor platform from 7/1/2020-7/31/2020. As today is 6/19/2020, the price of the July 1mo Ameribor future is no more than the trade-able expession of “the market’s best guess” as to what the average rate will be over the month of July. As expectations and money flow change, the future price will trade up and down accordingly.
During the futures ‘valuation month’, as rates become known, the futures price will accrue to greater certainty of final price (each day fixes one or more days of rates for the final settlement calculation). Whatever rate is published for cash Ameribor preceding a weekend or holiday, will be the rate for the non-trading days. So, the rate for Wednesday, July 3rd, will be the rate that is used for holiday July 4th and ‘averaged in’ to the final settlement value of the July Futures Contract.
To frame an example, a 6-month term rate from July 1, 2020 through Dec 31, 2020 will be used.
Step 1: Rendering Annualized Term Rates from Ameribor Futures:
- A) First, we gather the specifics on the 1mo Ameribor futures covering our 6-month period:
- B) The Ameribor futures are priced such that:
- C) Adding to our table for all involved 1mo Ameribor futures:
- D) One of the less-obvious components to using 1mo Ameribor futures to calculate a term forward rate stems from the ‘average’ (not compound) daily settlement values over a month. To calculate term rates from average rates, it is necessary to first calculate 1-day Rate of Return values for the futures. To calculate the 1-day implied return on $1.00, we use the expression:
- E) Expanding the calculation grid to include 1-day returns & implied 1mo compound returns:
Also, notice (via the GREEN arrowhead, that calculating the compound 6-month return is now simple. Take the product of the six 1-month returns.
- F) Finally, in the pink box above, annualized rate may be calculated by annualizing the 6-month futures-implied return:
Step 2: “Show me the money!” Does all this math tie out?
Let’s choose a big and convenient number: $600,000,000. Each 1mo Ameribor future has a notional value of $6mm. Thus, to fix $600mm in Ameribor from July 1 to Dec 31, we’ll need a short of 100 of each of the Jul, Aug, Sep, Oct, Nov and Dec 1mo Ameribor futures. In Selling Short 100 of the 1mo futures in each of the six months, we will lock up the ‘fixed rate’ calculated above: 0.0825%. We lend principal out to a borrower (BLUE BOX below) and receive a fixed rate, borrow the principal on the Ameribor Cash Platform, and short the futures to hedge the term rate:
OR, the opposite where we are PAYING a fixed rate, such as a CD or commercial paper we issue:
Using the BLUE BOX example, ‘LEND at a Fixed Rate, Borrow Overnight on Ameribor platform, Sell Short Ameribor Futures, we adjust our grid to:
Let’s further stipulate that Ameribor remains unchanged for the entirety of the six-month period; steady at 0.10% for 184 days. We can then render a P&L for the 1mo Ameribor futures over the period:
Looking at the economics:
The 0.0825% rate calculated, and ‘fixed’, via the 1mo Ameribor futures, would equate to:
Notional $ * Rate * Days in Period / 360
If we hedged a 6-month loan, borrowing overnight at 0.10% every night for the 184 days, cost of funds would be:
That leaves the short futures component to the P&L (from the above grid), if Ameribor daily rates settled at 0.10% every day, the futures would all settle to their respective monthly averages, 0.10%– or, 9990 futures price. Recall that the Ameribor futures are $50 per basis point per contract. So a move from 9995 to 9990 would be 5 basis points. A SHORT position would ‘earn’ 5bps per contract: 5bps*$50/bp=$250 per contract short. These settlements of futures over the six months would result in the following P&L:
Completing out the cash-flow-based, total P&L:
As to ‘position hedged ineffectiveness’:
1 – (($253,037.05+$52,500)/306,666.67) = .00368
Or, 99.632% effective.
JC, for the Fixed Income Group at R.J. O’Brien
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