A conversion factor is the approximate decimal price at which a security would trade if it had a 6% yield-to-maturity. They are used for bond futures contracts that require the physical delivery of the underlying security at expiration. Given that there are often many different securities eligible to be delivered at the expiration of a certain contract, traders will seek to identify the cheapest-to-deliver bond to fulfil the delivery requirements. Employing a conversion factor standardizes the price of all bonds eligible to be delivered into a given futures contract and enables the identification of the cheapest-to-deliver security.

We thus have three of four pieces of our P&L calculation as we know that there are 24 days between 18 Nov 2022 and 12 Dec 2022. The only remaining variable is the financing rate that the trader will receive on the repo-ed proceeds:

Again, the repo rate is a key component here and is a main driver of a profitable trade. CME Group’s Germany RepoFunds Rate helps traders understand and hedge movements in repo rates over a given period. Below are the accumulated and to-be-accumulated Germany RepoFund Rates for the Dec 22 Germany RFR futures contract. This contract provides a compounded average repo rate for a three-month period using actual German repo market transactions and creates a futures price using the 100 – rate methodology common in other short-term interest rate futures products. 

At this point in time (as of 17 Nov 2022), the trader knows that: 

• There is a 24-day period from 18 Nov 2022 to 12 Dec 2022 where both the bond future and Germany RFR future will be active
• There is an additional nine-day period from 13 Dec 2022 to 21 Dec 2022 where the bond future has expired and only the Germany RFR Future will be active
• The Germany RFR future thus has a total active period of 33 days from the opening of the position to the contract’s settlement¹

We will use this data to walk through two potential scenarios that could occur ahead of our delivery date of 12 Dec 2022 for our reverse cash-and-carry example.

In this scenario, we will assume that there are no major changes in the repo market –the final 24 days of the trade go as market expectations dictate. In this case, we can calculate the annualized repo rate by first determine the compounded daily interest accumulation factor (DIAF) for realized days in the Germany RFR futures contract: 

DIAF = Product [all realized DIAF figures for period] = 1.000833%

To determine what the implied remaining rate is, use the Germany RFR futures price of €99.210 and a total accumulation of 91 days in the contract:

Rate implied by RFR Futures Price:  ( (100-99.210)/100) * (91/360) ) + 1 = 1.001997%

Dividing the implied rate by the compounded DIAF gives the remaining rate expectation:

Finally, annualize this rate based on the 33 remaining unrealized days in the contract accumulation period:

This final figure can be used to determine R and estimate the total P&L of the trade, assuming that the annualized repo rate for the 24-day period of the futures contract is the same as it is for the 33-day period of the RFR contract:

Total P&L is thus positive:

P&L = (€84,702,000 + €71,651.54) - €84,581,680 = €191,971.54

In this scenario, we will assume that major disruptions in the repo market rapidly and unexpectedly lower repo rates, and that this change is reflected the price of Dec 22 German RFR futures moving to a price of €100.50 immediately after the reverse cash-and-carry trade is initiated. Using the same data set as above demonstrates how this affects P&L.

The compounded daily interest accumulation factor (DIAF) for realized days in the Germany RFR futures contract remains the same:

DIAF = Product [all realized DIAF figures for period] = 1.000833%

To determine what the implied remaining rate is, use the new Germany RFR futures price of €100 and a total accumulation of 91 days in the contract:

Rate implied by RFR Futures Price:  ( (100 - 100.50) / 100) * (91 / 360) + 1) ) = 0.9987%

Dividing the implied rate by the compounded DIAF gives the remaining rate expectation:

Finally, annualize this rate based on the 33 remaining unrealized days in the contract accumulation period:

This final figure can be used to determine Repo Interest Income and estimate the total P&L of the trade, assuming that the annualized repo rate for the 24-day period of the futures contract is the same as it is for the 33-day period of the RFR contract:

Total P&L is thus negative:

P&L = (€84,702,000 + -€129,053.38) - €84,581,680 = -€8,733.38

Imagine that prior to initiating the reverse cash-and-carry trade, that the trader covered downside risk by hedging the position with CME Group’s Germany RepoFunds Rate futures. In Scenario #2, used above, this would entail entering a long position in Germany RFR futures at a price of €99.210 prior to the price of this contract moving to €100.50. 

To determine how many contracts we should use to hedge, we must understand two data points: first, that the notional value we are trying to hedge against is the cash value of the transaction (€84,702,000); and second, that the bond future expires 24 days forward and the German RFR future 33 days forward. Again, we assume that the rates between the 24-day period and 33-day period will remain constant. This gives us the proportional cash value of our short sale:

We then divide this figure by the German RFR futures notional index value to arrive at our number of contracts:

62 contracts with a value of €25 per basis point change results in a value of: 

P&L from hedge = (100.50 - 99.210) * €25 * 62 contracts = €199,950

This hedge would cover all the loss from the un-hedged trade in Scenario #2 above and yield a net profit of €191,216.62, which is nearly identical from the total trade P&L in Scenario #1 of €191,971.54:

Total P&L from Trade = €199,950 - €8,733.38 = €191,216.62

This example demonstrates how CME Group RepoFunds Rate futures can help hedge exposure to repo rates during a basis trade. However, it should be noted that unhedged risks remain in this example.  

Recall that the trader is repeatedly borrowing via the repo market in exchange for cash and the security used in the initial cash market short sale. Borrowing a specific security in the repo market exposes the borrower to specialness risk. Specialness occurs when a particular security becomes in high demand and its financing rate falls to less than that of general collateral. Specialness can significantly decrease the financing rate of a particular security, often into negative territory. 

While Scenario #2 above deals with negative repo rates, these rates generally reflect the financing rate for the repo market’s general collateral pool and only a portion of the special collateral pool as the benchmark administrator employs a filtering mechanism for special collateral². This means that a situation could occur where general collateral repo rates (and thus RRF benchmark rates) remain relatively high while the trader is uniquely exposed to low specialness financing rates in a particular security.

¹ Consult Appendix A for a full overview of referenced dates and corresponding realized repo values
² Consult this link for full details on the RepoFunds Rate methodology: https://www.cmegroup.com/market-data/cme-group-benchmark-administration/files/repofunds-rate-benchmark-methodology.pdf

1. https://www.eurex.com/ex-en/markets/int/fix/government-bonds/Euro-Bund-Futures-137298
2. https://corporatefinanceinstitute.com/resources/derivatives/cash-and-carry-arbitrage/