# Term Risk Free Rates from FX Forwards

The case for a Term Risk Free Rate (TRFR) to support the transition of cash instruments and products has been made by BoE and US ARRC over the past year. The TRFR is defined as a rate known in advance (similar to the current Libors) but based on RFRs in the relevant currency.

But the issue of how to construct an IOSCO-compliant TRFR has been a challenge for market participants and benchmark administrators. The UK working group for transition to RFRs has made a good start in attracting submissions from three credible administrators to produce a Sterling TRFR.

These submissions all depend on liquid and trading futures and OIS markets in GBP, but what happens if these markets do not exist in a currency?

Well we can still calculate the TRFR but via the FX Forward market.

## The alternative method – one TRFR and a liquid FX Forward market

Chris recently published an article on the Singapore SOR market calculation. The article shows SOR has largely replaced the former benchmark of SIBOR for cross currency trades. SOR is calculated from the relevant Libor and the FX Forwards and the cross currency market basis trades relative to SOR rather than SIBOR.
The same calculation can be used to calculate and implied TRFR ‘SOR’ from a USD TRFR (SOFR) using the same equation:

$$SGDTRFR=\left(\frac{ForwardRate}{SpotRate}.\left(1+\frac{USDTRTR.NoDays}{360}\right)-1\right).\frac{365}{NoDays}.100$$

This equation could be used to calculate the SGD TRFR from the Term SOFR in the same way SOR is currently derived from USD Libor and the FX Forwards. Just a reminder on the Singapore rules for FX Forwards from ABS:

• Notional >=\$1 mm;
• At least one side is in Singapore and considered an “interbank’ counterparty
• Electronically traded via an Approved Broker (i.e. MAS registered) between 07:30 and 16:30 Singapore time.

This technique can be used for most currencies to create a synthetic TRFR even if the underlying RFR does not exist in a currency. Also, where the RFR does exist but the basic components for creating the TRFR (i.e. a liquid futures and OIS market) are not developed.

## Including the cross currency and TRFR/Libor margins

As attractive and elegant as this simple technique seems to be, it ignores a critical component if the ‘real’ SOR TRFR is to be calculated which would be consistent with the underlying RFR: it is the cross currency and TRFR/Libor margins.
In his blog, Chris outlined the USD Libor/SOR cross currency margins sourced from the SDRView (Professional). For the purposes of this calculation, let’s use the 3 month tenor point which trades on average at -8.25 bps (interpolated from SDRView). This equates to: $$SOR-8.25 bps=USDLibor flat.$$ This TRFR version of the cross currency basis will likely follow a similar approach to the Libor basis, $$SGDTRFR-X bps=USDTRFR.$$ So far so good – but USD SOFR TRFRs do not exist yet!

## Creating the USD TRFR

Two options are available to calculate the USD TRFR:

• Using the futures and OIS trades as per the technique described in the BoE consultation; or
• Implying the USDTRFR from FX Forwards.

The development of the USD SOFR OIS market and futures is still at an early stage so could we estimate a USDTRFR from the FX Forwards similarly to that used in Singapore?

One of the more active RFR markets is the GBP SONIA OIS and futures. The equation for estimating the USDTRFR is similar to the SGD version but adjusted for the currency (i.e. GBP/USD rather than USD/SGD): $$USDTRFR^*=\left(\frac{ForwardRate}{SpotRate}.\left(1+\frac{GBPTRFR.NoDays}{365}\right)-1\right).\frac{360}{NoDays}.100$$

Where USDTRFR* is the cross currency, unadjusted USDTRFR rate. We will adjust this later for the cross currency margin to compare with the USD 3 month OIS (i.e. a proxy for the USDTRFR).
Using current 3 month market data: $$GBPTRFR=0.713 \text{(from SDRView)},$$ $$GBP⁄USD spot=1.2585,$$ $$GBP⁄USD \text{ 3 month FX Fwd}=50.80 .$$
With the 3 month run from 8th July 2019 of 92 days gives: $$USDTRFR^*=2.286$$

This differs from the USD 3 month OIS of 2.132 (SDRView) by 15.4 bps: so why is there a difference?
This can be explained via the cross currency spread (embedded in the USDTRFR*calculation) and the Libor/OIS spreads.
If we return to Chris’ analysis from SDRView for SOR but run it for GBP, the results look as per below:

The GBP/USD 3 month cross currency basis is GBP – 6.75 bps.

Also, if we also adjust for the GBP Libor/OIS spread (5 bps) and the USD Libor/OIS spread (16 bps) then by simple substitution, we arrive at an adjustment of USDTRFR* of 17.75 bps (i.e. 16 – 5 – {-6.75}).
Comparing the two calculations for the USDTRFR we get:
OIS approximation 2.132
FX Forward calculation 2.286 – .1775 = 2.109

There is a 2.3 bps difference which probably within the tolerance of the input rate bid/offer estimates for the basis spreads.

Although this is a rather ‘clunky’ process to get to the USDTRFR it suggests the calculation works for liquid markets where there is a reasonable check for the result.

## Extending the SOR example to other currencies

The Singapore example is an interesting way to form a TRFR for any currency if a liquid and transparent FX Forward or NDF market and a known TRFR (e.g. GBP or USD when available) can be found.

As on the SOR example, the derived rate is not adjusted for cross currency effects so the actual rate at which the currency is funded will trade at a rate that incorporates the cross currency spread.

The TRFR cross currency spread will be a function of the relevant Libor/OIS spreads in each currency as well as the Libor cross currency spreads. However, this will likely develop more as trading in RFR/RFR cross currency basis makes progress.

Although this may be complicated, I expect the TRFR cross currency spread to trade as a separate basis and replace the current Libor versions as the cross currency markets migrate to the RFRs as supported in the recent ARRC report.

## Summary

The Singapore markets seem to have adapted well to a derived rate and SOR has dominated trading in cross currency basis. The same technique can be extended to other currencies for TRFRs if:

• The FX Forward or NDF market is liquid and observable; and
• A TRFR can be found for one side of the currency pair.

The USD example suggests this aligns well with market prices (i.e. OIS as a proxy for the TRFR).

It is also noted that even in the absence of a RFR in a currency, it is still possible to create the TRFR in this manner. But, the calculated TRFR will include a cross currency basis spread and would have to be adjusted for IBOR/OIS spreads in order to be compared with the OIS market (if it exists for the currency).

Stay informed with our FREE newsletter, subscribe here.