# Beware of cliff edge in Libor fallbacks

## Derivatives users may see a sudden change in the value of payoffs when Libor ends, Coremont analysts write

Everyone knows it’s happening, but nobody knows exactly when – or how.

The Libor benchmark is going away, but the precise date and timing of its discontinuation is still uncertain. Best guesses are that the rate will cease publishing at the end of 2021 or in early 2022.

Once Libor ends, financial contracts referencing the rate will rely on any fallback clauses they contain. Most derivatives will use fallback language developed by the International Swaps and Derivatives Association. The clauses will be inserted into legacy Libor contracts covered by Isda agreements via a voluntary protocol, which is expected to be published in July with an effective date of November.

The Isda fallback works by replacing the forward-looking Libor term rate with a compounded overnight risk-free rate (RFR) over the same term, plus a fixed spread to account for the difference between the two.

The adjustment spread will be a single static number for each Libor currency and tenor calculated at the point of discontinuation using historic fixing data. It is calculated by taking the five-year historical median of the basis between each Libor currency and tenor and its compounded RFR – for instance, three-month US dollar Libor and three-month compounded SOFR.

Clearing houses have signalled they will adopt the Isda protocol uniformly, meaning all cleared trades will have the fallback language when Libor ceases. Counterparties to bilateral Isda covered trades will need to adopt the protocol on a case-by-case basis.

But adopting the protocol does not solve all the problems associated with the switch. While the adjustment spread is designed to reduce the likelihood – and the size – of any value transfer between parties, it can’t eliminate this risk altogether.

At the time that Libor ceases, there is a good chance the fallback spread will be relatively close to the historic median. However, there is also a possibility that the spread will be significantly above, or even below, the historic median. This year, the three-month USD Libor/SOFR spread has climbed to around 140 basis points, 115bp above the historic spread. The current fallback methodology exposes users to the possibility of a large arbitrary jump in the value of Libor-indexed payoffs around the discontinuation date.

Short of completely closing all Libor exposure, this risk is unhedgeable.

The adjustment spread is calculated as the median of every Libor/compounded RFR spread within a historic window of five years. This means the fallback rate for a given Libor fixing cannot be determined until the end of its underlying period.

For example, to calculate the USD three-month Libor fallback as of today, we must wait for the risk-free rate, SOFR, to fix over the next three months. At the end of that period the three months’ worth of SOFR fixings are compounded up and the historic spread applied. In the case of a six-month Libor level, we must wait six months to know the level a trade fixes at, and a year for a 12-month fixing.

To enable users to know the spread at discontinuation, Isda has introduced a time lag to make sure all the RFR data is available. The lag is different for each tenor, meaning that the historic spreads will reference different historical periods of Libor fixings (figure 2).

The decision to lag the Libor window results in an inconsistency in the Libor dates being included across different tenors – assuming all Libors are discontinued simultaneously. A period of elevated Libor/RFR spread in the year prior to discontinuation would increase the historic spread disproportionately for short-dated tenors.

Given the historic window length is five years it is unlikely that the above will have a significant impact. Any impact is further muted by the decision to calculate the historic spreads using a median average, which limits the effect of outliers in a dataset compared to using a mean average.

### Distribution of the historical spread

Using a median average, though, has the effect of placing an upper and lower bound on the historic spread once half of the history is known. Assuming a discontinuation date of January 2022, the upper and lower bound for the USD three-month historic spread would be around 35bp and 19bp, respectively.

Figure 3 shows the USD three-month Libor/compounded SOFR spread since the start of 2015. The current spread (blue) is frequently outside the highlighted (orange) upper and lower bounds of the historic spread – about 60% of the time. In other words, the spread is relatively insensitive to the next 18 months of fixings – the spread could fix at +500bp from now until 2022 and the historic spread would only be 35bp.

Similarly, figure 4 shows the distribution of USD three-month Libor/compounded SOFR spread over the past one year and five years. The distribution is wide and the spread can be very high, particularly in times of stressed markets. The historic median is approximately 25bp.

As part of the consultation on Libor fallbacks, Isda proposed a one-year transition period. This would have transitioned the applied spread linearly from the final published Libor/RFR spread to the historic spread over a one-year period. The transition period would have eliminated the cliff-edge problem described above. However, the proposal was not adopted due to concerns over its complexity.

### Implications for the market

We show the possible effect of a transition period on market behaviour leading up to Libor discontinuation. This scenario assumes that the market expects Libor to cease at some point in the first quarter of 2022 but does not know the exact date. It also assumes that the stressed funding market conditions of March 2020 apply as we approach discontinuation. So, three-month USD Libor is at 1.4% and compounded three-month SOFR at around 0.0%. The spread of 140bp compares to a long-term historic spread of 25bp. For convenience, we use USD three-month Libor and assume the underlying RFR curve is completely flat at 0%.

In this scenario, the market knows that at some point in the first quarter of 2022 the value of Libor-indexed payoffs will fall from 1.4% to 0.25%. It does not know exactly when this will happen so will naturally price a probability-weighted average of the different possible times.

Figure 5 below shows how we would expect the Libor forward curve to look, with and without a transition period.

The orange graphic depicts a no-transition scenario. The dashed paths are the potential overnight jumps from prevailing real-world Libor levels to the fallback. The solid line is the sum of these assuming all are equally probable.

The blue graphic depicts a transition scenario. The dashed paths slope due to the one-year linear transition to the fallback level. This means they are more similar to the probability-weighted solid line.

As soon as the discontinuation date is announced, all probability will shift to one of the dashed lines. In figure 6, we assume that discontinuation is announced to happen on March 9, 2022.

In a no-transition scenario (orange), the solid line snaps to the new certain dashed line. This causes the implied fixings to jump up or down depending on their date relative to discontinuation.

For an imperfectly hedged swap with a small date mismatch, the fixing jumps up by around 80bp one day before discontinuation, and jumps down by around 35bp one day after discontinuation.

In a transition scenario (blue), there is little impact as the solid curve snaps to the discontinuation curve. Even in this relatively extreme example, consecutive fixings are only moving by a few basis points.

These scenarios show the risk of large and sudden jumps in the value of consecutive Libor indexed payoffs in the absence of a transition period.

If significant Libor risk still exists in the market at this time, there is the potential for very large arbitrary value transfers between market participants. The value of these transfers would be highly sensitive to the exact choice of discontinuation date – changing it by even a day could make a huge difference.

This undesirable effect is mitigated by a transition period.

An early announcement of a Libor discontinuation date would give participants more opportunity and time to mitigate the risk of mismatched swaps while the implied forward Libor/RFR spread levels are near the historical spread levels, but it would not eliminate the possibility of a cliff-edge change when discontinuation happens.

Edmund Allen and Christopher Willis are part of the quantitative analysis group at Coremont LLP, an FCA-regulated financial services firm that provides web-based portfolio management tools and outsourcing services across investment management functions, including risk analysis, treasury and operations

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