Funding imbalances between currencies create cross currency basis.
The Front Roll is the physical manifestation of that imbalance, anchoring the whole curve.

Definition

Front Roll: The Front Roll is the 3-month funding spread implied by spot FX and FX forwards relative to OIS rates. It forms the first period of every spot-starting cross currency swap.

Mechanics

The derivation is as follows, using EURUSD as the example.

• Look at EURUSD spot rate. Let’s say it’s 1.20.
• Take a $1.2m deposit in USD and calculate the interest you will earn over 3 months at the 3-month SOFR OIS rate. At 3.6666% currently, that is $11,000 (note the nice round numbers here!).
• Take a €1m loan in EUR and calculate the interest you will pay over 3 months at the 3-month €STR OIS rate. At 1.93%, that is €4,825.
• Now, look at 3 month EURUSD FX Forward points- currently 50 pips.
• Calculate the net USD payment over the life of the FX forward trade. 50 pips on €1m is $5k.
• Calculate your net cash-flow from the deposit and loan after 3 months (+ve USD, -ve EUR) using the forward FX rate. At 1.2050 that is $5,185.68.
• The forward FX under delivers $185.68 relative to the two OIS trades. That difference is the cash manifestation of the 3M basis (the difference between what you earn on the FX Forward for exchanging EUR for USD and the two interest rate swaps).
• To convert this to basis points, we express those $ in € using the forward FX rate (€154.09 at 1.2050).
• €154.09 on €1m for 3 months is equal to: $154.09 / 1,000,000 * 360/90 * 10,000 = 6.16bp$

Structure

A single-period spot starting 3-month cross currency basis swap, exchanging a set of floating index cashflows in one currency for a set of floating index cashflows in another. It has an initial and final exchange of notional at the same FX rate (equal to current spot). The price of the Front Roll is the spread, in basis points, that must be added to the OIS rate so that spot FX, FX forwards and OIS are internally consistent.

Mathematical Notation

Let:

• $S$ = spot FX rate
• $F$ = forward FX rate
• $r_{USD}$​ = USD OIS rate
• $r_{EUR}$​ = EUR OIS rate
• $b$ = Front Roll
• $\alpha$ = accrual fraction for the period (day count / 360)

For a 3-month period on Act/360:

$α= 90 / 360 = 0.25$

Our starting point is interest parity adjusted by the Front Roll:

$F=S×\frac{1+r_{USD}​α}{1+(r_{EUR}+b)α}​$

Rearranging:$$1+(r_{EUR}+b)\alpha = S \times \frac{1+r_{USD}\alpha}{F}$$

Plugging in the numbers:

$1+(r_{EUR}​+b)α=1.0049790871$

$(r_{EUR}​+b)α=0.0049790871$

$r_{EUR}​+b=0.0199163485$

$b=0.0006163485$

$b=6.16 bps$

What Does This Mean?

In simple terms, the front roll (or implied basis) means that you would have to pay 6.16 basis points more than the current EUR OIS rate to be “kept whole” on your currency swap relative to an FX Forward.

No-arbitrage requires identical cash flows to have identical value. A 3-month FX forward and a 3-month cross currency swap are simply two routes to the same funding position – and so their prices must be the same.

Trading the Front Roll

The Front Roll to XCCY traders is akin to the SOFR front future to USD Rates traders.

It is the most observable/transparent point on the curve and anchors the rest of the basis curve.

It is common for XCCY basis traders to monitor the evolution of the front-roll in forward space. You see hedge funds looking at the front roll out of ECB and FOMC dates, and IMM-dated structures are very common.

It will typically be the first trade that a junior cross currency swaps trader does. It can be readily traded in/out of via the FX forward markets.

Before the financial crisis it was a common carry trade to play the front-roll versus the 1 year basis.

The front-roll is the first period on every spot-starting XCCY basis swap. If the front-roll moves by 4bp:

• The 1 year moves by 1bp.
• The 2 year moves by 0.5bp.
• And so on up to about three years (0.3bp).

The maths suggest that 10 years should also move (by 0.1bp), but in reality the market dynamics of the basis market do not operate like that. You don’t see the 10 year impacting the front roll and the opposite applies.

It is fair to say that the front roll is most impactful on the short-end of the curve, up to about 3 years.

It hence “anchors” the whole curve and is a crucial input to pricing screens.

It rarely trades outright in the interbank XCCY market now – the risk is typically recycled directly through FX swaps instead – whilst hedge funds will typically trade it out of forward space to avoid physical delivery.

Macro Implications

On a macro level;

• It is the measurable desire for term-funding in EUR relative to USD (or in the currency pair of your choosing).
• It is not a credit spread, but it does track funding provision.
• It can be thought of as the relative price of balance sheet provision between two currencies.
• It is impacted by both ECB and FOMC interest rate policy, and in particular the growth or shrinkage of their respective balance sheets.
• The premium/discount can be monetised if you have access to balance sheet. Either enter into term funding at OIS rates or roll your overnight funding at Tom/Next in the FX forward markets.

There has been a lot of talk in the past 20 years that the front roll is the “USD premium” or a signal regarding the “scarcity of USD funding”. Now, with the basis positive and seasonal, we are back to more balanced and nuanced interpretations.

It is (and always has been) the relative demand for term funding in one currency versus the other.

Remember about that funding. It involves the physical exchange of cash in one currency for another.

Hedge funds are well reminded of that. It is the physical nature of this product that causes the basis.

In Summary

• The Front Roll is the 3-month funding spread implied by spot FX and FX forwards relative to OIS rates.
• It is the most transparent and observable point on the cross-currency curve and anchors the term structure.
• It measures the relative price of term funding between currencies.
• It is an observable price of balance sheet – influenced by credit conditions, regulation and liquidity – but far more than just a credit spread.