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Pick out the main drivers of the cross-currency swap basis.

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Covered Interest Parity Lost: Understanding the Cross-Currency Basis · FRM2.LTR.16.b

The idea

The cross-currency basis is the deviation from covered interest parity, quoted as the spread added to the non-dollar floating rate in a cross-currency swap. Defined here as the cash dollar rate minus the dollar rate implied by the swap, a negative basis means raising dollars through the swap costs more than borrowing them directly. It reflects an imbalance between demand for dollars and the supply of dollars through the swap market. Demand comes from non-US banks funding dollar assets. It also comes from foreign investors, such as Japanese insurers and European asset managers, who buy dollar bonds and hedge the currency risk, which means borrowing dollars through the swap. Divergent monetary policy, with expected higher US rates, raises this demand. Supply is limited because arbitrageurs face balance sheet costs, and the basis widens at quarter-ends. The interest differential itself does not move the basis, since it is priced into forward points. Exam point: the drivers are hedging demand, dollar funding demand and limited arbitrage capacity.

Formulas

Cross-currency basis

Basis = r(cash) − r(implied)

r(cash)
the cash market dollar rate
r(implied)
the dollar rate implied by the FX swap

Negative means dollars cost more through the swap than in cash markets. Reversing the subtraction flips the sign, and a basis worked out over a quarter must be annualised.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which is a main driver of a negative EUR/USD cross-currency basis?

  1. A higher level of US interest rates compared with euro rates, taken on its own, in any given quarter.Why not: The interest differential is already priced into forward points, so it does not by itself create a deviation from covered interest parity.
  2. Dollar demand in the swap market from non-US banks and foreign investors hedging dollar assets exceeds supply. - correct
  3. Excess supply of dollars in the FX swap market from US banks lending to foreign borrowers and investors.Why not: Reverses the imbalance: a negative basis arises when dollars are scarce in the swap market, not abundant.
  4. A rise in euro deposit insurance limits that makes euro funding cheaper for borrowers in the euro area.Why not: Not a recognized basis driver. Deposit insurance limits do not change dollar demand or arbitrage capacity.

The basis measures a price imbalance for dollars in the swap market. Foreign banks funding dollar assets and foreign investors hedging dollar bonds both demand dollars through FX swaps, and arbitrage capacity to meet that demand is limited.

A harder one

Japanese life insurers buy large amounts of US Treasuries and hedge the dollar exposure with rolling 3-month FX swaps. What does this do to the USD/JPY cross-currency basis, other things equal?

  1. It widens the basis (more negative), because the hedge means borrowing dollars via the swap. - correct
  2. It narrows the basis toward zero, because insurers supply dollars to the swap market and relieve pressure.Why not: The insurers buy dollar assets and use the swap to obtain dollars, so they demand dollars rather than supply them.
  3. It has no effect, because the hedge removes the currency exposure.Why not: Confuses removing currency risk with removing price effects. The hedging flow itself pushes on the price of dollars in the swap market.
  4. It widens the basis only if US rates fall, since insurers then hedge more.Why not: Ties the effect to the direction of US rates. The hedging flow raises dollar swap demand regardless of the direction of rates.

A hedged purchase of a dollar asset is funded by selling yen spot and buying dollars, and the reverse at maturity. That is borrowing dollars via an FX swap, so heavy hedged buying raises the price of swap-market dollars.

The hardest tier

EUR/USD spot is 1.0800 USD per EUR and the 3-month forward is 1.0835. The 3-month EUR rate is 2.00% and the 3-month cash USD rate is 3.00%, both annualized with simple interest. The basis is defined as the cash USD rate minus the swap-implied USD rate. Which is the closest basis, in bp annualized?

  1. +30 bpWhy not: Reverses the subtraction (implied minus cash), which flips the sign of the basis.
  2. -30 bp - correct
  3. -8 bpWhy not: Leaves the figure unannualized: -30 bp over a 3-month period is about -7.6 bp, which is not an annual rate.
  4. +170 bpWhy not: Annualizes the forward premium alone as the USD rate and forgets to add the EUR rate to get the implied USD rate.

Implied USD = ((1.0835/1.0800) x (1 + 0.02 x 0.25) - 1) / 0.25 = 3.30%. Basis = 3.00% - 3.30% = -0.30%, so about -30 bp. A negative basis means dollars via the swap cost more than cash dollars.

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