5: Intuition behind a cross currency basis swap

Mini Chapter Five

Intuition behind a cross currency basis swap

Now as a follow-up here’s the intuition behind the cross currency basis product – the term basis refers to the difference between the yield differential that should get reflected in FX swaps as per covered interest parity vs what actually gets reflected owing to the relative demand for the foreign currency vs the base currency or vice versa.

To understand this numerically, it’s best to consider cash flows – let’s take the eg. of one of the more actively traded markets – SGD FX points and the corresponding SGD OIS vs USD SOFR.

FX swap trade

Paying 6m USDSGD points or a sell buy on the 6m FX swap would entail:

Near leg (spot in this case): Lend USD and borrow SGD
At maturity do the reverse: return the SGD and receive back USD

Recall that an FX swap is a fixed base currency notional exchange versus the foreign currency at a zero coupon and the FX points for the tenor of the swap determines the foreign currency notional at maturity which in theory implies the FX rate after 6m as per covered interest parity. But let’s see what happens in reality:

Current Spot: 1.37
Base currency fixed notional: USD 100 mio
SGD notional at spot = SGD 137 mio
Market mid on 6m USDSGD FX points: -50pips
6m FX outright: 1.37 – 0.0050 = 1.3650

If we were to do the same trade assuming market interest rates:

• Lend USD at 6m USD SOFR @ 4.70

• Borrow SGD at 6m SGD OIS @ 4.00

• Both above interest rates need to be adjusted for day count but for the below calculations we have assumed a semi bond day count convention applicable to the above coupons

\( \text{USD Cash Flow} = \)

\[ 100 mio (1+ \dfrac{ 4.70\%}{ 2} ) \]

\[ = USD 102.35 \]

\( \text{SGD Cash Flow} = \)

\[ 137 mio (1+ \dfrac{ 4.00\%}{2} ) \]

\[ = SGD 139.74 \]

\( \text{Implied USD SGD outright in} 6m = \)

\[ (\dfrac{ 139.74}{ 102.35} ) \]

\[ = 1.3653 \]

\( \text{Implied} 6m \text{points as per covered interest parity} = \)

\[ 1.3653 - 1.3700 = -47 \]

In conclusion: market traded 6m USDSGD outright shows a larger SGD FX appreciation than what’s implied by interest rate parity. Thus the implied SGD yield against USD SOFR should be lower than the local market SGD OIS rate. The difference between the two rates is known as the cross currency basis for SGD against USD SOFR.

Mathematically then for a specific tenor,
Fixed Rate CCS – Fixed Rate IRS = Basis for that tenor