# how to calculate a cross-currency swap in basis pt?

This question has been bugging me for awhile now and I've been trying to find a definite answer, however, no avail...

My question, in specific, relates to the USD/CNH CCS rate. From what I understand (which is barely the surface), you can add this USD/CNH CCS rate on top of a %YTM of a CNH denominated bond, and the summation will be the %YTM in USD.

I've tried to ask my colleagues/read internet sources but no one can produce a simple numerical example that can derive the USD/CNH CCS rate. I'm wondering if anyone here can provide for an example with a simple 2 year bond and derive the USD/CNH CCS rate for me?

Thank you so much.

• What is the collateralisation of the CNH leg? CNH or USD? And is that cash, accruing at FedFunds rate? – Phil H Nov 4 '14 at 17:39

You're thinking of a "cross-currency basis swap", not a CCS. A CCS is a floating-for-floating swap that would, for example, let you switch 3m SHIBOR into 3m USD Libor.

A cross-currency basis swap, on the other hand, is a swap of funding spreads (loosely speaking, LIBOR - OIS equivalent). It's essentially the liquid way of exchanging currency for long periods of time as the FX swap market only goes out to about 18 months.

For example, the 5yr EURUSD x-ccy basis swap is quoted as "-15bp" right now. The standard is to quote it vs 3m USD Libor.

An example:

• You are a USD-denominated investor and want to buy \$10m worth of a 5yr EUR-denominated bond. • For convenience and without loss of generality, say 3m USD Libor is 25bp and 3m EUR Libor is also 25bp. Also assume the 5yr EURUSD x-ccy basis swap is -15bp as previously stated. • You go to a bank and enter into a 5yr x-ccy basis swap: you hand over \$10m and get the equivalent in EUR (at the current rate) in return.
• Euros in hand, you then go and buy the EUR-denominated bond you wanted.
• Every 3 months, you pay 0.25 * (25bp - 15bp) = 2.5bp on the Euros you received and receive 0.25 * 25bp = 6.25bp on the USD you handed over.
• At the end of 5 years, you have a pile of Euros (because your bond matured or you sold it) which you hand back to the bank, and in exchange you are given back your USD. Note that since both parties are simply returning the notionals they exchanged at initiation, the effective exchange rate at termination is the same as the initial rate. Any interest rate differentials are resolved through the quarterly payments.

The key here is that during the lifetime of the trade, you are receiving both the yield on the bond and a "discount" of 15bp/year through the basis swap.

The implicit assumption is that you're a "spread investor" rather than an "all-in yield" investor, and therefore the only thing you're interested in is the pick-up over your Libor funding rate.

The fact that the x-ccy basis swap is negative in our example suggests that non-USD investors are willing to pay a premium (effectively 15bp/year in this case) to obtain USD funding.

During the crisis there was a significant shortage of dollar funding around the world, which led to most x-ccy basis swaps plummeting. If I remember right, AUD and EUR x-ccy basis went to -100bp.

I am not sure what you are asking but the example below might be useful : if you are talking about foreign denominated bonds then,

1. Current USD/CHN exchange rate = 1.5
2. %YTM in CHN = 14%
3. %YTM in US =3%

Then USD/CHN on maturity will be = 1.5*1.14/1.03 = 1.66