FX Cross-Currency Basis Swaps and Hedging Costs

One interesting topic in the FX market that has been closely studied by both academics and practitioners over the past decade is the violation of the covered interest parity (CIP). CIP is a textbook no-arbitrage condition that states that interest rate differential between two currencies should equal the differential between the forward and spot exchange rates. In other words, in discrete time, we have the following condition:

Where S is the spot exchange rate, F is the forward exchange rate, i is the domestic interest rate and i* is the foreign currency interest rate. The problem is that the above equation has held since the Great Financial Crisis; as it started to become more expensive to borrow US Dollars against most currencies during periods of stress, the cross-currency basis swap (CCBS) has been diverging from zero for the Euro, the British pound and the Japanese Yen. Figure 1 (left frame) shows the evolution of the 3-month CCBS for the three currencies (against the USD) since 2012.

Low interest rates combined with the significant divergence in unconventional monetary policies run by the BoJ and ECB over the years has put pressure on the exchange rates and the CCBS, and therefore has increased the hedging costs for Euro and Japanese investors. The current rate on the US 10Y Treasuries (3.15%) looks certainly very interesting for unhedged international investors (relative to domestic bonds such as in the Euro area or Japan), however changes drastically when we adjust for hedging costs. Figure 2 represents the cash-flows that occur at the start, during the term and at maturity when a Euro investor (A) enters a cross currency basis swap. As you can see, each quarter A pays the 3M USD Libor and receives the 3M Euribor and the basis. Hence, the more negative is the basis, the higher the hedging cost. With the 3M Euribor at -0.316%, the 3M CCBS at -44bps and the 3M Libor USD at 2.61%, the current return on a FX-hedged 10Y US Treasuries is negative (-20bps). Figure 1 (right frame) shows that despite the rise in US yields since the middle 2016, it has been falling for Euro and JPY investors after adjusting for FX hedging costs. A UK investor would get an annual return of 1.35%, which is 15bps below he can get in holding a 10Y Gilt.

Figure 1


Source: Eikon Reuters


Figure 2


Source: BIS


Introducing the Swaptions (and IRS)

Today, let’s expand our finance knowledge and study what HF portfolio managers and IB traders ‘constantly’ look at: swaptions and the implied interest rate volatility. A swaption, as you may know, is an option to enter an IRS (interest rate swap) with a specified rate at no cost on a future date.

For those who are not familiar with swaps, let’s review quickly the structure of a ‘vanilla’ IRS.

An IRS is a bilateral agreement to swap a fixed rate of interest for a floating rate of interest. It is a derivative contracts (traded OTC) and it involves two counterparties (at least), the fixed receiver (receives a fix rate) and the fixed payer (floating rate). Unlike currency swaps, principal amounts are not exchange in an IRS ‘vanilla’ contract, and only the difference between the fixed and the floating rate is paid/received. In order to trade (hedging/speculating), you need four parameters: the date, the notional amount, fixed rate and the floating rate.

At the inception of the swap, the Net Present Value or the sum of expected PnL should add up to zero. If you type IRS on Bloomberg, you get to the swap manager page that you can see below.

Irs page

(Source: Bloomberg)

This contract is a 5-year IRS contract, 10Mio USD nominal between Leg 1 ‘Receiver’ and Leg 2 ‘Payer’. Therefore, with a fixed coupon of 1.796627% and October 10th as the effective date (date when interest begins to accrue, the first fixed payment will occur 6 months after that date (on April 10 2014) totalling an amount of 89,831.35 USD.

Fixed rate payment = Fixed rate * (Nb Days / 360 basis) * Notional

Nb of Days = 180, therefore Fixed Payment rate = 89,831.35 USD

On the other side, floating payments will occur every quarter, using the 3-month LIBOR as a benchmark (USD0003M Index). With a 3-month LIBOR trading at 0.23110% at the moment, the first floating-rate payment will occur on January 12 2014 (94 days) totalling an amount of 6,034.28 USD (same computation as the Fixed –rate payment replacing Fixed rate by floating rate). On page 9 (Cashflow, see appendix), you will see all the future payment details.

As all the future payment of Leg 1(Fixed Receiver) will rely on the evolution of the forward LIBOR curve, the swap valuation changes over time and therefore existing swaps become off-market swaps. For the curious ones, you can easily find the math equation on Internet, but the important thing to remember is that the payer (Leg 2) will start to lose money if interest rate started to fall unexpectedly.

Here we are now, back to swaptions and the 1Y10Y implied volatility that we like to watch quite a bit. There are two kinds of swaptions, a payer swaption (option to pay fixed-rate, eq. to call option with PnL rising if rates are rising) and a receiver swaption (option to receive fixed-rate, eq. to a put option with PnL rising if rates are falling).  If you buy a 1Y10Y 2% receiver swaption, it basically means that you have the right to receive a 2-percent rate on a 10 year basis starting in 1 year. Therefore, as we use the VIX in order to measure the market expectations of near-term volatility in the US stock market (S&P500), we use the 1Y10Y to ‘measure the temperature’ of the interest rate market. Quants use generally the Black’s model, a derived version of the Black and Scholes model (used for calls and puts), as a standard way of quoting prices on swaptions (two other methods of stochastic interpolation to model LIBOR forward rates are CEV and SABR.

If we have a look at 1Y10Y JPY implied volatility back in April/May 2013, we saw a surge in JPY volatility after the BoJ announced its QE plan which consists in doubling its monetary base within the next 2 fiscal years. As you can see it on the graph below, when the IR volatility (white/blue line) rose more than 60% in May, the ten-year JGB yield doubled and touched 1% (May 29th), while Japanese stocks dropped 7% the same day with a USDJPY down 3 figures.

Vol irs

(Source: Bloomberg)

Investors are still concerned about the volatility of the bond market which would force domestic financial institutions to reduce their JGB holdings. As a reminder, more than 90% of the Japanese government debt is hold by domestic ‘investors’, and 95% of this amount is held by institutional investors (GPIF, Japan Post Bank.. and of course the BoJ). Domestic banks and small/midsize financial institutions account for more or less 29% now, and still remember the ‘VaR shock’ of summer 2003 when 10 JGB yield tripled from 0.5% to 1.6% in June.

According to a study done by JP Morgan [a little while ago], a rise in the ‘JGB volatility’ increasing interest rate by 100bps would cause a loss of 10Tr Yen for Japanese banks. Therefore, if you are holding a LT position on USDJPY or any other asset (bonds, equities), you should pay close attention to the forward curve and the 1Y10Y implied volatility we just presented you.

Appendix: Cash Flows of the IRS

Cash flows

(Source: Bloomberg)