The document provides a basic overview of forward FX concepts including: 1) How zero coupon curves are built using overnight indexed swap (OIS) rates and futures contracts to extrapolate interest rates. 2) How bill futures and eurodollar contracts settle based on 3-month rates and can be thought of as forward-forward rates. 3) How "bootstrapping" uses cash rates and futures to build the 3-month zero coupon curve. 4) How OIS discounting is now preferred to value instruments given its risk-free nature under credit support annexes.

1. Forward FX
Basic Principles
Adam Pallister
Sep 2016

2. Overview
 A very brief and broad overview of zero coupon curve building – the cornerstone of
all interest rate derivatives!
 The ‘modern’ approach of OIS discounting
 Basis as implied from the forward
 Basic forward fx terminology and conventions
 This is just a very basic overview – I have over-simplified the concepts in order to
paint the picture – STOP ME AT ANY TIME AND ASK QUESTIONS!

3. Bill Futures and Eurodollars
 Settle in Mar, Jun, Sep or Dec at the 3 month bill (AUD, NZD futures) or 3mth LIBOR (ED’s)
rate. The implied rate from the future is not what the cash rate will be on settlement, but
what the expected 3 month bill or LIBOR rate will be at time of settlement.
 Can be thought of as a forward-forward rate eg. if it is currently July, the 1st future is Sep
expiry – the implied rate from the 1st future is actually the 3 month rate, 2 months from
now (so a 2 month-5 month fwd fwd). The 2nd future (Dec) would be the 3 month rate, 5
months from now (so a 5’s-8’s), and so on.
 When building a zero coupon curve, we use the OCR and 1,2 and 3 month bill (or LIBOR) to
fix the short date rates, then use a technique called ‘bootstrapping’ to extrapolate the
rates from the futures. This allows us to calculate the implied rate of any tenor from today
(see next slide).
 Remember, bills (and LIBOR) are the rates banks will lend to each other, so credit risk is
imbedded in the price. In times of credit stress, these yields will increase, as banks
demand a higher price to lend to compensate for increased (perceived) risk of default of
counterparties.

4. Visualising ‘Bootstrapping’
Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul
• Thinking of the futures as forward-forwards (what the expected 3 month rate is, x months from now)
• Then adding cash, 1, 2 & 3 month bill
You have now ‘bootstrapped’ the 3 month zero coupon curve!

5. OIS & CSA Discounting
 The OIS rate is calculated by averaging the expected future cash rate, compounded daily.
 For example, if RBA decision is in 15 days, and 100% chance of a cut priced in, the 1 month
OIS would be calculated as 1.75% pa compounded daily for 15 days, then 1.50% pa
compounded daily for the remainder of the month.
 Banks are more and more now discounting their cash flows against the OIS curves due to
CSA.
 CSA’s (Credit Support Annex) require deals to be revalued daily, with collateral (OTC) or
margin (centrally cleared) to be posted by the counterparty who is out of the money.
 As such credit risk on collateralised swaps can be argued to be almost zero (‘risk free’).
 Therefor, to correctly price instruments and discount cash flows accordingly, OIS
discounting is now preferred as this more accurately can be referred to as the ‘risk-free
rate,’ as opposed to a bill or LIBOR curve.
 OIS is also the intuitive instrument to use to match the daily revaluation of collateralised
swaps (like-for-like… why use a 1 month bill rate, for example, to make daily calculations?)

6. Implied Basis
 Forwards very rarely trade par to the underlying bill curve. In EUR for example, the
forwards trade at a lower implied EUR rate than the underlying zero coupon curve. This
reflects the negative cross-currency basis as European banks have continued difficulty
raising USD ( they are happy to lend EUR below EURIBOR, in order to swap into USD)
 In AUD and NZD on the other hand, banks have historically issued bonds offshore, and
therefor need to pay the basis swap to hedge their USD exposure, resulting in positive
cross-currency basis, and forwards trading higher than the underlying bill curve. Basel,
Volker, HQLA, collateral requirements etc has dramatically narrowed these spreads in
recent times however.
 During the GFC, for example, global demand for USD was such that all cross-currency
curves traded negatively. Supply and demand for USD in short dated forwards (< 3month)
recently has seen native currencies (AUD, NZD etc) implied yield in the forward trade below
cash rates.
 Banks are now pricing more off forward / OIS basis, rather than implied bill / LIBOR, due to
OIS discounting reasons mentioned earlier, as counterparty risk in the forwards are
somewhat mitigated by the swapping of notionals at inception and settlement risk
mitigated by CLS.

7. Enough of the Technicalities!
 An FX forward is simply the interest rate differential (derived from zero coupon curve or
OIS curve) between 2 currencies, expressed as a spot rate. Market convention is to quote
as native currency vs USD (AUDUSD, NZDUSD, USDJPY, EURUSD etc).
 Terminology is buy/sell (sell/buy) – but this can be thought of as borrow/lend (vice versa).
Think of it as a simple interest loan where the interest and principal is paid back in one
single payment at the end of the loan. You borrow (buy) today and pay back (sell) on the
agreed far date, and vice versa.
 The number quoted is the forward margin (or forward points). This are the number of pips
needed to be added (or subtracted) from the spot rate on the near leg of the deal, to
calculate the spot rate for the far leg of the deal (see next slide)
 Remember this is a swap! – whenever you borrow (or lend) AUD, you are simultaneously
lending (borrowing) USD.

8. Enough of the Technicalities!
 Thinking of it in this way, this explains why AUDUSD forward margins are currently
negative;
• If you currently are long AUD (which has a higher interest rate vs USD), you lend (sell today/buy
back later) this out at for 1 month at 1.80%, for example, while simultaneously borrowing USD at
the lower 0.4%. You are receiving (swaps guys should recognise this word!) a positive interest
rate differential ie making money.
• To express this the same way in spot terms, if you are long AUDUSD and sell (lend) today, you
have to be buying it back at a lower spot price in 1 month’s time in order to make the same
money you would in the above money market transaction. So sell at .7600 and buy back at
.7500, for example, is a forward margin of -100, as .7500 is 100 pips lower than the initial spot
price of .7600. Arbitrage opportunities would arise if this wasn’t the case.

9. A Simple (interest) Formula
𝑆𝑝𝑜𝑡 ∗
1 + 𝑇𝑟 ∗
𝐷
𝑇𝑑
1 + 𝐵𝑟 ∗
𝐷
𝐵𝑑
− 𝑆𝑝𝑜𝑡
Tr = Interest rate of term currency
Br = Interest rate of base currency
Tr = Days per year of term currency
Bd = Days per year of base currency
D = Number of days of swap
• ‘Base’ and ‘Term’ refer to currency quotation convention. Base is the left hand side of a currency pair and
always fixed at ‘1’ eg AUD/USD = 0.7500. AUD is the base, USD is the term, therefor, 1 AU dollar = 0.7500
US dollar. USD/JPY for example; USD is the base currency, JPY is the term currency. Basically, USD is the
base for every currency pair except AUD, NZD, GBP and EUR.
• Different countries recognise either 365 or 360 days per year for financial calculations. A general rule of
thumb is Commonwealth nations use 365 days (AUD, NZD, CAD, GBP), everyone else uses 360.
• When calculating basis, we hold the underlying USD interest rate constant. The difference between where
the fx forward is actually trading vs where the above formula says it ‘should’ trade is the basis ie “The 1
year forward is trading 7bp above the OIS.” In the past, this has been referred to as “the arb.”

10. Visualising Forward Moves
0_ +
• Let’s consider AUD/USD. If both interest rates were equal, and basis was zero, the forward margin would be 0
• As the interest rate differential moves in favour of the base currency (ie the left hand side currency, AUD in this
example), the forward margin becomes more negative (moves further left on the below continuum).
• Alternatively, if the interest rate differential favours the term currency (right hand side side), the forward margin
will move to the right.
AUD USD
Let’s look at what affects the interest rate differential, everything else held constant;
o Higher AUD yield (lower futures / higher OIS)
o Wider basis
o Higher spot
o Lower USD yield
• Higher USD yield
• Narrower basis
• Lower spot
• Lower AUD yield

11. Many Ways to Trade
 Can take an outright view on the future direction of rates via the forward and hedge
the AUD or USD side, or neither if you think rates of the 2 economies are moving in
opposite directions.
 As a funding play – if day-to-day (tom-next) or short term tenors (< 3month) have a
lower implied interest rate than longer tenors, you can S/B (receive) 1 year, for
example, and fund the position over time by B/S (paying) cheaper shorter dates.
 As a basis outright or funding play – as above, but hedge both sides, leaving only
basis exposure
 Potential to arb implied rates or basis in forward vs physical market (depo, bill -
growing less common)
 Funding stresses are often seen via the forward market prior to other markets – can
be the ‘canary in the coal mine.’

12. A Final Word
 Hopefully you can take something away from this that enables you to better
approach your clients from ‘their’ perspective
 Many banks are operating separate CSA desks to isolate that risk from the trading
books – maybe in the future there will be CSA broking desks?
 Forward / OIS basis may become a physical swap like bills/libor?
 I am far from an expert, and my experience has been isolated to 1 trading shop.
Your clients will have different perspectives and experiences than me – I am sure
there are plenty of other opportunities out there.
Thank You!