FX & Rates
Reading and making prices in the two biggest markets: which side a client deals on, crosses built through the dollar, forwards set by the interest-rate gap, the swap rate that makes floating worth par, and curve trades sized so only the shape matters.
FX and rates are the markets where the arithmetic is simplest and the conventions trip the most people. An FX quote is a price for one unit of the first currency, paid in the second; hold that and the side, the pip and the inverted quote all follow. Crosses go through the dollar. Forwards are spot adjusted for the interest-rate gap and forecast nothing. On the rates side, a swap rate is the fixed coupon that makes a fixed stream worth a floating one, and a curve trade is two bonds sized in DV01 so that only the spread between them matters.
What moves spot is a different question. Relative growth, inflation, policy rates, trade flows and risk appetite all move currencies, and an interview may ask for a view. This lesson is the arithmetic underneath any such view: the forward tells you what the rate gap is worth, not where spot is going; the carry trade is a bet that spot will not move as far as the forward implies. Bond prices, duration and DV01 are taught in Bond Math and used here without re-deriving them.
- Quoting conventions. Which side, the quote-currency amount, pip values in the quote currency and in dollars, pips from a P&L, inverting a quote, the cost of a wider spread.
- Cross rates. Multiply or divide through the dollar, a two-way cross from two two-way quotes, the implied EUR/USD, a yen move traced through, why crosses are wider.
- Forward points. The outright from spot and two deposit rates, the dollars a hedge locks in, the rate the points imply, what a hike does to the points, the arbitrage when a bank is off parity, premium or discount.
- Swap rates. The par rate from discount factors, bootstrapping the next factor, a swap's value to the fixed payer, its DV01, a rate move, which side fixes a loan.
- Curve trades. Sizing a DV01-neutral steepener, its P&L, the legs for a target, the spread move a goal needs, the equal-face mistake, which trade fits a view.
Write the units and take the side that is worse for you. Dollars per euro times yen per dollar; the bid where the bank buys; the forward from two interest streams; the fixed rate that balances a floating one; two DV01s that cancel. Every chapter is one of those, and every one has a backwards question.
From a quote to a curve trade
Each step points to the chapter that practices it.
- 4Find the swap rate
Fixed leg equals floating leg; the annuity turns basis points into dollars.
Chapters
Reading an FX quote
10 minAn FX quote is a price for one unit of the first currency, paid in the second. That sentence settles which side a client deals on, what a pip is worth, and how to turn a quote round.
- Say which side of a two-way price a client deals on, and how much of the quote currency changes hands
- Value a pip on a notional, in the quote currency and in dollars
- Read the size of a move off a P&L
- Invert a two-way quote, and cost a round trip on a wider spread
Building a cross through the dollar
11 minAlmost everything trades against the dollar, so a rate between two other currencies is built by going through it. Write the units and the multiply-or-divide takes care of itself; cross two spreads on the worse side each time and you have a two-way price.
- Build EUR/JPY and EUR/GBP from the dollar pairs, knowing when to multiply and when to divide
- Make a two-way cross from two two-way dollar quotes, and see why it is wider than either leg
- Recover EUR/USD from EUR/JPY and USD/JPY
- Trace a move in one dollar pair through to the cross and to a holding's value
Forward points: the rate gap in pips
11 minAn FX forward is not a forecast. Anyone can manufacture one by borrowing one currency, converting and depositing the other, so the forward is spot adjusted for the interest-rate gap and nothing else.
- Compute an outright forward from spot and the two deposit rates, and express it as points
- Say from the rate gap alone whether a currency is at a forward premium or discount
- Read the dollar rate the forward points imply
- Size the risk-free profit when a bank quotes a forward away from parity
Swap rates: the fixed rate that makes floating worth par
12 minAn interest rate swap exchanges fixed for floating on a notional that never moves. At the start it is worth nothing to either side, which pins the fixed rate; afterwards, the annuity turns every basis point of rate difference into dollars.
- Compute the par swap rate from a strip of discount factors
- Bootstrap the next discount factor and zero rate from a par swap rate
- Value an existing swap to the fixed payer, and its DV01 through the annuity
- Choose the right side of a swap to fix a floating-rate loan
Curve trades: betting on the shape, not the level
11 minMost rate views are about the shape of the curve. Buy one maturity, sell another, and size the legs so their DV01s match: a parallel move then makes nothing, and the P&L depends only on the spread between them.
- Size a DV01-neutral 2s10s steepener or flattener
- Compute its P&L from the moves in the two yields
- Size the legs for a target dollars-per-basis-point of spread, and the spread move a dollar target needs
- Say what an equal-face "curve trade" is really exposed to