FX · 9 lessons

Revision sheet

Every FX lesson’s essentials, formula and takeaway on one page. Each heading opens the full lesson.

X1The FX market

Exchange rate: The price of one currency in another. GBP/USD 1.25 means £1 buys $1.25, so dividing dollars by the rate gives pounds: $500,000 is £400,000.
Who trades, and where: Dealer banks quote prices to companies, investors and central banks. More than $9 trillion changed hands a day in April 2025, about 38% of it in the UK, as London’s day overlaps Asia’s and New York’s.
Spot and forwards: Spot exchanges currencies at today’s rate, usually settling two working days later. An fixes a rate today for a later date; the share of expected revenue a firm sells forward is its hedge ratio.
FX swaps: A spot trade and an opposite forward done together: in effect, borrowing one currency against another. FX swaps are the most traded FX product, about two-fifths of all turnover in 2025.
Options and cross-currency swaps: An FX option gives the right, not the duty, to exchange at a set rate, for a fee paid up front: it suits money that may never arrive. A cross-currency swap turns a loan in one currency into another for years.

Dollar revenue in pounds, part-hedged

£ = (h × R) ÷ F + ((1 − h) × R) ÷ S

R: the dollars the company expects to receive
h: the hedge ratio: the share sold forward
F: the forward rate agreed today (GBP/USD)
S: the spot rate when the money arrives

Remember: £ value = $ amount ÷ GBP/USD. FX is a dealer market centred on London; a forward fixes a company’s home-currency revenue, but only for the share it hedges.

X2Quotes, pips and two-way prices

Base and terms currency: In GBP/USD 1.2500, sterling is the , the one being priced, and the dollar the : £1 costs $1.25. A higher number means a stronger base currency.
Which way round: Each pair is written one agreed way, such as EUR/USD, GBP/USD (nicknamed ) and USD/JPY. The reciprocal turns a rate round: at GBP/USD 1.25, $1 is £0.80.
Pips and what they are worth: A is 0.0001, or 0.01 in yen pairs. One pip on 10m of the base currency is worth 1,000 of the terms currency: $1,000 on £10m of cable, ¥100,000 on $10m of USD/JPY.
Bid and offer: In a such as EUR/USD 1.0850/52, the dealer buys the base currency at the bid and sells it at the offer. The client gets the worse side: selling euros, or buying dollars, deals at 1.0850.
The spread: The gap between bid and offer: 2 pips in 1.0850/52. It pays the dealer for the risk of holding a position until it can pass it on, and widens for large trades, quiet hours and big news.
The big figure: Dealers skip the leading digits, the , and quote the last two: EUR/USD 1.0850/1.0852 is said “50/52”. If the offer’s digits are below the bid’s, the big figure has ticked up.

P&L from a move in pips

P&L (terms currency) = N × pips × pip size

N: notional in the base currency
pips: pips moved in your favour (negative if against you)
pip size: 0.0001, or 0.01 in yen pairs

Remember: 1 pip on 10m = 1,000 of the terms currency. The client always deals on the worse side, and a pip is worth notional × 0.0001 (0.01 in yen pairs) in the terms currency.

X3Value dates and settlement risk

Spot and the value date: The is the day the currencies change hands. Spot settles two working days after the trade (one for USD/CAD), counting only days open in both currencies’ countries.
Forward dates: Counted from spot, not from the trade: one month after a 15 June spot is 15 July. A weekend or holiday moves the date to the next working day, or back if that would cross into the next month (modified following).
End-end rule: If spot is the last working day of a month, a monthly forward settles on the last working day of its month: from a 31 August spot, one month is 30 September.
Settlement (Herstatt) risk: Paying one currency and not receiving the other because the counterparty fails in between. The whole principal is at risk. removes it for the main currencies by paying both sides together or neither.
Replacement risk: The cost of replacing a deal if the counterparty fails before settlement. £10m bought forward at 1.2500 and replaced at 1.2800 costs $300,000; you lose only if the rate had moved your way.

Spot and forward value dates

Spot = trade date + 2 working days (USD/CAD + 1); forward = spot + n months

working day: a day open in both currencies’ countries
n months: counted from spot, then moved to a working day in the same month

Remember: Spot = T+2 good days (USD/CAD T+1). Count good days in both centres, roll forward dates with modified following, and remember that paying before you are paid risks the whole principal.

X4Cross rates

Cross rate: A pair without the dollar, such as EUR/GBP or EUR/JPY. Built from two dollar pairs it is the synthetic rate: EUR/USD 1.0850 and GBP/USD 1.2650 give EUR/GBP 0.8577.
Divide or multiply: Make the dollar cancel. If it sits on the same side of both pairs, divide; if it sits on opposite sides, multiply: dollars per euro × yen per dollar = yen per euro, so 1.10 × 150 gives EUR/JPY 165.
The cross’s bid and offer: When dividing, pair bid with offer: a client selling euros for pounds sells euros at the EUR/USD bid and buys pounds at the GBP/USD offer. When multiplying, it is bid × bid and offer × offer.
Why crosses cost more: A synthetic cross crosses two spreads, so in percentage terms it is about as wide as both added together: 0.02% plus 0.03% gives about 0.05%.
When the cross is off: A cross quoted away from the synthetic rate can be traded against the two dollar pairs for a profit: 3 on €10m is £3,000. Such gaps close within moments, so they are rare.

Cross rate through the dollar

EUR/GBP = EUR/USD ÷ GBP/USD; EUR/JPY = EUR/USD × USD/JPY

÷: the dollar is on the same side of both pairs; bid = bid ÷ offer
×: the dollar is on opposite sides; bid = bid × bid

Remember: EUR/GBP = EUR/USD ÷ GBP/USD. Make the dollar cancel: divide when it sits on the same side of both pairs, multiply when it sits on opposite sides, and pair bid with offer when you divide.

X5Spot positions and P&L

Long and short: Buying £10m of GBP/USD at 1.2500 leaves you long £10m and short $12.5m: you gain if sterling rises. Desks name the position by the pair’s first currency: “long £10m of ”.
P&L comes in the terms currency: Spot P&L is the amount times the change in rate, paid in the pair’s second currency: long £10m from 1.2500 to 1.2560 makes $60,000. A sterling desk converts it at today’s rate: about £47,771.
Average rate: The size-weighted average of the rates dealt, and the position’s break-even: £5m bought at 1.2600 and £15m at 1.2680 average 1.2660.
Realised and unrealised: An open position is at today’s rate, so its P&L is unrealised and still moving. Closing the position realises the P&L and fixes it.
Which currency strengthened: A rising pair means a stronger first currency. The % move depends on where you stand: GBP/USD from 1.25 to 1.30 is +4.0% for sterling but −3.8% for the dollar.
Sizing from a stop: Size a position from its : a $50,000 loss limit with a stop 50 away allows £10m of cable. In a fast market a stop can fill beyond its level: .

Spot P&L

P&L (terms) = N × (S_exit − S_entry); P&L (base) = P&L (terms) ÷ S_now

N: position in the base currency, negative if short
S: the pair’s rate: terms currency per unit of base
S_now: the current rate, used to convert the P&L

Remember: P&L = N × (exit − entry), in the terms currency. Spot P&L arrives in the terms currency and has to be converted to report it; size a position from its stop, not the other way round.

X6Forwards and covered interest parity

Outright forward: An exchange rate agreed today for an exchange on a later date. It is set by spot and the two currencies’ interest rates, so it says nothing about where traders expect spot to go.
Covered interest parity: Converting now and depositing, or depositing and selling forward, must pay the same, or someone makes a riskless profit. So at spot 1.2500, with sterling at 5% and dollars at 3%, one year forward is 1.2262.
Forward premium and discount: The higher-yielding currency trades at a forward discount and the lower-yielding one at a . With sterling rates above dollar rates, the GBP/USD forward sits below spot.
Forward points: The forward minus spot, in . Roughly spot × rate gap × time: 1.27 × 0.75% × 91 ÷ 360 is about 24 pips; with sterling deposits counting 365 days, nearer 22.
Points quoted two ways: Bigger number first (35/33): subtract from spot, as the first currency is at a discount. Smaller first (20/22): add. Spot 1.3000/1.3002 with points 35/33 gives a forward of 1.2965/1.2969.

Covered interest parity

F = S × (1 + r_terms × d/B_terms) ÷ (1 + r_base × d/B_base); points = F − S

S: spot, in terms currency per unit of base
r: deposit rate for each currency, as a decimal
d: days from spot to the forward date
B: day basis: 365 for sterling, 360 for dollars and euros

Remember: F = S × (1 + r_terms × t) ÷ (1 + r_base × t). The higher-yielding currency trades at a forward discount of about the rate gap times time: the forward evens out the interest, it doesn’t forecast spot.

X7FX swaps, funding and carry

FX swap: A spot exchange and an opposite forward agreed together: in effect a loan of one currency backed by another. The two legs nearly cancel the exchange-rate risk, so a swap trades the gap between the two interest rates.
Near leg and far leg: The near leg is usually at spot; the far leg is the near rate plus the swap points. A near leg at 1.2700 with points of −22 gives a far leg of 1.2678.
Uneven swaps: If the legs differ in size, the difference is an position with exchange-rate risk: buy £10m spot and sell £12m forward, and you are short £2m for the forward date.
Tom/next and short swaps: Traders keep a spot position open by rolling it a day at a time with a swap. Other short swaps run overnight (today to tomorrow), spot/next and spot/week.
Carry: What each roll pays or costs: a day’s interest gap. Long $10m against euros with dollars paying 2 points more earns about $556 a night; long the lower-yielder, it costs you. A Friday roll covers three nights.
The carry trade: Borrowing a low-rate currency to hold a high-rate one. It breaks even if the high-yielder falls by the rate gap over the period held; in a rush to exit, the jumps, as the yen did in August 2024.

Swap far leg and daily carry

Far = near + points × pip; carry per night ≈ N × rate gap ÷ 360

points: swap points, negative when the first currency pays more interest
pip: 0.0001, or 0.01 in yen pairs
N: size of the position
rate gap: rate on the currency you hold minus the one you owe (use 365 for sterling)

Remember: Carry per day ≈ N × rate gap ÷ 360. An FX swap trades the interest gap, not the exchange rate; carry pays you to wait, until a jump in the funding currency takes it back.

X8FX options

What an FX option is: The right, not the duty, to exchange at a set rate, the , on a set date, bought for a paid up front. The strike can sit above, at or below spot.
A call on one is a put on the other: The right to buy euros with dollars is also the right to sell dollars for euros, so it is named both ways: a EUR call / USD put. Against the pair it is a call on EUR/USD, gaining as EUR/USD rises.
Premium and break-even: Premiums are quoted as a % of the amount or in : 1.2% of £10m is £120,000. A call breaks even at the strike plus the premium in pips, a put at the strike minus it: a 1.0900 EUR/USD call costing 120 pips, at 1.1020.
Option or forward: A forward fixes the rate with nothing paid up front and no upside. An option sets a worst rate and keeps the upside, for the premium, so it suits money that may never arrive, such as a bid for a foreign contract.
Risk reversals: A compares out-of-the-money calls with equally out-of-the-money puts on the first currency. Positive means the calls cost more: the market is paying to protect against the pair rising.

Break-even and premium

Call break-even = K + premium; put break-even = K − premium; premium = % × notional

K: strike, in terms currency per unit of base
premium: in terms-currency pips per unit of base, for the break-even
%: premium as a % of the notional it is quoted on

Remember: Call break-even = strike + premium in pips. An FX option is a call on one currency and a put on the other; it sets a worst rate for a premium, where a forward fixes the rate outright.

X9What moves currencies

Interest rates and surprises: Higher interest rates, or expected rises, tend to lift a currency, because holding it earns more. What moves it is the surprise against pricing: a rate rise everyone expected barely moves sterling.
Real rate gap: Investors compare interest rates after inflation. A 4% rate with 3.5% inflation is 0.5% real, so it trails a 3.75% rate with 2.5% inflation (1.25% real) by 0.75 points, despite the higher headline rate.
Growth and terms of trade: Strong growth tends to lift a currency. Commodity exporters gain when the prices of what they sell rise, an improvement in their : the Australian dollar often moves with iron ore.
Safe havens: When markets are scared, the dollar, the yen and the Swiss franc tend to rise, and commodity and emerging-market currencies to fall. The yen gains partly as Japanese investors bring money home.
Intervention and pegs: is the authorities trading their own currency. Buying it uses reserves, which can run out, and fails if rates push the other way. A lasts when policy backs it, as in Hong Kong.

Real rate gap and real exchange rate

Real gap = (i_A − π_A) − (i_B − π_B); real rate = S × P_base ÷ P_terms

i: nominal policy or short-term interest rate in each economy
π: inflation: expected, or the latest year
S: nominal exchange rate, terms currency per unit of base
P: price level in each economy

Remember: Real gap = (i_A − π_A) − (i_B − π_B). Currencies follow expected real rate gaps, growth and risk appetite; surprises move them, priced news doesn’t, and intervention lasts only when policy backs it.