Compute a bid-ask spread and explain why spot quotes and forward quotes may carry different spreads.
The idea
The bid-ask spread is ask minus bid, often quoted in pips (0.0001 for most pairs). The mid rate is (bid + ask) ÷ 2, and as a percentage of it the spread is: Percentage spread = (ask − bid) ÷ mid rate. The spread pays the dealer for order processing, for holding inventory risk and for trading against better-informed clients, so it widens when volatility rises or liquidity falls. Forward quotes usually carry wider spreads than spot. Both trade over the counter, but forwards are less liquid and longer-dated, so the dealer bears more credit exposure and more uncertainty about funding and hedging costs. Mechanically, the outright forward bid is the spot bid plus the bid points, and the forward ask is the spot ask plus the ask points. Points are negative when the forward trades at a discount. Subtracting the forward bid from the forward ask, the spread on the outright forward is: Forward spread = spot spread + (ask points − bid points). Compare spreads in the same units, and expect the forward spread to exceed the spot spread.
Formulas
Bid-ask spread as a percentage of the mid rate
percentage spread = (ask − bid) ÷ ((bid + ask) ÷ 2)
- ask
- the rate at which the dealer sells the base currency
- bid
- the rate at which the dealer buys the base currency
Compare spreads in the same units. Dividing by the bid or the ask instead of the mid gives a slightly different number.
Spread on an outright forward
forward spread = spot spread + (ask points − bid points)
- spot spread
- spot ask minus spot bid
- ask points
- the forward points added to the spot ask
- bid points
- the forward points added to the spot bid
Points keep their sign, negative at a forward discount. Expect the forward spread to exceed the spot spread, since forwards are less liquid and longer-dated.
A practice question
A dealer quotes GBP/USD spot at 1.2650/1.2654. The bid-ask spread as a percentage of the mid-market rate is closest to:
- 0.316%Why not: Decimal slip: 0.0004/1.2652 is 0.0316%, not 0.316%.
- 0.0316% - correct
- 0.0004%Why not: Reports the raw spread of 0.0004 as a percentage without dividing by the rate and scaling to percent.
- 3.16%Why not: Multiplies by 100 twice; the spread in percent is 0.0316%, and 3.16% would be an enormous spread.
Spread = ask - bid = 0.0004, which is 4 pips. As a percentage of mid (1.2652) it is 0.0004/1.2652 = 0.0316%.
A harder one
A dealer's EUR/USD spot spread widens from 2 pips to 9 pips immediately after a surprise central bank announcement. Which explanation is most consistent with standard dealer pricing?
- Trading volume has risen sharply, which lowers the dealer's costs per trade and so widens the spreadWhy not: Higher volume normally narrows spreads; the widening here comes from risk, not volume.
- The central bank has set a regulatory minimum spread on the pairWhy not: Spreads are set by dealer competition; there is no such regulatory minimum on a major pair.
- The spot rate itself has moved, and spreads are always a fixed percentage of the rateWhy not: Spreads are not a fixed percentage and a change in level alone does not explain a four-fold widening.
- Volatility and inventory risk have risen, so the dealer wants more pay for providing liquidity - correct
Spreads compensate dealers for order-processing costs, inventory risk and adverse selection. A surprise raises volatility and uncertainty, so dealers widen their quotes to cover the higher inventory risk.
The hardest tier
A treasurer buys EUR 5 million one year forward at the dealer's quote of 1.0985/1.0996 (USD per EUR), then immediately reverses the trade by selling EUR 5 million at the same quoted forward rate. Spot is quoted 1.0840/1.0844. What is the round-trip cost in USD?
- USD 2,000Why not: Applies the spot spread (4 pips) rather than the forward spread (11 pips).
- USD 5,500 - correct
- USD 55,000Why not: Decimal slip: 11 pips is 0.0011 per EUR, not 0.011.
- USD 3,500Why not: Uses only the difference between the forward points (7 pips) instead of the full forward spread (11 pips).
The client buys at the ask 1.0996 and sells at the bid 1.0985, so the cost is the forward spread: 0.0011 x 5,000,000 = USD 5,500. The spot spread of 4 pips (USD 2,000) is irrelevant to a forward round trip.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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