Free lesson · FX and commodities
Invert both units and bid/ask sides
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Start with the idea
The reciprocal of a currency price reverses which currency is being bought and sold.
Symbols, units & horizon
- b_B/A,a_B/A: bid and ask measured in currency B per unit of currency A
- b_A/B,a_A/B: inverted bid/ask measured in A per B
- positive quotes with bid≤ask
- the subscripts denote units, not a vendor ticker convention
When and why to use this
Validate cross-currency conversion and prevent accidentally using the favorable side of a spread.
The reciprocal of a currency price reverses which currency is being bought and sold.
If a dealer quotes dollars per euro, its bid is what it pays in dollars to buy one euro; its ask is what it charges to sell one euro. When the pair is inverted, the old ask becomes the reciprocal bid.
Write the conversion as a unit-canceling equation before using a price feed. Pip size, lot multiplier, settlement lag and fees depend on the actual contract; this example teaches spot arithmetic only.
Invert both units and bid/ask sides
- Buying A at the original ask spends B; reversing that exchange sells B for A.
- Therefore one B sold receives 1/original ask units of A, the inverted bid.
- Similarly the inverted ask is 1/original bid; check bid remains no larger than ask.
USD per EUR quote 1.10/1.12 becomes EUR per USD bid 1/1.12≈.892857 and ask 1/1.10≈.909091.
Apply it in a strategy
- Freeze inputs at the stated decision time and record their units.
- Validate cross-currency conversion and prevent accidentally using the favorable side of a spread.
- Recompute the example, then change the material assumption and explain the difference.
Research deliverable
Invert both units and bid/ask sides: produce the worked calculation, a timestamped input record and a written decision addressing this limitation: Inverting mid-prices hides the actual conversion spread and does not model depth or settlement costs.
These are synthetic mechanics examples, not historical performance or paper replications. Module evidence and research boundaries record the 12 September 2026 review.
Research sources, review dates and limitations
Python implementation
Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.
# Python 3.10+; standard library and NumPy only.
# Synthetic teaching inputs; conventions and units are defined in the notation above.
def invert_quote(bid,ask):
if not 0<bid<=ask: raise ValueError('Positive ordered bid/ask required')
return 1/ask,1/bid
bid,ask=invert_quote(1.10,1.12)
assert bid<ask and abs(bid-.892857142857)<1e-10
print(bid,ask)Continue learning
FX & Commodities: Quotes, Carry, Curves & Hedges — all lessons- Invert both units and bid/ask sides
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- Covered interest parity by matching currency cash flows
- Unhedged carry leaves exchange-rate risk
- Storage and convenience yield in a commodity forward
- Futures profit and margin cash demands
- Rolling futures without inventing a cash profit
- Minimum-variance cross hedging and basis risk
Quantitative finance and development glossary · Python resources and libraries · Research sources and limitations