Reading and inverting a quote
Pair BASE/QUOTE = n means 1 unit of BASE costs n units of QUOTE
Base to quote: multiply by n
Quote to base: divide by n
Indirect quote = 1 / direct quote
Every conversion. Name the base currency before touching the arithmetic, and sanity-check the answer's size against the weaker currency.
- BASE
- First currency in the pair, the single unit being priced
- QUOTE
- Second currency, how much of it buys one base unit
Bid-ask spread
Spread % = ((Ask - Bid) / Ask) x 100
Dealer's earnings = (Ask - Bid) x quantity
Whenever two rates are quoted. Divide by the ask. A narrow spread means high liquidity and low transaction cost; a wide one means lower liquidity or higher risk.
- Bid
- Rate at which the bank buys foreign exchange, the lower rate
- Ask (offer)
- Rate at which the bank sells, the higher rate
Covered interest rate parity
Forward rate = Spot rate x (1 + r_quote) / (1 + r_base)
To find the no-arbitrage forward rate, or to test whether a quoted forward is mispriced. Convert annualised rates to the forward's tenor first: halve for 180 days, quarter for 90.
- r_quote
- Risk-free rate on the quote currency, for the forward's tenor
- r_base
- Risk-free rate on the base currency, for the same tenor
Appreciation and depreciation
Change % = (new value - old value) / old value x 100
For the other currency: invert both rates first, then apply the same formula
Any question about how much a currency has moved. The two currencies' percentages are never equal, so compute each on its own denominator.
- old value
- Starting rate, expressed in the units of the currency whose change you want