Covered interest arbitrage margin
Margin = interest differential - forward discount
on the foreign currency
A forward premium is a negative discount, so it adds.
Deciding whether moving short-term funds abroad with the exchange risk covered is worth doing. Positive means yes; zero means covered interest parity holds.
- Interest differential
- Foreign rate less domestic rate, both per year
- Forward discount
- Annualised, from ((FR - SR) / SR) x (12 / n) x 100; work out the sign from the quotes
- Holding-period gain
- Annual margin x n / 12, applied to the sum placed
Speculative profit on a forward position
Short (sold forward): profit = amount x (contract rate - spot at maturity)
Long (bought forward): profit = amount x (spot at maturity - contract rate)
Any question giving a forward contract rate, an amount and the spot rate that actually occurred. Decide the direction of the position first; the sign follows.
- Contract rate
- The forward rate agreed when the position was opened
- Spot at maturity
- The rate at which the position is closed out
- Short and long
- Short is selling or borrowing, expecting a fall; long is buying or holding, expecting a rise
Covered interest parity
Interest differential = forward discount on the foreign currency
so that the margin is zero
Checking whether a set of quotes is internally consistent, or explaining why an arbitrage opportunity disappears. It does not imply equal interest rates or equal spot and forward rates.
- Enforcement
- Spot purchases and forward sales by arbitrageurs raise the spot rate and depress the forward rate until the gap matches the differential
- Residual decision
- With the margin at zero, going abroad unhedged is a speculative view on the spot rate, not an arbitrage