Forward points: the rate gap in pips

Spot EUR/USD is 1.0800. Borrow $1.0800, buy one euro, deposit it for 90 days at 3%: you will own 1.0075 euros. Your dollar loan at 5% will cost 1.0935. So the rate at which 1.0075 euros must convert to 1.0935 dollars in 90 days is fixed today: 1.0935 ÷ 1.0075 = 1.0854. That is the forward, and it is 53.6 pips above spot: the forward points. Nobody forecast anything. The euro is dearer forward because it pays less interest, and the forward gives back exactly the gap.

The currency with the higher rate trades at a forward discount, the lower-rate currency at a premium, always by the interest arithmetic. If a bank quoted the forward anywhere else, the same borrow-convert-deposit trade would lock in a risk-free profit, so it does not. That also lets you read a deposit rate off the forward: given spot, the points and one rate, the other rate is pinned. In practice a few pips of mispricing never survive bid-offer on four legs and the balance sheet the trade uses.

• The conventions here: EUR/USD, dollars per euro. Covered interest parity with simple money-market interest on an actual/360 basis in both currencies. Points are (forward − spot) × 10,000, printed to one decimal, and the implied-rate question works from the printed points. No bid/offer, no credit or basis. Arbitrage is sized on a euro amount converted at spot and settled at delivery.
• Two routes to the same place. Hold dollars for the period, or convert to euros, hold euros, convert back forward. If the two routes did not give the same dollars, the worse one would be abandoned and the better one crowded until they matched. The forward is where they match.
• Why the high-rate currency is at a discount. Holding it pays you more interest; the forward must take that back or you would earn the gap for free. The forward is a price for giving up one interest stream for another.
• Points scale with the gap and with time. Roughly spot × rate gap × days ÷ 360 × 10,000. A hike barely moves one-month points and shifts one-year points a lot.
• Forwards are poor forecasts. They are arithmetic, not opinion. Betting that spot will not move as much as the forward implies is the carry trade: borrow the low-rate currency, hold the high-rate one unhedged, and earn the gap until the funding currency suddenly strengthens.
• Run it backwards. Forwards are often deeper than cash deposits, so traders read the cost of borrowing a currency synthetically off the points. When that differs from the cash rate, the gap is the cross-currency basis, itself a signal of dollar funding stress.