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  1. 093The rupee trades at 83 per dollar. One-year interest rates are 7% in India and 5% in the US. What should the one-year forward rate be, and what could you do if the quoted forward were far from it?Rates, risk and optionsCoreDebt capital marketsSales and trading

    Try it first

    Where should the one-year forward sit?

    Show the worked solution

    About 84.58 rupees per dollar. Rs 83 invested at 7% grows to 88.81. Converted to 1 dollar and invested at 5% it grows to 1.05 dollars. Both routes are riskless once the forward is agreed, so they must end equal: 1.05 x F = 88.81, giving F of about 84.58. If the quoted forward sat far above that, you could borrow rupees, invest in dollars and sell them forward to lock in a gain.

    Why is the forward set by interest rates and not by a forecast?

    Imagine two banks next door, one paying 7% on rupee deposits and one paying 5% on dollar deposits, and a counter that promises today to swap your dollars back into rupees in a year at a fixed rate. If that promised rate were 83, everyone would ignore the dollar bank. The forward rate must exactly cancel the interest difference, otherwise one route earns more than the other with no risk, and the gap would be traded away. That rule is called covered interest parity, covered because the forward removes the currency risk.

    Two ways to hold Rs 83 for a year must end in the same placeTodayIn one yearRupeesDollarsRs 83.00Rs 88.81$1.00$1.05invest at 7% in Indiainvest at 5% in the USconvert at spot 83convert back at forward FEqual endings: 1.05 x F = 88.81, so F = 84.58 rupees per dollarQuoted at 86 instead? Borrow Rs 83 (owe 88.81), buy $1, earn 5%, sell $1.05 forward at 86 = Rs 90.30.Locked-in gain Rs 1.49 per dollar with no view on the rupee, until the quote moves back.
    Investing Rs 83 at 7% gives Rs 88.81 in a year, and converting to 1 dollar at 5% gives 1.05 dollars, so the forward must be about 84.58 for the two routes to match, and a quote of 86 would let a trader lock in Rs 1.49 per dollar.

    What would you actually do if the forward were quoted at 86?

    At 86, dollars are expensive in the forward market relative to parity, so sell dollars forward and build the dollars cheaply today. Borrow Rs 83 at 7%, owing 88.81 in a year. Convert to 1 dollar at spot and deposit it at 5%, which grows to 1.05 dollars. Sell those 1.05 dollars forward at 86 for Rs 90.30. After repaying the rupee loan you keep about Rs 1.49 per dollar, without taking any view on where the rupee goes. Traders doing exactly this pushes the quote back toward 84.58.

    The relationship
    F=S×1+rINR1+rUSD=83×1.071.05≈84.58F = S \times \frac{1 + r_{\text{INR}}}{1 + r_{\text{USD}}} = 83 \times \frac{1.07}{1.05} \approx 84.58
    Fthe one-year forward, rupees per dollar
    Sspot, 83
    r_INR, r_USDone-year rates in India and the US, 7% and 5%
    What it says in wordsThe forward equals spot scaled by the ratio of the two currencies' interest growth.

    The forward rupee is about 1.9% weaker than spot, roughly the 2 point rate difference. A quick approximation is spot times one plus the difference, 83 x 1.02 = 84.66, close enough to sanity-check. The limitation: in practice, capital controls, transaction costs and limits on who can borrow in each currency let small gaps persist, so the arbitrage is cleaner on paper than on a dealing desk.

    Where candidates lose it

    The common answer is that the forward is the market's forecast of the rupee, so it should be 83 or whatever you expect. Interviewers on rates and FX desks ask this precisely to hear you say it is an arbitrage relationship, not a forecast.

    The second slip is flipping the ratio and getting a stronger forward rupee. Check the direction: the higher-yielding currency trades weaker forward.

    What the interviewer asks next

    • What is the six-month forward on the same numbers?
    • An importer must pay 1 million dollars in a year. How does the forward help, and what does it cost?
    • Why might the quoted forward differ from parity for an extended period?