Forward Contract on a Bond: Premium or Discount?

This interview question focuses on pricing a short-dated forward contract written on a long-dated riskless bond, first without coupons and then with coupons that are high relative to current interest rates. The candidate must compare the spot value of the bond to the theoretical forward price and reason about whether the bond effectively trades at a premium or discount to the forward. When the setup is varied to include coupons, the problem becomes closer to standard fixed-income or derivatives interview material used for trading and structuring roles, where understanding how cash flows alter relative value is essential.

To answer, the candidate must apply no-arbitrage forward pricing, discounting, and cash-and-carry logic, and translate these into qualitative statements about "rich" versus "cheap." It leans on understanding the relationship between spot and forward prices when the underlying has no income versus when it pays coupons above prevailing risk-free rates. Interviewers watch for a clear replication argument, correct handling of financing and income, and consistency across both versions of the problem, rather than rote use of formulas.

What it tests

The core structure behind forward pricing is the no-arbitrage principle, which ensures that the forward price reflects the opportunity cost of capital and any income generated by the underlying asset. For any asset, the forward price is set so that buying the asset now and carrying it (including financing costs and subtracting any income, like coupons or dividends) yields the same result as entering the forward contract. This is formalized as $F = S e^{(r-q)(T-t)}$, where $q$ represents the continuous yield (like coupons or dividends). The pattern holds because, if the forward price deviated from this relationship, arbitrageurs could lock in riskless profits by exploiting the difference, quickly restoring equilibrium. The key is that the forward price adjusts for both the time value of money and any cash flows the asset provides during the contract period, ensuring no arbitrage is possible.