Pricing and Valuation of Forward Contracts and Underlying with Varying Maturities

### Which of the following statements best describes the value of a forward contract at initiation? - [ ] It is always strictly positive. - [ ] It is always strictly negative. - [x] It is zero to both parties if priced fairly. - [ ] It oscillates unpredictably from day one. > **Explanation:** A properly priced forward contract has zero initial value to both the long and the short. ### In a simple world with no dividends, no storage costs, and continuous compounding, what is the fair forward price F₀ for an asset that has a current spot price S₀ and a risk-free rate r for T years? - [ ] F₀ = S₀ × e^(-rT) - [x] F₀ = S₀ × e^(rT) - [ ] F₀ = T × r × S₀ - [ ] F₀ = S₀ / (1 + r)^T > **Explanation:** Under continuous compounding and no other costs or yields, F₀ = S₀ × e^(rT). ### How does the existence of a convenience yield (CY) typically impact the forward price of a commodity? - [x] It reduces the forward price compared to a situation with zero convenience yield. - [ ] It raises the forward price compared to a situation with zero convenience yield. - [ ] It has no effect. - [ ] It mirrors a dividend yield. > **Explanation:** A positive convenience yield is an extra benefit from holding the physical commodity, so the forward price tends to be lower. ### If a company entered a forward contract to buy an asset at F₀ = $100, and three months later the “fair” forward price for the same maturity is $105, what does that indicate for the value to the long position (ignoring discounting)? - [ ] It's at a $5 loss since the forward price rose. - [x] It's at a $5 gain since the original forward price is lower than the new fair price. - [ ] It remains unchanged because the contract can’t be marked to market. - [ ] It depends on whether interest rates have decreased. > **Explanation:** If the new fair forward price is higher, the original long locked in a cheaper price, so the position has gained in value by $5 (before discounting). ### At the expiration of a forward contract, what is the payoff to the short if the final spot price (Sᵀ) is below the originally agreed forward price (F₀)? - [ ] 0 - [ ] Sᵀ + F₀ - [x] F₀ − Sᵀ - [ ] Sᵀ ÷ F₀ > **Explanation:** The short’s payoff is F₀ − Sᵀ at expiration. If Sᵀ is below F₀, the short benefits. ### What does it mean if a commodities forward curve is in “contango”? - [ ] Shorter-dated contracts have higher prices than longer-dated ones. - [x] Longer-dated contracts trade at progressively higher prices compared to nearer contracts. - [ ] Forward prices for all dates are identical. - [ ] The underlying commodity is expected to vanish by maturity. > **Explanation:** Contango refers to a situation where forward prices are higher at longer maturities, often driven by storage costs and other factors. ### A forward rate agreement (FRA) is primarily used to: - [x] Lock in a borrowing or lending rate for a future period. - [ ] Hedge currency exchange risk. - [ ] Gain exposure to equities without ownership. - [ ] Commit to a commodity delivery at a future date. > **Explanation:** FRAs are specifically designed to lock in an interest rate for a future borrowing/lending period. ### Suppose you have a bond paying an annual coupon of 5%. When pricing the forward contract on this bond, how would the coupon typically affect the forward price? - [x] It lowers the forward price relative to a zero-coupon bond. - [ ] It raises the forward price relative to a zero-coupon bond. - [ ] It has no effect whatsoever. - [ ] It can either raise or lower the forward price, depending on stock market volatility. > **Explanation:** Cash flows like coupons reduce the forward price because the holder of the underlying bond receives these payments directly. ### Which statement best describes the role of “cost of carry” in forward pricing? - [x] It encapsulates storage costs, financing costs, and any income from holding the asset. - [ ] It is solely the interest rate used for discounting. - [ ] It only applies to perishable commodities. - [ ] It only applies to equity markets. > **Explanation:** Cost of carry includes all relevant costs (including financing rates, storage, etc.) and benefits (e.g., dividends, convenience yield) associated with holding the underlying asset until maturity. ### True or False: A forward contract on a zero-coupon bond that matures at the same time as the bond itself would be identical to just owning the bond outright. - [x] True - [ ] False > **Explanation:** If the bond itself has no coupons and both the contract and the bond mature at the same time, the forward contract effectively replicates the same payoff as holding the bond (excluding credit risk differences if any).