A non-dividend-paying stock trades at $100 today. The annual risk-free rate is 5%. According to the cost-of-carry model, what should the 1-year forward price be?
A$100 — the forward price reflects the market's expected future spot price, which equals today's price under risk neutrality
B$105 — the forward price equals the spot price compounded at the risk-free rate
CMore than $105 — the forward must include a risk premium for stock price uncertainty
DIt cannot be determined without knowing the market's consensus forecast for the stock
The cost-of-carry model sets F = S₀ × e^(rT) ≈ $105.13 through no-arbitrage, not through forecasting. If F were higher, you could borrow $100, buy the stock, and lock in the forward sale — pocketing a riskless profit. If F were lower, you'd short the stock and buy the forward. Either deviation is arbitraged away. The forward price reflects financing cost, not a price forecast.
Question 2 Multiple Choice
A physical commodity (e.g., wheat) has a spot price of $50, annual storage costs of $2, a convenience yield of $5/year, and the risk-free rate is 10%. What does the cost-of-carry model predict about the 1-year forward price relative to the spot price?
AForward > spot by 10%, because only the financing rate matters for commodities
BForward < spot, because the convenience yield ($5) exceeds storage costs ($2) plus financing (~$5), making backwardation likely
CForward > spot by exactly $7, because storage and financing add while convenience yield subtracts
Net carry cost = r × S + storage − convenience yield ≈ $5 + $2 − $5 = $2. The convenience yield of $5 exceeds storage costs of $2, which when combined with the financing of ~$5 produces a net positive carry. Actually: F = (S₀ + storage − convenience yield) × e^(rT) ≈ ($50 + $2 − $5) × 1.105 ≈ $51.68. This is close to spot but above it. However, the point is that high convenience yield (during supply shortages) can push F below S₀ (backwardation). Option B captures the key insight that convenience yield acts as a drag on the forward price, which can dominate.
Question 3 True / False
According to the cost-of-carry model, the forward price on a non-dividend-paying stock equals the current spot price compounded at the risk-free interest rate.
TTrue
FFalse
Answer: True
Yes — F = S₀ × e^(rT) (or S₀ × (1+r)^T in discrete compounding). The logic is pure no-arbitrage: holding a position in the forward and holding the actual stock financed at the risk-free rate must cost the same. The risk-free rate is the cost of tying up capital in the position from now until delivery, which is exactly what the forward buyer avoids and thus must compensate the forward seller for.
Question 4 True / False
The forward price of an asset is the market's best forecast of what the spot price will be on the delivery date.
TTrue
FFalse
Answer: False
The forward price is the no-arbitrage cost-of-carry price, not a forecast. For a non-dividend-paying stock, F = S₀ × e^(rT) regardless of whether anyone expects the stock to rise or fall. The forward price tells you what it costs to synthetically defer the purchase, not where the market thinks the price is going. Under risk-neutral pricing the two coincide mathematically, but conceptually they are distinct — and for commodities with convenience yields, the forward can be below the spot even when most participants expect prices to rise.
Question 5 Short Answer
Explain the cash-and-carry arbitrage that occurs when a forward price is higher than the cost-of-carry price, and why this trading activity restores the no-arbitrage price.
Think about your answer, then reveal below.
Model answer: If F > S₀ × e^(rT), an arbitrageur can: (1) borrow S₀ at the risk-free rate, (2) buy the asset at spot S₀, and (3) simultaneously sell a forward contract at the inflated price F. At maturity, the arbitrageur delivers the asset against the forward, receiving F, and repays the loan for S₀ × e^(rT). The riskless profit is F − S₀ × e^(rT) > 0. As arbitrageurs execute this trade, demand for the spot asset pushes S₀ up and selling pressure on the forward pushes F down, until F = S₀ × e^(rT) and the profit disappears.
Cash-and-carry arbitrage is what keeps forward markets honest. The ability to replicate the forward payoff by borrowing and buying spot means the forward price must equal the replication cost. Any gap is a free money opportunity that market participants will exploit until it closes. This is why cost-of-carry is a pricing formula derived from no-arbitrage, not an empirical regularity.