The current price of the HD stock is $51.25 and the 6-month spot rate is 3.7% (expressed as APR). What is the fair price of a 6-month futures contract on 200 shares of HD if the HD stock pays a $1.02 dividend just before the futures’ maturity?

Question

The current price of the HD stock is $51.25 and the 6-month spot rate is 3.7% (expressed as APR). What is the fair price of a 6-month futures contract on 200 shares of HD if the HD stock pays a $1.02 dividend just before the futures’ maturity?

BlackTom AI · Accepted Answer

We are given: current stock price S0 = 51.25, 6-month APR r = 0.037, dividend D = 1.02 paid just before futures’ maturity, and the contract is for 200 shares. The goal is to determine the fair 6-month futures price for 200 shares.

Step 1: Convert the annual rate to the 6-month rate. Since the rate is quoted as an APR, over 0.5 years the interest factor is (1 + rT) with T = 0.5. So the growth factor over 6 months is 1 + 0.037 × 0.5 = 1.0185.

Step 2: Account for the known dividend paid before maturity. A dividend paid before the contract settles reduces the forward price by its present value. A common approach in basic futures pricing is to subtract the PV of the dividend from the current price before applying the carry factor. With a simple (discrete) discount over 0.5 years, the present value of the dividend is approximately PV(D) ≈ D / (1 + rT) = 1.02 / 1.0185 ≈ 1.0015.

Step 3: Compute the adjusted price underlying the carry. Subtract the PV of the dividend from the spot price: S0 − PV(D) ≈ 51.25 − 1.0015 ≈ 50.2485.

Step 4: Apply the carry to obtain the 6-month futures price per share. Multiply the adjusted price by the 6-month growth factor: F_per_share ≈ 50.2485 × 1.0185 ≈ 51.18 (approximately).

Step 5: Scale to the total contract size. The futures contract covers 200 shares, so the fair futures price for the contract is F_contract ≈ 51.18 × 200 ≈ 10,236.00.

Rounding considerations and the precise method for discounting the dividend can shift the final figure slightly. Using the stated inputs and the standard discrete discounting approach for the dividend, you arrive in the neighborhood of 10,220 to 10,236 for the 6-month, 200-share futures contract. The key ideas are: (a) apply the 6-month carry factor to the stock price net of the present value of the dividend, and (b) multiply the per-share futures price by the contract size to get the total fair futures value.

COEC_V 371 001 002 2025W1 Lecture 8 Practice Quiz

The current price of the HD stock is $51.25 and the 6-month spot rate is 3.7% (expressed as APR). What is the fair price of a 6-month futures contract on 200 shares of HD if the HD stock pays a $1.02 dividend just before the futures’ maturity?

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