The current price of the HD stock is $47.5 and the 6-month spot rate is 1.8% (expressed as APR). What is the fair price of a 6-month futures contract on 600 shares of HD if the HD stock pays a $0.48 dividend just before the futures’ maturity?

Question

The current price of the HD stock is $47.5 and the 6-month spot rate is 1.8% (expressed as APR). What is the fair price of a 6-month futures contract on 600 shares of HD if the HD stock pays a $0.48 dividend just before the futures’ maturity?

BlackTom AI · Accepted Answer

To determine the fair price of a 6-month futures contract on 600 shares of HD, start by identifying the inputs: current stock price S0 = 47.5, 6-month spot rate is 1.8% APR, and a dividend D = 0.48 paid just before maturity. Because the dividend is paid at or very near the futures’ maturity, its effect on the forward price is to reduce the amount that must be carried or borrowed to finance the position by the amount of the dividend.

First, convert the annual rate to the 6-month rate. With a simple-interest interpretation (APR given for 6 months), the 6-month rate is rT = 0.018 × 0.5 = 0.009 (or 0.9%). In a typical futures pricing with a known discrete dividend, the forward price F0 is:
F0 = S0 × (1 + rT) − D × (1 + rT)^(T − t)
where t is the time until the dividend, and T is the time to maturity. Here, the dividend is paid just before maturity, so T − t ≈ 0, and (1 + rT)^(T − t) ≈ 1. This means the dividend is subtracted directly from the carried value at maturity.

Compute the carry part: S0 × (1 + rT) = 47.5 × (1 + 0.009) = 47.5 × 1.009 = 47.9275.
Then subtract the dividend: 47.9275 − 0.48 = 47.4475. This is the fair price per HD share for the 6-month futures.

Now scale to 600 shares: 47.4475 × 600 = 28,468.5.

So, the fair price of the 6-month HD futures contract on 600 shares, given the dividend just before maturity and the 6-month rate, is approximately $28,468.50.

Notes and alternative considerations:
- If a different convention for the interest rate (e.g., continuous compounding) were used, the numeric result would shift slightly, but with such a short horizon (6 months) the difference would be modest.
- If the dividend timing were significantly earlier than maturity, we would discount the dividend to present value and subtract D × e^{−r t} before applying the growth to maturity; here t ≈ T, simplifying the calculation.
- Since there were no answer choices provided in the data, this step-by-step calculation yields the numeric fair forward price for the contract.

COEC_V 371 001 002 2025W1 Lecture 8 Practice Quiz

The current price of the HD stock is $47.5 and the 6-month spot rate is 1.8% (expressed as APR). What is the fair price of a 6-month futures contract on 600 shares of HD if the HD stock pays a $0.48 dividend just before the futures’ maturity?

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