An index is at 5,000 with 73 days to a futures expiry. Financing is 5.2% and the dividend yield is 1.6%, both simple on a 360 day basis. The future trades at 5,042. Compute fair value and say whether the trade is on if your own funding is 5.6%.

An index is at 5,000 with 73 days to a futures expiry. Financing is 5.2% and the dividend yield is 1.6%, both simple on a 360 day basis. The future trades at 5,042. Compute fair value and say whether the trade is on if your own funding is 5.6%.

Approach: Build the fair value from the net carry over the period, then repeat the calculation with your own funding rate to see how much of the basis survives at the rate you actually pay.

5,036.5. Fair value is S * (1 + (r - d) * days/360) = 5,000 * (1 + 0.036 * 73/360) = 5,000 * 1.0073 = 5,036.5, so at 5,042 the future is 5.5 points rich. At your own funding of 5.6% the net carry is 4.0% and fair value is 5,000 * (1 + 0.04 * 0.202778), which is 5,040.6, leaving only 1.4 points of basis. Selling the future against the basket at 1.4 points gross has to cover the basket's execution cost, the dividend estimate over 73 days and the funding of variation margin, so the cash and carry is marginal at that rate. The same futures price is therefore rich to one participant and fair to another, because the arbitrage is really a trade on the funding rate.

Follow-up: The dividend estimate turns out to be 20 basis points too high. How does that move fair value and which way does the error bias the position?

Key concepts: cash and carry, fair value, net carry, funding rate, basis.