You need $50m of index exposure for three months. The future implies financing at 40 basis points over the risk free rate. The ETF charges a 9 basis point annual expense ratio and you can borrow at 15 basis points over the risk free rate. Which is cheaper and by how much in dollars?

You need $50m of index exposure for three months. The future implies financing at 40 basis points over the risk free rate. The ETF charges a 9 basis point annual expense ratio and you can borrow at 15 basis points over the risk free rate. Which is cheaper and by how much in dollars?

Approach: Put both instruments on the same quarterly basis, counting the futures richness as implied financing and the fund as expense ratio plus your own borrowing cost.

$20,000. The ETF is cheaper. The future costs 40 basis points a year of implied financing above the risk free rate, which is 10 basis points over three months. The ETF costs a quarter of its 9 basis point expense ratio, 2.25 basis points, plus your own borrowing at 15 basis points a year, 3.75 basis points, for 6 basis points in total. The 4 basis point difference on $50m is $20,000. The comparison flips whenever futures richness falls below your funding spread plus the expense ratio, so it has to be redone at every roll. Two items the arithmetic leaves out are dividend withholding drag inside the fund and the tracking error of holding a fund against the index the future settles to.

Follow-up: At what level of futures richness does the decision flip, expressed in basis points of implied financing?

Key concepts: implied financing, expense ratio, tracking error, quarterly cost.