How this number is made
The fair futures price is the spot grown at interest and reduced by the dividends you give up. The basis is that futures price minus the spot. A traded futures price above fair is rich. Below fair is cheap. This uses a continuous yield, not a list of cash dividends, and it ignores the cost of borrowing the stock.
- A quarter of a year is 0.25.
- The dividend yield is the annual yield you expect over that window, not last year’s trailing yield unless you mean that.
Formula
Fair futures = spot × e^((interest − dividend yield) × years). Basis = fair futures − spot.
Worked example
With the figures already in the form, fair futures price is $5,043.94.
Questions
Why is the futures price above the index?
When interest is higher than the dividend yield, carrying the stocks costs more than the dividends pay, so the future is higher.
Is the basis a profit?
Only if you can hold the basket, finance it, and receive the dividends at the yield you typed, and the futures converge.