Question:
Assume the Standard and Poor’s Index currently stands at 1400; the dividend yield on the index is 2%; and the riskless rate is 4%.
(i) What is the price of the four-month futures contract?
(ii) Is this contango or backwardation?
(iii) Tough: Do we expect normal contango or normal backwardation?
Answer:
(i) The “universal” cost of carry formula above will handle most situations (if the costs/benefits can be expressed as constant %). Costs of carry are: r = riskless rate, u = storage costs. Benefits of carry are: q = income/dividend, y = convenience yield.
In this case, F(0) = (1400)EXP[(4%-2%)(4/12)] = about 1409
(ii)
Contago because F > S
(iii)
First, we don’t know with certainty. “Normal backwardation” is possible with “contango.” “Normal contango” is possible with “contango.” I don’t know is a good answer!
Second, see p 121 of Hull. Where there is positive correlation btwn asset (stock) and underlying (S and P), we expect forward price to understate the expected future spot. As here, where systemic risk exists, we can expect normal backwardation (consistent with traditional theory, somewhat empirically verified, that normal backwardation ought to be the state of things because speculators [i.e., those taking a long position in the futures contract] demand compensation in the form of a risk premium). So, for both those reasons, we could *expect* or theorize normal backwardation.
