Question

Assume you observe that the ABC stock index (S) is at a level of 290.00 and that the A&B 500 futures contract (F) expiring in exactly three months is at a level of 291.50. if the riskless rate of interest ( r) is 6.5 percent annually, what is the implied dividend yield on the ABC stock portfolio if no costless arbitrage opportunities exist in the marketplace?

Answer 1

Value of ABC stock index or spot rate = 290

Value of future contract expiring in 3 months = 291.50

Time in year = 3/12 = 0.25

Risk free rate = 6.5%

Value of future contract = Spot rate*(1+(Risk free rate-Dividend yield))^t

291.50 = 290*(1+(6.5%-Dividend yield))^0.25

291.50/290 = (1+(6.5%-Dividend yield))^0.25

(1.005172414)^(1/0.25) = 1+(6.5%-Dividend yield)

1.020850733-1 = 0.065 - Dividend yield

Dividend yield = 0.065-0.020850733

=0.044149267 or 4.41%

so dividend yield is 4.41%