Question

The S&P 500 stock index is at 1,100. The annualized interest rate is 3.5 percent, and the annualized dividend is 2 percent.

Refer to Exhibit 15.9. If the futures contract was currently available for 1,250, calculate the arbitrage profit.

a. -$133.41

b. $147.25

c. $133.41

d. $0

e. -$147.25

Answer 1

Given,

Stock index = 1100

Annual interest rate = 3.5% or 0.035

Annual dividend rate = 2% or 0.02

Futures price = $1250

Solution :-

60 day interest rate = 0.035 x 60/360 = 0.0058333333

60 day dividend rate = 0.02 x 60/360 = 0.0033333333

Now,

Arbitrage profit = Futures price - stock index - stock index (60 day interest rate - 60 day dividend rate)

= $1250 - $1100 - $1100 (0.0058333333 - 0.0033333333)

= $1250 - $1100 - $1100 (0.0025)

= $1250 - $1100 - $2.75 = $147.25