Question

The risk-free rate of interest for borrowing is 4.2% per annum with continuous compounding, and the corresponding risk-free rate for lending is 0.7% per annum lower. The dividend yield is 0.4% per annum. The current value of a stock index is 1,404. There are no other transactions costs involved in spot-futures arbitrage. What is the width of the no-arbitrage window of a futures contract with six months to maturity? Use one decimal place for your answer.

Answer = 5

Answer 1

Risk free rate of borrowing = 4.2% continuous compounding

Risk free rate of lending = 0.7% lower

The differential of 0.7% per annum lower is on continuous compounding. Converting the differential to annual rate, (e^0.7%)-1 =( 2.71828^0.7%)-1 = 1.00702-1 = 0.00702 per annum or 0.00351 for 6 months (0.00702/2)

Current value of stock = $1,404

When there are no arbitrage window, the value of stock will equal the differential interest of 0.7%.

Width of the no-arbitrage window of future contract with six months to maturity = Differential between Risk free rate of borrowing and lending per annum * current value of stock = 0.00351% * $1,404 = 4.9 or 5.

(Dividend yield will be common in both buying and selling and hence not considered).