Question

The multiplier for a futures contract on a certain stock market index is \(250. The maturity of the contract is one year, the current level of the index is 1,000, and the risk-free interest rate is .2% per month. The dividend yield on the index is .1% per month.

Suppose that after one month, the stock index is at 1,020.

a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.

b. Find the holding-period return if the initial margin on the contract is \)10,000.

Short answer

a. $4,802.5

b. 48.03%

Step-by-step solution

Given information

Based on the input template:

Spot Price (S₀) = $1000

Risk-free rate (R_f) = .002

Dividend (d) = .001

Future priceF₀= ?

Calculation of future price ‘a’

Futures price F₀= S₀(1 + r_f- d)¹²

= $1,000 (1 + .002 - .001)¹²

= $1,012.07

Maturity in one month = F₀= S₀(1 + r_f- d)¹¹

= $1,020 (1 + .002 - .001)¹¹

= $1,031.28

The increase in future price = $1031.28 - $1012.07 = $19.21

Calculation of cash flow and holding period return ‘b’

Cash flow = $19.21 x $250 = $4,802.50

Holding period return = Increase in Margin Value/Margin Paid

= $4,802.50 / $10,000

= 48.03%