Question

The multiplier for a futures contract on the stock-market index is \(250. The maturity of the contract is one year, the current level of the index is 800, and the risk-free interest rate is .5% per month. The dividend yield on the index is .2% per month. Suppose that after one month, the stock index is at 810.

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

Short answer

Answer

a. $1,965

b. 19.65%

Step-by-step solution

Given information

Based on the input template:

Spot Price (S0) = $800

Risk-free rate (rf) = 5% or .005

Dividend yield (d) = 2% or .002

Future price (F0) = ?

Calculation of initial future price ‘a’

Futures price F0= S0(1 + rf- d)T

= $800 (1 + .005 - .002)12

= $829.28

In one month, the future price = $810 (1 + .005 - .002)11

= $837.14

This implies increase in futures price = $837.14 - $829.28 = $7.86

Hence the cash flow = $7.86 x $250= $1,965

Calculation of one month holding period return ‘b’

Holding period return = Net Cash Inflow/Margin

=$1,965 / $10,000

= 0.1965

= 19.65%