Question

The spot price on the S&P 500 is $20,000 and the 1-year futures price is $20,609.09. The

1-year risk-free rate is 3% per annum with continuous compounding.

a. Draw the profit and payoff function for the long future. (Provide labels for the axes

and label a point on the functions above, below and at the futures price)

b. Note an S&P 500 futures contract is for 250 times the S&P 500. Calculate what

the payoff and profit at expiration is if the spot price is _______.

i. $19,500

ii. $20,000

iii. $21,100

Answer 1

b)

Future Price = 250 times Spot Price. This means Lot Size = 250.

Future price = $20609.09

1) Spot price = $19500

Payoff = (Spot Price - Futures price ) * Lot Size

= ( 19500 - 20609.09) *250

= $-277272.05

Loss of $277272.5

2) Spot price = $20000

Payoff = (Spot Price - Futures price ) * Lot Size

= ( 20000 - 20609.09) *250

= $-152272.05

Loss of $152272.5

3) Spot price = $21100

Payoff = (Spot Price - Futures price ) * Lot Size

= ( 21100 - 20609.09) *250

= $122727.5

Profit of $122727.5