Question

Assume that the FTSE 100 is 4500, the three month interest rate is 3% per annum and the expected rate of dividend yield on the FTSE 100 over the next three months is 2% per annum

a) what is the fair price of a futures contract due to mature in three months?

b) if financial institutions face transaction costs of 0.1% on both purchases and sales of stock, plus 0.2% tax on purchases, what is the no-arbitrage band of futures prices?

c) if speculators expect that the FTSE 100 will be 4700 in three months from the present, what would you expect to happen in the future and spot markets?

Answer 1

(a) Contract Value = £ 10 per Index Point and Current Value of Index = 4500 points

Contract value = 4500 x 10 = £ 45000, Risk-Free Rate = 3 % and Dividend Yield = 2 %

Futures Tenure = 3 months

Therefore, No-Arbitrage Fair Price of a 3-month long Futures = 45000 x e^[(0.03-0.02) x 0.25] = £ 45112.641

(b) For the financial institution, any cost incurred while holding/buying/selling the underlying stock should be added to the opportunity cost (risk-free rate) of holding the contract.

Therefore, No-Arbitrage Fair Price of Future = 45000 x e^[(0.03+0.001 + 0.001 + 0.002 - 0.02) x 0.25] = £ 45157.776

(c) If speculators feel that the cost of index futures will increase in the future, they will start taking long positions in Index Futures in the Futures Market without taking a corresponding position in the Spot Market.