Question

Futures Question:
Suppose that the risk-free rate (continuously compounded) is 5% p.a.
The stock-market index is currently at £ 5,000 and the futures price for a contract deliverable in 3 months is £ 5,050.
Question - what arbitrage opportunities does this create? how would you exploit them?

Answer 1

Firstly we re-calculate the interest rate: 0,05/12*3= 0,0125
Then we compound the sum: 5000*(1+0,0125)=5062
The arbitrage opportunity is 5062-5050=12

We can exploit AO by selling above mentioned futures contract and investing into the stock-market index for 3 months.

Answer 2

Hmm, 2 mistakes there (one big, one small), anyone else?

Answer 3

I see .. Its continuously compounded not annual percentage rate. Then its ...

3 month interest rate: [(\sqrt[12]{1,05})^{3}-1=0,0123\]
Then we compound the sum: 5000*(1+0,0123)=5062
The arbitrage opportunity is 5062-5050=12
We discount the profit back to t=0: 12*\[e^{-0,0123}\]=11,85

Answer 4

correct on the continous compounding :-)

Think of the pair of trades you suggested for the AO though ...

Answer 5

Its vice-versa. Futures contract allows you to buy stock index for less money :)

Answer 6

Good answer.
- Buy the stock index future (it's underpriced at £5,050)
- Short the index spot in the cash market
- Invest the proceeds in Treasuries (£5,000) for 3 months.
At maturity, at 3months:
- Cash out the risk-free investment at £5,062
- take delivery of the index, for £5,050; close out the short index position (now you're flat).
- pocket the $11.85 difference. :-) risk-free Arbitrage opportunity.