The current price for a stock index is 1350 and there are stock index futures contracts on the index with exactly three and six months to expiration. The three months contract trades in the market with a current price of 1340 while the six month contract has a value of 1333. The current risk free continuously compounded interest rate is 3 per cent per year for both the three and six month maturities and the dividend yield on the index is 5.2 per cent per year, also continuously compounded. 

What is the raw, theoretical and value basis on the index futures? 

What is the appropriate spread to set up to exploit any mispricing between the three and the six months futures contracts based on a view that the underlying stock market will continue to rise?

Briefly explain why the spread you set up should make money as the futures move towards expiration?