Oriana,
Yes, future will converge with cash. The reason for this being a future, on an index for example, represents the value of the current underlying index (the "cash" or "spot") at some point in the "future".
The future value is the "cost-of-carry"(?) of the cash index.
From the future's value, the underlying (theoretical) cash index value can be determined by discounting the future's value.
For example,
Cash index = 6840, interest rate = 4%, future expiry = 51 days.
Future value = Cash index x exp(interest rate) x (days/365)
= 6840 x exp(0.04 x 0.14) = 6878.
Cash value = Future value / exp(interest rate) x (days/365)
= 6878 / exp(0.04 x 0.14) = 6840.
Assuming no change in the value of the cash index, with 17 days to expiry the future value will equal 6852, ie less than the future value with 51 days to expiry. Another way to look at this is to think in terms of time value (days to expiry), ie the greater the time value, the greater the value of the future.
Assume the cash index at expiry has fallen to 6800. The future value is:
6800 x exp(0.04) x (0/365) = 6800, ie it has converged with the cash index.
Theoretically, if either cash and future diverge significantly from their theoretical values an arbitrage opportunity (risk-free trade) is available.
For example, if our future value is at 6903 (25 points above its theoretical value) then one would sell the over-priced future at 6903 and buy the constituents of the cash index for 6840. At expiry, assuming cash at 6800 we will have:
sell underlying constituents at 6800 = -40 (notice we have a loss here but it doesn’t matter)
buy future at 6800 = 103 ( we sold at 6903 and bought back at a lower price)
net = 103 – 40 = 63.
Someone said (one of the posters to T2W, Dashing Blade?) to the effect that all financial markets can be reduced to present, discounted and future (or forward) values. That’s pretty much it.
Grant.