You observe on 28/10/05 that the US Treasury 7.125% 15/2/16 bond for settlement 29/10/05 is trading at 124-09 and the December long bond future at 109-00. If the conversion factor is 1.1300, the implied repo rate is 0.49% and the actual repo rate is 1.69%, estimate the gross basis for the bond in 32nds.

The current S+P 500 index is trading at 1200 with a dividend yield of 2.5% and a short-term interest rate at 6%. What would be a fair price at which you would be willing to buy the S+P index forward in 90 days. Assume both dividend yields and interest rates are given on a 360 day year basis.