if 6 months MRR is 5% and 9 months MRR is 5.5% then 6 X 9 FRA will be 6.34%, if thats the case then who will short FRA for 9 months at 5.5% if they can lock it at 6.34%, that seems illogical right?
The point is not the ninth month but the nine months period. It doesn’t mean that you could receive 6.34% at the point of the ninth month but you receive 6.34% for three months and pay the floating rate during this period.
For 9 months MRR, the interest rate of 5.5% lasts for 9 months. But for 6*9 FRA, the 6.34% only lasts for the end of 3 months of that 9 months. You will receive less than 5.5% over the first 6 months.