I have derived the convexity adjustment expression for futures rates using the Ho-Lee model, to arrive at the following: $$ ForwardRate = FuturesRate - \frac{1}{2}\sigma^2T_1T_2 $$ where $T_1$ refers to the time when the forward rate starts, $T_2$ when it finishes and $\sigma$ refers to the volatility of the short rate process.
I have derived the above expression in continuous time assuming continuous compounding, but my futures rate is a simply compounded rate. Is the following conversion to simple compounding correct? $$ \left(1 + ForwardRate\times(T_2-T_1)\right)^{(T_2-T_1)} = \left(1 + FuturesRate\times(T_2-T_1)\right)^{(T_2-T_1)} - \frac{1}{2}\sigma^2T_1T_2 $$
I am under the impression I'm terribly wrong!