Bond Hedging with Duration and Convexity

1) Hedging against 2 Futures (Barbell)

you can work out a linear system which take into account the duration and the convexity to calculate the quantities needed against the 2 futures :

hedging with convexity and duration

it could be a good guess for long term maturity and/or high coupon bond which have high convexity

2) adjust the hedging with a yield beta as a risk factor