I have only government bond yields with different maturities. How can I obtain sythetic future prices on bonds? After obtained the future prices, I am supposed to compute the return and carry returns.
This is pretty much impossible to do, but if you must, you'll have to make some assumptions.
You can assume that the yields given are par yields. In other words, they represent both the yield AND the coupon rates of bonds trading at par. And assuming you also have short-term interest rates, you can compute forward price on this hypothetical par bond and use that as the basis for futures price (you won't need to worry about delivery option, but you still have to account for the conversion factor). Carry is simply the difference between spot price (assumed to be 100) and forward price.
To compute returns, you take this bond and reprice at at the next period (i.e., holding coupon rate constant and reducing time to maturity, you reprice it at the new yield). That allows you to compute returns.