We analyze the effect of unconventional monetary policy, in the form of collateralized lending to banks, on sovereign borrowing costs. Using our unique dataset on monthly security- and bank-level holdings of government bonds, we document that Portuguese banks increased their holdings of domestic public debt during the allotment of the three year Long-Term Refinancing Operations (LTRO) of the European Central Bank. We argue that domestic banks engaged in a "collateral trade", which involved the purchase of high-yield bonds with short maturities that could be pledged as collateral for low cost and long-term borrowing from the ECB. This significant increase in bond holdings was concentrated in shorter maturities, as these were especially suited to mitigate funding liquidity risk. The resulting steepening of the sovereign yield curve and the timing and characteristics of government bond auctions are consistent with a strategic response by the debt management agency.