Hedging and speculative motives of market makers often require strategies involving positions in both the futures and spot market. These are basis strategies. The risk involved in the payoff of these strategies depends on the basis risk and cannot be diversified away. Hence, any security that contains a higher basis risk should be compensated through a higher yield. Using simulations based on a risk-averse model, we find that a market maker increases his quoted spread modestly when basis risk increases. However, if the basis risk becomes very large, the quoted spread increases more than proportionally. This convexity in spread suggests the following: the market maker increases his spread as a compensation for the increased hedge difficulty. When the basis volatility becomes very large however, the quoted spread becomes even larger indicating his unwillingness to trade. Based on these findings, we study the basis risk for four fixed income securities in Europe. Using a state space approach applied to trading data, we estimate the basis risk volatility and find that bonds that are traded at a premium, like Germany and France, have a lower basis volatility. This gives an additional explanation why some European bonds are traded at a significant premium even when we take differences in liquidity or credit risk into account.