Safe and liquid assets, such as Treasury bonds, are money-like instruments that command a convenience yield. We analyze this in a search model of two assets that differ in liquidity and safety. In contrast to the reduced-form approach, which puts the safe and liquid asset in utility function, we explicitly model investors' trading needs and the trading friction. One new implication from this approach is that the marginal investor's preference for safety and liquidity is not enough in determining the premium. Instead, the distribution of investors' preferences plays a direct role. Our model implies that an increase in the supply of the liquid asset may increase or decrease the liquidity premium, depending on the distribution of investors' liquidity preference. Our model shows that investors may over- or underinvest in the search technology relative to a central planner, and that overinvestment occurs when investors' expected trading frequency is in the intermediate region.