## ASSET PRICING MODEL: LAPM 4

Single state of liquidity shortage.

Suppose liquidity is scarce in a single state, шн, which has probability /я-According to (10), the liquidity premium on asset к is then proportional to the asset’s payoff conditional on the occurrence of the bad state:

as the single factor. That is, if дь is the date-0 price of a bond delivering one unit of good at date 1, the liquidity premium on asset к perfectly covaries with the liquidity premium on the bond:

With more than one state of scarce liquidity, (10) results in a multi-factor model where the factors can be chosen as the liquidity premia of any subset of assets that spans the states in which liquidity shortages occur.

The Arrow-Debreu economy.

Assets do not command a liquidity premium under the following additional assumptions:

According to this assumption, liquidity is valueless when it comes to maximizing pledgeable income. To understand its role, suppose that the corporate sector hoards no liquidity, and so L = 0. Suppose that in state of nature ш, there exists L such that

Thus, all liquidity premia are zero in an Arrow-Debreu economy.