ASSET PRICING MODEL: The yield curve 5

The yield curve may be upward sloping even in the absence of a coupon risk. In the absence of any coupon risk, q = Q. Let i\ and *2 denote the yields on short and long bonds at date 0. These yields are negative in our model because the consumers’ rate of time preference is normalized to zero. We have
This trivial example makes the point that riskiness of long-term bonds is not a necessary condition for the existence of a term premium. The yield curve can be upward-sloping, as here, simply because the corporate sector has no liquidity demand at date 2. This suggests that an upward slope is associated with relatively more pressing short-term liquidity needs, perhaps because the firm has less flexibility to adjust plans in the short term.

Other shapes of the yield curve. Suppose the income shock x and reinvestment decision у take place at date 2, and the private benefit accrues at date 3. Investments and financing still occur at date 0. In this temporal extension of the model, date 1 is just a “dummy date,” at which nothing happens. Suppose that the government still issues short-term bonds (maturing at date 1) and long-term bonds (maturing at dates 2 and 3). Short-term bonds offer no liquidity service and so q = 1. Hence the short rate (equal to 0) exceeds the long rates, and we obtain an inverted yield curve.

This example makes the simple point that if the corporate sector does not expect to face liquidity needs in the short run, it does not pay a liquidity premium on short-term securities, and so they will yield more than long-term securities.

Coordination failures in the creation and utilization of liquidity

The analysis so far has assumed that the corporate sector makes efficient use of liquidity, but has no control over the aggregate supply. This is a reasonable assumption for assets such as Treasuries whose (i) supply /./, and (ii) state-contingent payoffs 0fc(u>) can be considered exogenous. We now show by means of simple examples that the corporate sector’s date-1 policy can affect aggregate liquidity in ways that are relevant for policy making. In the first example, the aggregate supply of liquidity can be directly influenced by the corporate sector. In the second example, the effect is indirect as asset prices depend on corporate decisions. In both cases, coordination failures may occur despite the fact that we continue to assume that the corporate sector makes optimal use of its liquid assets. Throughout this section, there are no bonds or other forms of external liquidity.

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