The **liquidity preference theory** of the term structure posits that investors demand a liquidity premium for holding long-term bonds relative to short-term bonds due to the added risk and uncertainty associated with tying up funds for an extended period. This liquidity premium compensates investors for forgoing the flexibility to react to changing market conditions or investment opportunities.

#### Contents

## Understanding the liquidity preference theory

In the previous lesson, we explained that according to the expectations hypothesis, forward rates *f _{t}* are

*equal*to expected short rates

*E[r*:

_{t}]*f _{t}* =

*E[r*

_{t}]Liquidity preference theory disagrees with that and argues that forward rates are *higher* than expected short rates:

*f _{t}* >

*E[r*

_{t}]And, the difference reflects a liquidity premium *λ _{t}*

*> 0*:

*f _{t}* =

*E[r*+

_{t}]*λ*

_{t}The reason is that according to the liquidity preference theory, most investors in bond markets have a short investment horizon, and they find long-term bonds, which involve interest rate uncertainty, attractive only if they’re compensated by a sufficient liquidity premium. For this reason, this theory is sometimes referred to as the **term premium hypothesis **as well.

Note that the size of the liquidity premium doesn’t need to be the same for all maturities. We’ll pick up on this idea below.

## Interpreting different shapes of the yield curve

Let’s first discuss a few scenarios where the size of the liquidity premium is the same for all maturities (i.e., it’s a constant):

*λ _{t}* =

*λ*for all

*t*

When this is the case and when expected short rates are constant as well (i.e., *E[r _{t}]* =

*E[r]*, we can obtain the forward rates as:

*f _{t}* =

*E[r*+

_{t}]*λ*

_{t}*f* = *E[r]* + *λ*

This means that with constant liquidity premium and constant expected short rate, the forward rate is the same for all maturities as well. This would result in an *upward-sloping term structure *as shown in Figure 1 below.

What if the liquidity premium remains constant but the short rates are expected to decrease over time? In this scenario, forward rates would decline with maturity as well, and we would get a* hump-shaped yield curve* as illustrated in Figure 2.

Finally, let’s consider a scenario where the expected short rates are decreasing with time to maturity whereas the liquidity premium is no longer constant but increases with time to maturity. In this scenario, we could still observe an *upward-sloping yield curve* if the growth in liquidity premium is sufficiently strong (see Figure 3).

## Video tutorial

##### What is next?

We hope you found this lesson useful. If you’d like to learn more about the liquidity preference theory, the following papers can be useful.

Gehde-Trapp M, Schuster P, Uhrig-Homburg M. “The Term Structure of Bond Liquidity“. *Journal of Financial and Quantitative Analysis*. 2018;53(5):2161-2197.

Modigliani, Franco. “Liquidity Preference and the Theory of Interest and Money.” *Econometrica* 12, no. 1 (1944): 45–88.

In the next lesson, we’ll cover another popular theory of term structure: Segmented market theory.