InvestorQ : What does the liquidity premium tell us about the term structure of rates?

# What does the liquidity premium tell us about the term structure of rates?

3 years ago
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According to the Liquidity Premium Theory, a long-term rate of interest is an average of short-term rates plus a liquidity premium. In other words, investors expect to be compensated for holding long-term bonds instead of short-term bonds as long-term bonds are perceived to be riskier. This causes the yield curve to be steeper than it would be under the Expectations Theory. This is again a function of the state of the economy and is actually an improvement that is built on the Expectations Theory.

As an example, suppose that the one-year rates over the next five years are expected to be 5%, 6%, 7%, 8% and 9%, respectively. The liquidity premium for holding bonds of these maturities equals 0% for a one-year bond, 0.25% for a two-year bond, 0.5% for a three-year bond, 0.75% for a four-year bond and 1.00% for a five-year bond. What are the implied two-year and five-year rates under the:

§ Expectations Theory

Under the Expectations Theory, the implied two-year rate is computed as:

(1 + X)2 = (1 + 0.05)(1 + 0.06)

(1 + X)2 = 1.113

1 + X = 1.1131/2

X = 1.1131/2 – 1

X = 0.055 = 5.5%

Under the Liquidity Premium Theory, the implied two-year rate is computed as:

(1 + X)2 = (1 + 0.05 + 0)(1 + 0.06 + 0.0025)

(1 + X)2 = (1.05)(1.0625)

(1 + X)2 = (1.115625)

1 + X = 1.1156251/2

X = 1.1156251/2 – 1

X = 0.05623 = 5.623%

Under the Expectations Theory, the implied five-year rate is computed as:

(1 + X)5 = (1 + 0.05)(1+ 0.06)(1 + 0.07)(1 + 0.08)(1 + 0.09)

(1 + X)5 = 1.401939252

1 + X = 1.4019392521/5

X = 1.4019392521/5 – 1

X = 0.0699 = 6.99%

Under the Liquidity Premium Theory, the implied five-year rate is computed as:

(1 + X)5 = (1 + 0.05)(1+ 0.0625)(1 + 0.0750)(1 + 0.0875)(1 + 0.10)

(1 + X)5 = 1.43465889

1 + X = 1.434658891/5

X = 1.434658891/5 – 1

X = 0.0749 = 7.49%

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