Investments, tenth edition

Figure 15.4 

Yield curves.  Panel A,  Constant expected short rate. Liquidity 

premium of 1%. Result is a rising yield curve.  Panel B,  Declining expected short 

rates. Increasing liquidity premiums. Result is a rising yield curve despite falling 

expected interest rates. (continued on next page)

4.0

0

1

2

3

4

5

Maturity

6

7

8

9

10

4.5

5.0

5.5

Interest Rate (%)

6.0

6.5

7.0

YTM

E(r)

Forward Rate

Constant Liquidity

Premium

A

4.0

0

1

2

3

4

5

Maturity

6

7

8

9

10

4.5

5.0

5.5

Interest Rate (%)

6.0

6.5

7.0

YTM

E(r)

Forward Rate

Liquidity Premium

Increases with

Maturity

B

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bod61671_ch15_487-514.indd   499

7/17/13   4:03 PM

7/17/13   4:03 PM

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500

P A R T   I V

 Fixed-Income 

Securities

 implying that 1  1   y  

3

   5  1.0567. The plot of the yield curve in this situation would be given 

as in  Figure 15.4 , panel A. Such an upward-sloping yield curve is commonly observed in 

practice.   

 If interest rates are expected to change over time, then the liquidity premium may be 

overlaid on the path of expected spot rates to determine the forward interest rate. Then 

the yield to maturity for each date will be an average of the single-period forward rates. 

Several such possibilities for increasing and declining interest rates appear in  Figure 15.4 , 

panels B to D.