Chapter 6 interest rates
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CHAPTER 6 Interest Rates. Determinants of interest rates The term structure and yield curves. What four factors affect the level of interest rates?. Production opportunities The demand for money Time preferences for consumption The supply of money Risk

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Chapter 6 interest rates

CHAPTER 6Interest Rates

Determinants of interest rates

The term structure and yield curves


What four factors affect the level of interest rates
What four factors affect the level of interest rates?

  • Production opportunities

    • The demand for money

  • Time preferences for consumption

    • The supply of money

  • Risk

    • The chances of getting a zero or negative return

  • Expected inflation

    • Will your money buy less in the future?


Nominal vs real rates
“Nominal” vs. “Real” rates

r = represents any nominal rate

r* = represents the “real” risk-free rate of interest. Like a T-bill rate, if there was no inflation. Typically ranges from 1% to 4% per year.

rRF = represents the rate of interest on Treasury securities.


Determinants of interest rates
Determinants of interest rates

r = r* + IP + DRP + LP + MRP

r = required return on a debt security

r* = real risk-free rate of interest

IP = inflation premium

DRP = default risk premium

LP = liquidity premium

MRP = maturity risk premium



Yield curve and the term structure of interest rates
Yield curve and the term structure of interest rates

  • Term structure – relationship between interest rates (or yields) and maturities.

  • The yield curve is a graph of the term structure.

  • The November 2005 Treasury yield curve is shown at the right.



Sample problem constructing the yield curve for treasuries
Sample problem: Constructing the yield curve for Treasuries

  • Suppose most investors expect the inflation rate to be 5% next year, 6% the following year, and 8% thereafter.

  • The real risk-free rate is 3%.

  • The maturity risk premium is 0 for bonds that mature in 1 year or less, 0.1% for 2-year bonds, and then MRP increases by 0.1% per year thereafter for 20 years.

  • What is the interest rate for 1-year, 10-year, and 20-year Treasury bonds?

  • Draw a yield curve with this data.

    (Note: this is problem 6-21e on page 192)


Sample problem constructing the yield curve for treasuries continued
Sample problem: Constructing the yield curve for Treasuries (continued)

  • Step 1 – For each of the bonds, we will find the average expected inflation rate over years 1 to N:

Assume inflation is expected to be 5% next year, 6% the following year, and 8% thereafter.

IP1 = 5% / 1 = 5.00%

IP10= [5% + 6% + 8%(8)] / 10 = 7.50%

IP20= [5% + 6% + 8%(18)] / 20 = 7.75%


Sample problem constructing the yield curve for treasuries continued1
Sample problem: Constructing the yield curve for Treasuries (continued)

  • Step 2 – Find the appropriate maturity risk premium (MRP). For this example, the following equation will be used find a security’s appropriate maturity risk premium.

Using the given equation:

MRP1 = 0.1% x (1-1) = 0.0%

MRP10 = 0.1% x (10-1) = 0.9%

MRP20 = 0.1% x (20-1) = 1.9%


Add the ips and mrps to r to find the appropriate nominal rates
Add the IPs and MRPs to r* to find the appropriate nominal rates

r = r* + IP + DRP + LP + MRP, but for Treasury securities, liquidity premium (LP) and default risk premium (DRP) are 0.

Step 3 – Use IP and MRP to calculate the nominal rates.

rRF, t = r* + IPt + MRPt

We are told to assume real risk-free rate r* = 3%:

rRF, 1 = 3% + 5.0% + 0.0% = 8.0%

rRF, 10 = 3% + 7.5% + 0.9% = 11.4%

rRF, 20 = 3% + 7.75% + 1.9% = 12.65%


Use the data to draw the yield curve

Interest rates

Rate (%)

15

Maturity risk premium

10

Inflation premium

5

Real risk-free rate

Years to

Maturity

0

1 10 20

Use the data to draw the yield curve

  • An upward sloping yield curve.

  • Upward slope due to an increase in expected inflation and increasing maturity risk premium.


What is the relationship between the treasury yield curve and the yield curves for corporate issues
What is the relationship between the Treasury yield curve and the yield curves for corporate issues?

  • Corporate yield curves are higher than that of Treasury securities, though not necessarily parallel to the Treasury curve. For corporates:

    • Default risk is > 0

    • Default risk increases for longer maturities

    • Longer maturities are less liquid, so LRP increases

    • Spread over Treasuries widens as maturity increases

  • The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases (i.e., as default risk increases)


Illustrating the relationship between corporate and treasury yield curves

BB-Rated and the yield curves for corporate issues?

AAA-Rated

Illustrating the relationship between corporate and Treasury yield curves

Interest

Rate (%)

15

10

Treasury

Yield Curve

6.0%

5.9%

5

5.2%

Years to

Maturity

0

0

1

5

10

15

20


Pure expectations hypothesis
Pure Expectations Hypothesis and the yield curves for corporate issues?

  • The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.

  • If interest rates are expected to increase, L-T rates will be higher than S-T rates, and vice-versa. Thus, the yield curve can slope up, down, or even bow.


Assumptions of the peh
Assumptions of the PEH and the yield curves for corporate issues?

  • Assumes that the maturity risk premium for Treasury securities is zero.

    • For Treasuries, we used rRF, t = r* + IPt + MRPt ,

    • For PEH, we’ll use rRF, t = r* + IPt

  • Long-term rates are an average of current and future short-term rates.

  • If PEH is correct, you can use the yield curve to “back out” expected future interest rates.


Sample problem 6 21h on page 193
Sample problem 6-21h on page 193 and the yield curves for corporate issues?

MaturityYield

1 year 6.0%

2 years 6.2%

3 years 6.4%

4 years 6.5%

5 years 6.5%

  • If PEH holds, what does the market expect will be the interest rate on one-year securities, one year from now?

  • What does the market expect will be the interest rate on 3-year securities, 2 years from now?


Sample problem 6 21h continued calculate the one year forward rate
Sample problem 6-21h (continued): Calculate the one-year forward rate

6.0%

x%

0 1 2

6.2%

(1.062)2 = (1.060) (1+x)

1.12784/1.060 = (1+x)

6.4004% = x

  • PEH says that one-year securities will yield 6.4004%, one year from now.


Sample problem 6 21h continued calculate the three year forward rate expected 2 years from now
Sample problem 6-21h (continued): Calculate the three-year forward rate expected 2 years from now

6.2%

x%

0 1 2 3 4 5

6.5%

(1.065)5 = (1.062)2 (1+x)3

1.37009/1.12784 = (1+x)3

6.7005% = x

  • PEH says that three-year securities will yield 6.7005%, two years from now.


Conclusions about peh
Conclusions about PEH forward rate expected 2 years from now

  • Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.

    • rRF, t = r* + IPt + MRPt

  • Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.

    • Thus, investors demand a premium to persuade them to hold L-T securities (i.e., MRP > 0).


Other factors that influence overall interest rate levels
Other factors that influence overall interest rate levels forward rate expected 2 years from now

  • Federal reserve policy

  • Federal budget surplus or deficit

  • Level of business activity

  • International factors

    You probably remember these factors from your economics course. These factors are discussed on pages 183-185.


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