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CHAPTER 6 Interest RatesPowerPoint Presentation

CHAPTER 6 Interest Rates

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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

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

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

- 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

- 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)

- 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 (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

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%

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?

- 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)

BB-Rated and the yield curves for corporate issues?

AAA-Rated

Illustrating the relationship between corporate and Treasury yield curvesInterest

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 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 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 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

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

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 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 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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