Homework Chapter 4
Fall 2005
This homework is due on Wednesday October 26, at the beginning of your
class period. Show all work for credit.
1. If U.S. Treasury yields are as follows:
3 month 6.0%
6 month 6.3%
1 year 6.5%
2 year 6.6%
5 year 6.4%
10 year 7.5%
30 year 8.0%
a. What is the expected yield on notes from year 1 to 2, assuming the
PEH holds?
b. What is the expected yield on notes from year 2 to 5, assuming the
PEH holds?
c. If inflation for the next year is expected to be 4.5%, what would the
expected real rate of interest be on the 3-month T-bill?
d. If inflation spikes during this period, and the actual inflation
rate comes in ex- post at 6.3%, what would the actual real rate of
interest be on the 3-month Treasury bill?
e. It the expectations for inflation are as follows:
Years 1 and 2 4.5%
Years 3 to 6 4.0%
Years 7 to 15 3.5%
Years 16 to 30 3.2%
Assume the following for the MRP: Years 1 to 10 .1%
Years 11 to 20 .05%
Years 20 on 0%
What is the real rate of return on the 30 year T-Bond? On the 10 year
bond?
f. Using the information from part e, and assuming a real rate of return
of 3%, what would the nominal rate of return be on a 15-year Treasury
bond ?
g. Plot the yield curve for these Treasury securities..
h. Using the three theories we have discussed, explain how each one
helps explain the shape of this yield curve.
2. If the listed bonds have the following returns, identify the combined
DRP & LP’s.(assume that there is no ISP. ) Use the Treasuries above
as your benchmarks.
AAA 10 year 11%
BBB 30 year 15%
B 5 year 12.5%
If you would like to try additional problems from the text, you may try
4-5 through 4-7, 4-9, and 4-12. I have posted the solution set for
these problems. The text problems will not be collected.
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#53522
What is the expected yield on notes from year 1 to 2, assuming the PEH holds? If inflation for the next year is expected to be 4.5%, what would the expected real rate of interest be on the 3-month T-bill? Plot the yield curve for these Treasury securities. Using the three theories we have discussed, explain how each one helps explain the shape of this yield curve.
1. If U.S. Treasury yields are as follows:
3 month 6.0%
6 month 6.3%
1 year 6.5%
2 year 6.6%
5 year 6.4%
10 year 7.5%
30 year 8.0%
a. What is the expected yield on notes from year 1 to 2, assuming the PEH holds?
b. What is the expected yield on notes from year 2 to 5, assuming the PEH holds?
c. If inflation for the next year is expected to be 4.5%, what would the expected real rate of interest be on the 3-month T-bill?
d. If inflation spikes during this period, and the actual inflation rate comes in ex-post at 6.3%, what would the actual real rate of interest be on the 3-month Treasury bill?
e. It the expectations for inflation are as follows:
Years 1 and 2 4.5%
Years 3 to 6 4.0%
Years 7 to 15 3.5%
Years 16 to 30 3.2%
Assume the following for the MRP: Years 1 to 10 .1%
Years 11 to 20 .05%
Years 20 on 0%
What is the real rate of return on the 30 year T-Bond? On the 10 year bond?
f. Using the information from part e, and assuming a real rate of return of 3%, what would the nominal rate of return be on a 15-year Treasury bond ?
g. Plot the yield curve for these Treasury securities.
h. Using the three theories we have discussed, explain how each one helps explain the shape of this yield curve.
2. If the listed bonds have the following returns, identify the combined DRP & LP's. (assume that there is no ISP. ) Use the Treasuries above as your benchmarks.
AAA 10 year 11%
BBB 30 year 15%
B 5 year 12.5%
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HW Chapter 4.doc
ch04.ppt
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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)] / 10 = 7.75%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRFt = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
Blends
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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)] / 10 = 7.75%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRFt = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
Blends
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes.
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.
If interest rates are expected 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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
CHAPTER 4 The Financial Environment: Markets, Institutions, and Interest Rates
Financial markets
Types of financial institutions
Determinants of interest rates
Yield curves
What is a market?
A market is a venue where goods and services are exchanged.
A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds.
Types of financial markets
Physical assets vs. Financial assets
Money vs. Capital
Primary vs. Secondary
Spot vs. Futures
Public vs. Private
How is capital transferred between savers and borrowers?
Direct transfers
Investment banking house
Financial intermediaries
Types of financial intermediaries
Commercial banks
Savings and loan associations
Mutual savings banks
Credit unions
Pension funds
Life insurance companies
Mutual funds
Physical location stock exchanges vs. Electronic dealer-based markets
Auction market vs. Dealer market (Exchanges vs. OTC)
NYSE vs. Nasdaq
Differences are narrowing
The cost of money
The price, or cost, of debt capital is the interest rate.
The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains.
What four factors affect the cost of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
“Nominal” vs. “Real” rates
k = represents any nominal rate
k* = 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.
kRF = represents the rate of interest on Treasury securities.
Determinants of interest rates
k = k* + IP + DRP + LP + MRP
k = required return on a debt security
k* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
Premiums added to k* for different types of debt
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.
A Treasury yield curve from October 2002 can be viewed at the right.
Constructing the yield curve: Inflation
Step 1 – Find the average expected inflation rate over years 1 to n:
Constructing the yield curve: Inflation
Suppose, that 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%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn k* (before taxes).
Constructing the yield curve: Inflation
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.
Constructing the yield curve: Maturity Risk
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%
Notice that since the equation is linear, the maturity risk premium is increasing in the time to maturity, as it should be.
Add the IPs and MRPs to k* to find the appropriate nominal rates
Step 3 – Adding the premiums to k*.
kRF, t = k* + IPt + MRPt
Assume k* = 3%,
kRF, 1 = 3% + 5.0% + 0.0% = 8.0%
kRF, 10 = 3% + 7.5% + 0.9% = 11.4%
kRF, 20 = 3% + 7.75% + 1.9% = 12.65%
Hypothetical 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.
The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.
Illustrating the relationship between corporate and Treasury yield curves
Pure Expectations Hypothesis
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
Assumes that the maturity risk premium for Treasury securities is zero.
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.
An example: Observed Treasury rates and the PEH
Maturity Yield
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? Three-year securities, two years from now?
One-year forward rate
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
Three-year security, two years from now
6.5% = [2(6.2%) + 3(x%) / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that one-year securities will yield 6.7%, one year from now.
Conclusions about PEH
Some would argue that the MRP ≠ 0, and hence the PEH is incorrect.
Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.
Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).
Other factors that influence interest rate levels
Federal reserve policy
Federal budget surplus or deficit
Level of business activity
International factors
Risks associated with investing overseas
Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates.
Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.
Factors that cause exchange rates to fluctuate
Changes in relative inflation
Changes in country risk
Calculates the yield on treasury securities and plots the yield curve.
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