1. Chapter 6 The Risk Structure and Term Structure of Interest Rates
Chapter Seven
Chapter 6
The Risk Structure and Term Structure
of Interest Rates

2. Bonds Are Risky!!!
Bonds are a promise to pay a certain amount in the future. How can that be risky?
Default risk - the chance the bond’s issuer may not make payment.
Inflation risk - investor cannot be aware of the real of the payments made.
Interest rate risk - a rise in interest rates before bond is sold could mean a capital loss.

3. Default Case Study: What Happened Here?
Investors’ concerns about risk affect their demand for U.S. Treasuries.
1998, Russia defaulted and people lost confidence in emerging market countries.
Safest assets are U.S. Treasuries.
Demand increased, price increased, and yields declined.

4. Default Risk
Risk arises because an investment has many possible payoffs during the holding horizon.
We need to look at the risk the bondholder faces - what are the possible payoffs, and how likely each is to occur.
We will compare the risk of a bond’s return relative to the default risk-free rate – a US government bond.

5. Default Risk Corporate bond example:
Assume the one-year risk-free interest rate is 5 percent.
If the company is perceived as default risk-free, the company can issue a 5 percent coupon bond with a face value of $100.

6. Default Risk
If this bond was considered default risk-free, the price of the bond would be the present value of the $105 payment.
Price of risk free bond = ($100 + $5)/$1.05 = $100
Suppose, there is now a 5% probability that the company will go bankrupt before paying back the loan.
the outcome is either $105 or $0.

7. Default Risk
Suppose 5% probability firm goes bankrupt – you get nothing
Expected Value of bond payment
Possibilities
Payoff
Probability
Payoff x Probability
Full Payment
$105
.95
$99.75
Default $0
.05

8. Default Risk If the price of the bond is $95, what is the YTM?
Default risk premium is the YTM minus the risk-free rate:
Risk Premium = 10.53% - 5%
= 5.53 percent.
The higher the default risk, the higher the yield and risk premium.

9. Default Risk
Suppose 10% probability firm goes bankrupt – you get nothing
Expected Value of bond payment
Possibilities
Payoff
Probability
Payoff x Probability
Full Payment
$105
.90
$94.50
Default $0
.10
Expect to receive $94.50 one-year from now.
Discount at risk-free rate =
P = $90; YTM = $105/$90 – 1 = 16.67%
Risk premium = – 5 = 11.67%

10. Default Risk Premium
We can calculate the probability of repayment from the interest rates. Call it p.
Let 1+k be the return on a one-year corporate debt and 1+ i be the return on a one-year default risk-free treasury.
At equilibrium: 1+i = p(1+k)
The probability of repayment is
the probability of default is 1 – p
The probability of repayment:

11. Yields on 9/20/16 3mo 6mo 9mo 1yr 2yr 3yr 5yr 10yr 20yr 30yr+
BONDS
U.S. Treasury
0.29%
0.51%
0.60%
0.68%
0.82%
0.94%
1.23%
1.67%
2.01%
2.40%
U.S. Treasury Zeros --
0.56%
0.73%
0.89%
1.25%
1.82%
2.32%
Agency/GSE
0.71%
0.81%
0.96%
1.01%
1.13%
1.42%
1.62%
2.42%
3.13%
3.20%
Corporate (Aaa/AAA)
0.39%
1.05%
1.40%
1.59%
2.45%
3.35%
3.91%
Corporate (Aa/AA)
0.74%
1.15%
1.08%
1.22%
1.44%
1.96%
2.75%
3.60%
4.49%
Corporate (A/A)
0.93%
1.32%
1.84%
1.89%
2.65%
3.44%
4.25%
4.32%
Corporate (Baa/BBB)
1.21%
1.65%
2.15%
2.54%
4.48%
4.88%
5.13%
6.08%
6.42%
Municipal (Aaa/AAA)
0.77%
0.75%
0.97%
1.12%
1.43%
2.85%
2.93%
Municipal (Aa/AA)
0.86%
0.85%
0.88%
1.63%
1.61%
2.59%
3.07%
3.28%
Municipal (A/A)
0.80%
1.00%
0.99%
1.20%
1.68%
2.52%
3.45%
3.50%
Taxable Municipal*
1.11%
1.10%
1.72%
2.05%
2.09%
4.30%
3.94%
3.36%

12. Yields on 9/25/18 3mo 6mo 9mo 1yr 2yr 3yr 5yr 10yr 20yr 30yr+
BONDS
U.S. Treasury
2.25%
2.37%
2.53%
2.64%
2.84%
2.91%
2.98%
3.09%
3.15%
3.22%
U.S. Treasury Zeros --
2.52%
2.83%
2.90%
3.00%
3.17%
3.25%
3.21%
Agency/GSE
2.32%
2.43%
2.61%
2.76%
3.03%
3.19%
3.45%
3.88%
4.26%
3.85%
Corporate (Aaa/AAA)
1.99%
2.50%
2.72%
2.74%
3.02%
3.40%
3.92%
4.38%
Corporate (Aa/AA)
2.56%
2.71%
2.88%
3.12%
3.47%
3.57%
3.98%
4.21%
4.84%
Corporate (A/A)
2.99%
3.49%
3.83%
4.02%
4.56%
5.06%
5.32%
Corporate (Baa/BBB)
2.81%
3.36%
3.66%
6.04%
6.86%
6.92%
Municipal (Aaa/AAA)
1.87%
1.88%
2.00%
2.02%
2.10%
2.22%
2.45%
3.86%
3.71%
Municipal (Aa/AA)
1.95%
2.03%
2.36%
2.21%
2.35%
2.97%
4.07%
4.40%
Municipal (A/A)
2.01%
2.20%
2.18%
2.79%
3.61%
4.15%
Taxable Municipal*
2.24%
3.35%
2.85%
3.13%
3.78%
4.35%
4.13%
4.98%

13. Risk Structure of Interest Rates
Hold time to maturity constant and compare yields.
Default risk - occurs when the issuer of the bond is unable or unwilling to make interest payments or pay off the face value
U.S. T-bonds are considered default free
Risk premium—the spread between the interest rates on bonds with default risk and the interest rates on T-bonds
Liquidity - the ease with which an asset can be converted into cash
Income tax - taxable or non taxable

15. Ratings and the Risk Structure of Interest Rates
Default is an important risks a bond buyer faces.
Independent companies (rating agencies) evaluate the creditworthiness of potential borrowers.
These companies estimate the likelihood that the corporate or government borrower will make a bond’s promised payments.

16. Bond Ratings The best known bond rating services are
Moody’s
Standard & Poor’s
A high rating suggests that a bond issuer will have little problem meeting a bond’s payment obligations.

17. Bond Ratings The highest-rated bonds, Triple A.
Ex: ExxonMobil, Microsoft, and the government of Canada (also JNJ)
The top four rating categories are considered investment-grade bonds.
These bonds have a very low risk of default.
Reserved for most government issuers and corporations that are among the most financially sound.

19. Credit rating & historic default frequencies
Moody’s
Rating
1985
1990
1995
2000
2006
2008
2009
2010
Aaa 0% Aa A
1.201%
0.36%
Baa1
0.29%
0.271%
1.144%
Baa2
0.794%
0.74%
Baa3
0.98%
0.321%
0.70%
Ba1
2.67%
0.91%
2.27%
Ba2
1.63%
2.82%
0.66%
0.51%
0.60%
Ba3
3.77%
3.92%
1.72%
0.99%
2.715%
4.01% B1
4.38%
8.59%
4.35%
3.63%
1.783%
4.10%
0.85% B2
7.41%
22.09%
6.36%
3.84%
0.50%
0.825%
8.68% B3
13.86%
28.93%
11.72%
1.93%
3.198%
8.52%
0.56%

20. Bond Ratings
The distinction between investment-grade and speculative, noninvestment-grade (less than BBB or Baa) is important.
Some regulated institutional investors are not allowed to invest in bonds rated below investment grade, which is Baa on Moody’s scale or BBB on Standard and Poor’s scale.

21. Bond Ratings
Speculative grade bonds are bonds issued by companies and countries that may have difficulty meeting their bond payments but are not at risk of immediate default.
Bonds with grades below investment grade are often referred to as junk bonds or high-yield bonds.

22. The Impact of Ratings on Yields
Bond ratings are designed to reflect default risk.
The higher the risk of default.
The lower the rating
The lower the bond price and the higher its yield.
To understand quantitative ratings, it is easier to compare them to a benchmark.

23. The Impact of Ratings on Yields
U.S. Treasury issues are viewed as having little default risk, so they are used as benchmark bonds.
Yields on other bonds are measured in terms of the spread over Treasuries.
Bond yield is the sum of two parts:
= U.S. Treasury yield + Default risk premium

24. Supply/Demand Application: Response to an Increase in Default Risk on Corporate Bonds –24

25. The Impact of Ratings on Yields
If bond ratings properly reflect risk, then the lower the rating of the issuer, the higher the default-risk premium.
When Treasury yields move, all other yields move with them.
We can see this from a plot of the risk structure of interest rates.

26. Differences in Tax Status and Municipal Bonds
Taxes affect the yield on a bond.
Bondholders must pay income tax on the interest income they receive from owning privately issued bonds - taxable bonds.
The coupon payments on bonds issued by state and local governments, municipal or tax-exempt bonds, are specifically exempt from taxation.

27. Differences in Tax Status and Municipal Bonds
What are the tax implications for bond yields?
Consider a one-year $100 face value taxable bond with a coupon rate of 6 percent.
Par is $100, and yield to maturity is 6 percent.
Government sees this 6 percent as taxable income.
If tax rate is 30%, the tax is $1.80.
Bond yields $ after taxes, equivalent of 4.2 percent. This is the after-tax yield.

28. Taxes and Bond Prices 4.20% = 6% x (1 – 0.30)
Coupon payments on municipal bonds are exempt from federal Income taxes
For 30% tax bracket:
After tax yield = (taxable yield) x (1 – tax rate)
4.20% = % x (1 – 0.30)
Tax equivalent yield =

29. Interest Rates on Municipal and Treasury Bonds29