Chapter 6 The Risk and Term Structure of Interest Rates Terezia Chen Jody Giesbrecht.

Chapter 6The Risk and Term

Structure of Interest Rates

Terezia Chen

Jody Giesbrecht

Overview

Web Exercises Risk Structure of Interest Rates

Default risk Liquidity Tax Considerations

Term Structure of Interest Rates Yield Curves Expectations Theory, Segmented Markets Theory,

Liquidity Premium Theory, Preferred Habitat Theory

Web Exercises

1. What has the average rate of inflation been since 1995? What year had the highest and lowest levels of inflation?

Average rate of inflation: 2.04% Highest rate: 4.70% in Feb 2003 Lowest rate: 0.60% in Jan 1995

From www.bankofcanada.ca/en/cpi/htm

Web Exercises

2. What is the cost today of a car that cost $10,000 the year that you were born?

1914 - $189,830.51 – avg inflation rate of 3.22% 1950 - $90,322.58 – avg inflation rate of 3.94% 1975 - $38,356.16 – avg inflation rate of 4.29%

From www.bankofcanada.ca/en/inflation_calc.htm

Web Exercises

3. What happens to the difference between the adjusted value of an investment compared to its inflation-adjusted value as: Inflation increases (3 to 5%)?

Buying Power: 3% - $8626.09 5% - $7835.26 The investment horizon lengthens (5 to 10 years)?

Buying Power: 5yrs - $8626.09 10 yrs - $7440.94 Expected returns increase (5 to 8%)?

Buying Power: 5% - $12120.51 8% - $16064.43

From www.moneychimp.com/articles/econ/inflation_calculator.htm

Risk vs. Term

Relationships among interest rates can be defined by two aspects: Risk structure of interest rates – relationship

among the different interest rates on bonds with the same term to maturity

Term structure of interest rates – relationship among interest rates on bonds with different terms to maturity but with same default risk

Risk Structure of Interest Rates

Default Risk Occurs when issuer of a bond is unable or

unwilling to make interest payments or repay principle when bond reaches maturity

Default-free bonds – no default risk – Canadian Government Bonds

Risk Premium – spread between the interest rate on a risky bond and a default-free bond

Supply & Demand Analysis

Default Risk Information

Credit-Rating Agencies – investment advisory firms that rate quality of bonds in terms of probability of default Agencies used in Canada: Standards & Poors,

Moody’s Investors Service, Fitch Ratings Junk Bonds Fallen Angels

“The Junk Bond King”

Michael Milken Executive at Drexel Burnham Lambert Inc during

1980’s used high-yield junk bonds for corporate financing

and mergers and acquisitions

Bond Defaults in Canada

CBC article published Sept. 2003 Rate of default lower in Canada than US

Canada: 1.9% US: 2.4% Recovery rates for Canadian bonds lower

than in the US Canada: 30% of par US: 42% of par

From http://www.cbc.ca/money/story/2003/09/10/moodys_030910.html

Can Lack of Bond Defaults Last Forever? Article from the Financial Post by David Berman – June 2007

Default rate hit zero in 2006 More bond upgrades than downgrades What does this signal for the future?

Possible increase in speculative grade bonds Higher borrowing costs Decrease in corporate profit growth

From http://www.canada.com/nationalpost/financialpost/story.html?id=045d7cbd-3cc2-4591-abdf-8056956ef88b

Risk Structure of Interest Rates

Liquidity Ease with which a bond can be traded or sold Canada bonds considered most liquid If corporate bonds are traded less widely, liquidity and demand

will decrease. This will cause the price of the bond to fall and, conversely, the interest rate to rise

As the price falls from P1 to P2, the interest rate will move upwards

Risk Structure of Interest Rates

Income Tax Considerations In some countries, certain government bonds are

not taxable (ex: US municipal bonds) This might allow for a greater returns than a

taxable corporate bond with a higher stated return

 Tax-exempt equivalent yields

Marginal

Tax Rate

 4% Tax-Exempt

Yield 

 5%Tax-Exempt

Yield 

 6%Tax-Exempt

Yield 

 6.5%Tax-Exempt

Yield 

 7%Tax-Exempt

Yield 

 7.5%Tax-Exempt

Yield 

10 % 4.44 5.56 6.67 7.78 8.33 4.44

15 % 4.71 5.88 7.06 8.24 8.82 4.71

27 % 5.48 6.85 8.22 9.59 10.27 5.48

30 % 5.71 7.14 8.57 10.00 10.71 5.71

35 % 6.15 7.69 9.23 10.77 11.54 6.15

38.6 % 6.51 8.14 9.77 11.40 12.21 6.51

http://moneycentral.msn.com/content/Investing/Simplestrategies/P38652.asp

Term Structure of Interest Rates

Yield Curve – depiction of yields on bonds when risk, liquidity and tax considerations are equal but the terms to maturity differ

Term Structure Theories

Expectations Theory Segmented Markets Theory Liquidity Premium Theory Preferred Habitat Theory

Purpose of Theories

To explain why yield curves take on their specific shapes

To explain 3 empirical facts: Interest rates on bonds of different maturities

move together over time When ST rates are low, yield curves are likely to

be upward sloping; when ST rates are high, yield curves are likely to be inverted

Yield curves almost always slope upward

Expectations Theory

The interest rate on a long-term bond will equal an average of short-term interest rates that are expected to occur over the life of the long-term bond Assumption: bondholders do not prefer one

maturity over another but will hold bonds with highest expected returns (perfect substitutes)

Int=(it + it+1 + … + it+(n-1))/n

Segmented Markets Theory

Markets for different maturity bonds are completely separate and therefore the interest rate of each bond with a different maturity is determined by supply and demand for that bond Assumption: bonds of different maturities are not

substitutes, so expected return of one bond has no effect on demand for a bond with a different maturity

Liquidity Premium Theory

The interest rate on a long-term bond will equal an average of short-term rates expected to occur over the life of the bond, plus a liquidity premium Assumption: bonds of different maturities are

substitutes but not perfect substitutes (investors may prefer on maturity over another)

Preferred Habitat Theory

Investors will buy bonds that do not have their preferred maturity only if they earn a higher return. Assumption: investors have a preference for

bonds of one maturity over another in which they prefer to invest

Relationships Between Theories

Using the Yield Curve

Often unreliable as liquidity premiums may not be accurate

Slope of yield curve does not always help to predict future short-term interest rates

Useful for very short-term and long-term but lacks reliability for intermediate term

Impact of Inverted Yield Curves Article by Jim McWhinney - Feb 16, 2006

Occurs when short term rates exceed long term rates

Historical indicator of recession Consideration of supply and demand Impact on investors and consumers

Oil Prices & their Impact

Overall Global Economy Inflation Interest Rates

Summary

Looked at two influences on the interest rate of a bond: Risk Term to Maturity

Rational Investors will select portfolios to meet desired returns based on differing amounts of risk and varying terms to maturity

Questions?