1. THE STRUCTURE OF INTEREST RATES
CHAPTER 6
THE STRUCTURE OF
INTEREST RATES

2. Factors that Influence Interest Rate Differences
Term to Maturity
Default Risk
Tax Treatment
Marketability
Options on Debt Securities: Call, Put or Convertibility option
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Term Structure
Relationship between yield and term to maturity on securities that differ only in length of time to maturity
A yield curve is a graphical representation of the term structure; it shows the relationship between maturity and a security's yield at a point in time.
The yield curve may be ascending (normal), flat, or descending (inverted).
Several theories explain the shape of the yield curve.
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4. Yield Curves in the 2000s - Exhibit 6.1
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5. The Expectations Theory
The shape of the yield curve is determined solely by expectations of future interest rate movements, and changes in these expectations lead to changes in the shape of the yield curve .
Ascending: future interest rates are expected to increase.
Descending: future interest rates are expected to decrease.
Flat :interest rates are expected to be stable in the future.
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6. The Expectations Theory
Assumptions of the Theory:
1. Investors are profit maximizers.
2. Investors are risk neutral (indifferent between holding a long term security and holding a series of short -term securities).
3. Markets are assumed to be very efficient with excellent information and minimal trading costs.
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7. The Expectations Theory
Long-term interest rates are geometric averages of current and expected future (implied, forward) interest rates.
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8. tR3 = [(1 + 3%)(1+ 4%) (1+ 5%)]1/3 - 1 = 3.997%
Example
Example 1: Given the following information:
Current one – year rate = 3%,
Expected 1 – year rate, a year from now = 4%
Expected 1 – year rate, 2 years from now = 5%
What is the yield on a 3 – year security?
1 + tR3 = [(1 + 3%)(1+ 4%) (1+ 5%)]1/3
tR3 = [(1 + 3%)(1+ 4%) (1+ 5%)]1/ = 3.997%
The investor is indifferent between a 3- year security, and the average yield of three 1 – year securities.
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Example
Example 2:
A commercial bank made a 3 – year term loan at 10 %. The bank’s economics department forecasts that 1 and 2 years in the future, the 1 –year interest rate will be 10% and 14%, respectively. The current 1 – year rate is 8%. Given that the bank’s forecasts are reliable, has the bank set the 3 – year rate correctly?
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10. An Implied One Year Forward Rate
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11. Finding a One-Year Implied Forward Rate
Example 1:
Using the following term structure of interest rates, find the one-year implied forward rate two years from now.
1-year Treasury note 1.95%
2-year Treasury note 2.39%
3-year Treasury note 2.71%
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Example
Example 2:
Calculate the one – year forward rate three years from now if three and four years spot rates are 5.5% and 5.8% respectively?
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13. Liquidity Premium Theory
Long-term securities have greater risk and investors require greater premiums to give up liquidity.
Long-term security prices are more sensitive to interest rates (have more price risk).
Long-term securities have less marketability.
The liquidity premium explains why the yield curve slopes upward most of the time.
Liquidity premiums change over time.
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14. Market Segmentation Theory
Investors are assumed to be risk averse.
Maturity preferences by investors may affect security prices (yields), explaining variations in yields by time.
The shape of the yield curve is determined by the supply and demand of securities at each maturity.
Market participants have strong preferences for securities of particular maturity and buy and sell securities consistent with their maturity preferences.
If market participants do not trade outside their maturity preferences, then discontinuities and spikes are possible in the yield curve.
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15. Preferred Habitat Theory
The Preferred Habitat Theory (PH) is an extension of the Market Segmentation Theory.
PH allows market participants to trade outside of their preferred maturity if adequately compensated for the additional risk.
PH allows for humps or twists in the yield curve, but limits the discontinuities possible under Segmentation Theory. PH is consistent with a smooth yield curve.
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Which Theory is Right?
It is difficult to conclude that one theory is totally able to explain the shape of the yield.
Day-to-day changes in the term structure are most consistent with the Preferred Habitat Theory.
However, in the long-run, expectations of future interest rates and liquidity premiums are important components of the position and shape of the yield curve.
Markets participants tend to favor the preferred Habitat Theory, whereas economists tend to favor the expectation and liquidity premium theories.
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17. Yield Curves and the Business Cycle
Interest rates are directly related to the level of economic activity.
An ascending yield curve notes the market expectations of economic expansion and/or inflation.
A descending yield curve forecasts lower rates possibly related to slower economic growth or lower inflation rates.
Security markets respond to updated new information and expectations and reflect their reactions in security prices and yields.
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18. Yield-Curve Patterns Over the Business Cycle
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Uses of the Yield Curve
The slope of the yield curve can be used to assess the market’s expectations about future interest rates!
Issuers may use the yield curve to price their securities.
Investors can use the yield curve to identify under-priced securities for their portfolios and this strategy known as riding the yield curve.
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Uses of the Yield Curve
Riding the yield curve:
If the yield is expected to increase in the future, investors will prefer to buy short term bonds, while issuers will prefer to issue long term bonds.
If the yield is expected to decrease in the future, investors will prefer to buy long term bonds, while issuers will prefer to issue short term bonds.
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Default Risk
It is the probability of the borrower not honoring the security contract
Losses may range from “interest a few days late” to a complete loss of principal.
Risk averse investors want adequate compensation for expected default losses.
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Default Risk, cont.
Investors charge a default risk premium (above riskless or less risky securities) for added risk assumed
DRP = i - irf
The default risk premium (DRP) is the difference between the promised or nominal rate and the yield on a comparable (same term) riskless security (Treasury security).
Investors are satisfied if the default risk premium is equal to the expected default loss.
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23. Risk Premiums (December 2006)
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Default Risk, cont.
Default risk premiums increase (widen) in periods of recession and decrease in economic expansion.
In good times, risky security prices are bid up, which means that investors tend to buy bonds with high default risk because they seek the highest yielding investments and during expansion, there is little chance of default.
During economic recession, investors sell risky securities and buy “quality”, thus widening the DRP.
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Default Risk, cont.
Credit rating agencies such as Moody’s measure and grade relative default risk security issuers. The higher the credit rating, the lower the default risk.
Cash flow, level of debt, profitability, and variability of earnings are all indicators of default riskiness.
As conditions change, rating agencies revise credit ratings of debtors.
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Default Risk, cont.
Bonds are called investment - grade bonds if their Moody's and Standard & Poor's rating is Baa (BBB) and above.
Bonds are called speculative - grade bonds or junk bonds if their Moody's and Standard & Poor's rating is Below Baa (BBB).
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27. Corporate Bond-Rating Systems, Exhibit 6.7
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Tax Effects on Yields
The taxation of security gains and income affects the yield differences among securities
The interest rate most relevant to investors is the rate of return earned after taxes.
The after-tax return, iat, is found by multiplying the pre-tax return by one minus the investor’s marginal tax rate: iat = ibt(1-t)
Municipal bonds’ interest income is tax exempt.
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29. To Buy a Municipal or a Corporate Bond?
Example: Assume that the current yield on a Municipal bond is 7% (no tax treatment) and the current yield on a taxable Corporate bond is 10% (before tax), which bond should you purchase if your tax is 20%?
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30. To Buy a Municipal or a Corporate Bond?
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31. Impact of Marketability on Interest Yields
Marketability – The costs and speed with which investors can resell a security.
Cost of trade.
Physical transfer cost.
Search costs.
Information costs.
Securities with good marketability have higher prices and lower yields.
Treasury bills are the most marketable securities.
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32. Contract Options and Yields
Various option provisions may explain yield differences between securities
An option is a contract provision which gives the holder or the issuer the right, but not the obligation, to buy, sell, redeem, or convert an asset at some specified price within a defined future time period.
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33. Contract Options and Yields
A call option permits the issuer (borrower) to call (redeem) the bond before maturity at a prespecified price.
Callable bonds are sold at a higher market yield than non-callable bonds because they are to the benefit of the issuer. Hence, bondholder demand a call interest premium (CIP).
CIP = ic – inc
Borrowers call bonds if interest rates decline.
Investors in callable securities bear the risk of losing their high-yielding security.
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34. Contract Options and Yields
A put option permits the investor (lender) to sell the bond back to the issuer at a prespecified price before maturity.
The yield on a putable bond, ip, will be lower than the yield on the nonputable bond, inp, because they are advantage to the bondholder.
The difference in interest rates between putable and nonputable contracts is called the put interest discount (PID).
PID = ip - inp
Investors are likely to put their bonds during periods of increasing interest rates
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35. Contract Options and Yields
A conversion option permits the investor to convert a bond into another security (usually common stock).
Convertible bonds generally have lower yields, icon, than nonconvertibles, inconbecause it is an advantage to the bondholder.
The conversion yield discount (CYD) is the difference between the yields on convertibles relative to nonconvertibles.
CYD = icon - incon.
Bondholders tend to use the conversion option when the stock market prices are rising and bond prices are declining.
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