1. THE STRUCTURE OF INTEREST RATES
CHAPTER 6
THE STRUCTURE OF
INTEREST RATES
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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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3. 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 Expectation 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.
Long-term interest rates are geometric averages of current and expected future (implied, forward) interest rates.
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6. Term Structure Formula
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7. An Implied One Year Forward Rate
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8. Finding a One-Year Implied Forward Rate
Using the following term structure of interest rates, find the one-year implied forward rate for year three.
1-year Treasury note 1.95%
2-year Treasury note 2.39%
3-year Treasury note 2.71%
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9. 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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10. Market Segmentation Theory
Maturity preferences by investors may affect security prices (yields), explaining variations in yields by time.
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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11. 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 Market Segmentation Theory. PH is consistent with a smooth yield curve.
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12. Which Theory is Right?
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.
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13. 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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14. Yield-Curve Patterns Over the Business Cycle
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15. Issuers may use the yield curve to price their securities.
Uses of the Yield Curve
The slope of the yield curve can be used to assess the market’s expectations about future interest rates!
Investors can use the yield curve to identify under-priced securities for their portfolios.
Issuers may use the yield curve to price their securities.
Investors use the yield curve for a strategy known as riding the yield curve.
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16. 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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17. 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; yields move closer to those of riskless securities.
With increased economic pessimism, investors sell risky securities and buy “quality”, thus widening the DRP.
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18. 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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19. Risk Premiums (December 2011)
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20. Default Risk and the Business Cycle
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21. Bond Ratings
Credit rating agencies such as Moody’s measure and grade relative default risk security issuers.
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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22. Corporate Bond Rating Systems, Exhibit 6.7
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23. Tax Effects on Yields
The taxation of security gains and income affects the yield differences among securities.
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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24. To Buy a Municipal or a Corporate Bond?
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25. 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.
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26. 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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27. Contract Options and Yields
A call option permits the issuer (borrower) to call (redeem) the bond before maturity at a pre-specified price.
Borrowers call bonds if interest rates decline.
Investors in callable securities bear the risk of losing their high-yielding security.
Investors demand a call interest premium (CIP).
CIP = ic - inc
A callable bond, ic, will be priced to yield a higher return (by the CIP) than a non-callable, inc, bond.
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28. Contract Options and Yields
A put option permits the investor (lender) to sell the bond back to the issuer at a pre-specified price before maturity.
Investors are likely to put their bonds during periods of increasing interest rates. The difference in interest rates between putable and non-putable contracts is called the put interest discount (PID).
PID = ip - inp
The yield on a putable bond, ip, will be lower than the yield on the non-putable bond, inp, by the PIP.
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29. 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 non-convertibles, incon.
The conversion yield discount (CYD) is the difference between the yields on convertibles relative to non-convertibles.
CYD = icon - incon. Investors accept lower yields on convertibles because they have an opportunity for increased rates of return through conversion.
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30. Behavior of Interest Rates over the Business Cycle
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31. Conclusions
The real rate of interest has historically averaged about 3%.
The real rate of interest rises during expansionary periods and falls during contractionary periods.
The nominal interest rates tend to rise and fall with changes in the actual rate of inflation.
The nominal interest rates tend to rise during expansionary periods and decline during contractionary periods.
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