chapter 6 the structure of interest rates. factors that influence interest rate differences term to...

CHAPTER 6

THE STRUCTURE OFINTEREST RATES

Factors that Influence Interest Rate Differences

• Term to Maturity• Default Risk• Tax Treatment• Marketability• Options on Debt Securities: Call, Put or

Convertibility option

Copyright© 2008 John Wiley & Sons, Inc. 2

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.


Yield Curves in the 2000s - Exhibit 6.1


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.


The Expectations TheoryAssumptions 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.


The Expectations Theory• Long-term interest rates are geometric averages of

current and expected future (implied, forward) interest rates.


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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 - 1 = 3.997%

The investor is indifferent between a 3- year security, and the average yield of three 1 – year securities.

Copyright© 2006 John Wiley &

Sons, Inc. 8

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?


An Implied One Year Forward Rate


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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%

3

2 1 2

1 .02711 0.0335 or 3.35%

1 .0239f


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?


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.


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.


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.


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.


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.


Yield-Curve Patterns Over the Business Cycle


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.


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.

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.


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.


Risk Premiums (December 2006)


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.


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.


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).


Corporate Bond-Rating Systems, Exhibit 6.7


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.


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%?


To Buy a Municipal or a Corporate Bond?


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.


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.


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.


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


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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