01 fm&i chap 3

■ describe how characteristics of debt securities cause their yields to vary ■ demonstrate how to estimate the appropriate yield for any particular debt security ■ explain the theories b

Chapter 3: Structure of

Interest Rates

■ describe how characteristics of debt

securities cause their yields to vary

■ demonstrate how to estimate the

appropriate yield for any particular debt

security

■ explain the theories behind the term

structure of interest rates (relationship

between the term to maturity and the yield

of securities)

Why Debt Security Yields Vary

The yields on debt securities are affected:

Credit (default) risk

Factors Affecting Security Yields

⚫Risk-averse investors demand higher

yields for added riskiness

⚫Risk is associated with variability of

returns

⚫Increased riskiness generates lower

security prices or higher investor required rates of return

Default Risk

1 Credit (Default) Risk

⚫ Credit risk: Risk that borrower may not made payments

Default Risk

⚫ Rating Agencies - Rating agencies charge the issuers of debt securities a fee for assessing

default risk (Conflict of interest)

⚫ Accuracy of Credit Ratings - The ratings issued

by the agencies are useful indicators of default

risk but they are opinions, not guarantees.

⚫ Oversight of Credit Rating Agencies - The

Financial Reform Act of 2010 established an

Office of Credit Ratings within the Securities and Exchange Commission in order to regulate credit rating agencies Rating agencies must establish internal controls

Rating Classification by Rating Agencies

Liquidity Risk

⚫The Liquidity of a security affects the

yield/price of the security

⚫A liquid investment is easily converted to cash at minimum transactions cost

⚫Investors pay more (lower yield) for liquid investment

⚫Liquidity is associated with short-term, low default risk, marketable securities

T = investor’s marginal tax rate

⚫Break-even tax rate

Te = 1 – Ytax-free/Ytax-bearing

Tax Status

⚫Example: a taxable security that offers a

before-tax yield of 14 percent The

investor’s tax rate is 20 percent Calculate the after-tax yield

Y at = 14%(1 – 0.2)

= 11.2%

⚫The fully taxable pre-tax equivalent

corporate bond for a 11.2% municipal

bond is:

Y bt = 11.2%/(1 – 0.2) = 14%

Special Provisions

⚫Call Feature: enables borrower to buy

back the bonds before maturity at a

specified price

 Call features are exercised when interest rates have declined

 Investors demand higher yield on callable

bonds, especially when rates are expected to fall in the future

 Investors will accept a lower yield for

convertible bonds because investor returns

include expected return on equity participation

Estimating the Appropriate Yield

⚫The appropriate yield to be offered on a

debt security is based on the risk-free rate for the corresponding maturity plus

adjustments to capture various security

characteristics

Estimating the Appropriate Yield

Y n = R f,n + DP + LP + TA + CALLP + COND

Where:

Y n = yield of an n-day security

R f,n = yield on an n-day Treasury

(risk-free) security

DP = default premium (credit risk)

LP = liquidity premium

TA = adjustment for tax status

CALLP = call feature premium

COND = convertibility discount

Yield Differentials on Money Market

Securities

⚫The yield differential is the difference between the yield offered on a security and the yield on the risk-free rate

⚫Treasury bills have the lowest yield because

of their low default risk and high liquidity

⚫Yields on commercial paper and negotiable

CDs are only slightly higher than T-bill rates to compensate for lower liquidity and higher

default risk

⚫Market forces cause the yields on all

securities to move in the same direction

Yield Differentials on Capital Market Securities

⚫Municipal bonds have the lowest tax yield because they are free of tax at federal level but their after-tax yields are typically higher than Treasury bonds

before-⚫Treasury bonds have the lowest yield

because of their low default risk and high liquidity

Term to maturity

⚫Interest rates typically vary by maturity

⚫The term structure of interest rates

defines the relationship between maturity and yield

 The Yield Curve is the plot of current interest yields versus time to maturity

Yield Curve Shapes

Theories Explaining the Shape of Yield Curve

⚫Pure expectations theory

⚫Liquidity premium theory

⚫Segmented markets theory

Pure Expectations Theory

⚫Long-term rates are average of current term and expected future short-term rates

short-⚫Yield curve slope reflects market

expectations of future interest rates

⚫An expected increase in rates leads to an

upward sloping yield curve

⚫An expected decrease in rates leads to a

downward sloping yield curve

⚫Investors select maturity based on

expectations

Pure Expectations Theory

The Term Structure of Interest Rates

⚫ Expected higher

interest rate levels

⚫ Tight monetary policy

⚫ Expanding economy

⚫ Expected lower interest rate levels

⚫ Expansive monetary policy

⚫ Recession soon?

Sloping Yield Curve

Upward- Sloping Yield Curve

Downward-Liquidity Premium Theory

⚫Pure expectation theory cannot explain the

fact that yield curve is normally

⚫Explains upward-sloping yield curve

⚫When combined with the expectations theory, yield curves could still be used to interpret

interest rate expectations

Liquidity Premium Theory

⚫Estimation of Forward Rates Based on Liquidity Premium

(1+ti2)2 = (1+ti1)(1+t+1F1) + LP

Liquidity Premium Theory

Segmented Markets Theory

⚫Theory explaining segmented, broken yield curves

⚫Investors choose securities with maturities

that satisfy their forecasted cash needs

⚫Explains why rates and prices vary

significantly between certain maturities

Limitations of the theory:

Some borrowers and savers have the

flexibility to choose among various maturities

Preferred Habitat Theory

Implications: Preferred Habitat Theory

Although investors and borrowers may normally concentrate on a particular maturity market,

certain events may cause them to wander from their “natural” or preferred market, for example higher interest rates.

Research on the Term Structure

Theories

⚫ Interest rate expectations have a strong

influence on the term structure of interest rates

⚫ However, the forward rate derived from a yield curve does not accurately predict future interest rates, and this suggests that other factors may

be relevant.

⚫ General Research Implications - Although the results differ, there is evidence that expectations, liquidity premium, and segmented markets

theories all have some validity.

Integrating the Theories of the Term

Structure

⚫If we assume the following conditions:

 Investors and borrowers currently expect interest rates to rise.

 Most borrowers need long-term funds, while most investors have only short-term funds to invest.

 Investors prefer more liquidity to less.

⚫Then all three conditions place upward

pressure on long-term yields relative to short term yields leading to upward sloping yield curve

Integrating the Theories of the Term Structure

Use of Term Structure

⚫Forecasting Interest Rates

 The shape of the yield curve can be used to

assess the general expectations of investors and borrowers about future interest rates.

 The curve’s shape should provide a

reasonable indication (especially once the liquidity premium effect is accounted for) of the market’s expectations about future

interest rates.

⚫Forecasting Recessions - Some analysts

believe that flat or inverted yield curves

indicate a recession in the near future

Use of Term Structure

⚫Making Investment Decisions - If the yield curve is upward sloping, some investors may attempt to benefit from the higher yields on longer-term securities even though they have funds to invest for only a short period of time.

⚫Making Decisions about Financing - Firms can estimate the rates to be paid on bonds

with different maturities This may enable

them to determine the maturity of the bonds they issue

Potential Impact of Treasury Shift from Long-Term to Short-Term Financing

Yield Curves at Various Points in Time

Yield Curves among Different Countries (as of May 2011)