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Chapter 6

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Chapter 6

The Structure of Interest Rates

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- There are many factors affect a security yield.
- This chapter explains and studys most important factors effect on a security yield:
- Term of Maturity
- Default Risk
- Tax Treatment
- Marketability
- Contract Options

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- The Term – to – maturity of a financial claim: is the length of time until principal borrowed becomes payable.
- The Term Structure of Interest Rate: is the relationship between yield and term –to- maturity on securities that differ ONLY in length of time to maturity.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- Used to study term structure of interest rates by plotting the curve - yield curve - at a point in time.
- The yield curve may be ascending, flat, or descending.
- Several theories explain the shape of the yield curve.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- The key assumption that buyers of bonds do not prefer bonds of one maturity over another.
- The slope of the yield curve reflects investors’ expectations about future interest rates.
A. Ascending: future interest rates are expected to increase.

B. Descending: future interest rates are expected to decrease.

- Investors are assumed to trade in a very efficient market with excellent information and minimal trading costs.
- Long-term interest rates represent the geometric average of current and expected future interest rates.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

tRn = 1/n (tR1 + t+1f1 + t+2f1 + …….. + t+n-1f1)

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

Example:

Given the following

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?

Solution:

Formula 1

1 + tR3 =[(1 + 3%)(1+ 4%) (1+ 5%)]1/3

tR3=[(1 + 3%)(1+ 4%) (1+ 5%)]1/3 - 1 = 3.997%

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

Formula 2

tRn = 1/n (tR1 + t+1f1 + t+2f1 + …….. + t+n-1f1)

tR3 = 1/ 3 (3% + 4% + 5%) = 4%

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

Average of 3 – year securities = (3% + 4% + 5%) / 3 = 4%

3 – year security = 4% (3.997%)

The interest rate on a long – term bond will equal an average of short – term interest rates that people expect to occur over the life of the long – term bond.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- Class Works:
- Class Work 1:
- No. 3 Page 162
- A commercial bank made a 3 – year term loan at 10 %. The ban’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?
- Class Work 2:
- Calculate the 1 – year forward rate 3 years from now if 3 – and 4 year rates are 5.5% and 5.8% respectively?
- 6.2% B) 6.7%
- C) 5.6%
- The rate can not be calculated from the information above.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- Class Work 3:
- If 3- year securities are yielding 6% and 2-year securities are yielding 5.5%. Future short term rates are expected to ……………. , and outstanding security prices are expected to …………………..
- Fall ; fall
- Rise ; fall
- Fall ; rise
- Rise ; rise

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

Using the term structure formula to calculate Implied Forward Rates:

The term structure formula two adjacent spot rates (tRn) and (tRn-1) the formula used to calculate (f 1) is:

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

Example 1:

Given the following:

One year spot rate = 3%

Two - year spot rate = 4%

Three - year spot rate = 5%

1- Calculate the implied forward rate on one year bond originating one year from now.

2- Calculate the implied forward rate on one year bond originating two year in the future?

1-

[ (1 + 4%)2 / (1 + 3%)] - 1 = 5%

2- [ (1 + 5%)3 / (1 + 3%)2 ] - 1 = 7%

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

Example 2:

Calculate the one – year forward rate three – year from now if three and four year spot rates are 5.5% and 5.8% respectively?

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- Long-term securities have greater risk and investors require greater premiums to give up liquidity.
- Long-term securities have greater price variability.
- Long-term securities have less marketability.

- The liquidity premium explains an upward sloping yield curve.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- 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 are possible in the yield curve.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- The Preferred Habitat Theory is an extension of the Market Segmentation Theory.
- The Preferred Habitat Theory allows market participants to trade outside of their preferred maturity if adequately compensated for the additional risk.
- The Preferred Habitat Theory allows for humps or twists in the yield curve, but limits the discontinuities possible under Segmentation Theory.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- 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.
- short term analysis of yield curves supports the preferred habitat theory and is favored by the market participants.

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- 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.

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- At any point in time, the slope of the yield curve can be used to assess the general expectations of borrowers and lenders 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.

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- 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.
- Investors charge a Default Risk Premium for added risk of default. It is measured as:
DRP = i - irf

- The DRP is the difference between the promised or nominal rate and the yield on a comparable (same term) risk-free securities.
- Investors are satisfied if the default risk premium is equal to the expected default loss.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- 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 nearer that of riskless securities.
- With increased economic pessimism, investors sell risky securities and buy “quality” widening the DRP.
- Credit Rating Agencies Measure and Grade Relative Default Risk Security Issuers
- Cash flow, level of debt, profitability, and variability of earnings are indicators of default riskness.
- As conditions change, rating agencies alter rating of businesses and governmental debtors.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- Example 1:
- Bonds are called speculative - grade bonds or junk bonds if their Moody's and Standard & Poor's rating is
- a.above Baa (BBB).
- b.Baa (BBB) and below.
- c.Below Baa (BBB).
- Baa (BBB) and below.
- Example 2:
- Bonds are called investment - grade bonds if their Moody's and Standard & Poor's rating is
- a.Baa (BBB) and above.
- b.Baa (BBB) and below.
- c.Above Baa (BBB).
- Below Baa (BBB).

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- 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 marginal tax rate. iat = ibt(1-t)
- Municipal bond interest income is tax exempt.
- Coupon income and capital gains have been taxed differently in the past, but are now both taxed at the same rate as ordinary income for individuals.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

Example 1:

A bondholder in the 25 percent tax bracket owns a $1000 Treasury bond with an 7 percent coupon rate. Calculate the after-tax return on the bond.

Solution

Before tax yield = 7% , tax rate = 25% so:

After tax yield = 7% ( 1 – 0.25)

= 7% (0.75) = 5.25%

Example 2:

If the tax bracket in the previous example changes to 30%. What is the after tax yield?

Solution

Before tax yield = 7% , tax rate = 30% so:

After tax yield = 7% ( 1 – 0.3)

= 7% (0.7) = 4.9% (increase of tax treatment reduces the yield)

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6

- Marketability - The costs and rapidity with which investors can resell a security.
- Cost of trade.
- Physical transfer cost.
- Search costs.
- Information costs.

- Securities with good marketability have higher prices (in demand) and lower yields.

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- Varied option provisions may explain yield differences between bonds
- An option is a contract provision which gives the holder the right, but not the obligation, to buy, sell, redeem, or convert a bond at some specified price within a defined future time period.

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- A call option permits the issuer (borrower) to call (refund) the bond before maturity
- Borrowers will “call” if interest rates decline.
- Investors in callable bonds face the risk of losing their high-yielding bonds.
- With increased call risk, investors demand a call interest premium (CIP).
CIP = ic – inc > 0

- A callable bond, ic, will be priced to yield a higher return (by the CIP) than a noncallable, inc, bond.

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- A put option permits the investor (lender) to terminate the bond at a designated price before maturity
- Investors are likely to “put” their bond back to the issuer during periods of increasing interest rates. The difference in interest rates between putable and nonputable bonds is called the put interest discount (PID).
PID = ip – inp < 0

- The yield on a putable bond, ip, will be lower than the yield on the nonputable bond, inp, by the PID.

Dr. Hisham Handal Abdelbaki - FIN 221 - Chapter 6

- A conversion option permits the investor to convert a bond into another security
- 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 nonconvertibles.
CYD = icon - incon < 0.

- Investors accept the lower yield on convertible bonds because they have an opportunity for increased rates of return through conversion.

Dr. HishamHandalAbdelbaki - FIN 221 - Chapter 6