FINN 3222 Investments - Bond Prices and Yields

FINN 3222 Investments - Selcuk Karahan

Overview

Course Title: FINN 3222 - Investments
Instructor: Selcuk Karahan

Bonds

Definition: Bonds represent debt owed by the issuer to the investor.
Nature: Long-term debt obligations issued by corporations and government units when borrowing money.
Investor Rights: The issuer must pay interest (also known as coupon payments) periodically (can be annually or semiannually) and return the par value (face value or principal) at maturity.
Fixed Income Investments: Bonds provide fixed interest payments on known (fixed) dates, thus they are often called fixed income investments.
Interest Payment Tax Deductibility: Interest is recognized as a cost of doing business and thus is tax-deductible.

Bond Indenture

Definition: A legal contract that specifies the rights and obligations of the issuer and bondholders.
Basic Terms include:
    - Interest rate
    - Payment dates
    - Total amount of bonds issued
    - Trustees
    - Default procedures
    - Asset used as security (collateral), etc.

Protective Covenants

Purpose: Restrictions placed on the issuing firm that are intended to protect bondholders from increasing risk during the investment period.
Types:
  - Subordination Clause: Specifies that senior bondholders must be paid first in case of bankruptcy.
  - Sinking Fund Provisions: Indenture requiring the issuer to periodically repurchase a proportion of outstanding bonds before maturity.
  - Call Provisions: Specifies call dates and call prices, allowing the issuer to repurchase bonds under certain conditions.

Bond Ratings

Credit (Default) Risk: The risk that a bond will not make all promised payments, creating a discrepancy between promised yield and expected yield.
Default Premium: The increment added to the promised yield to compensate the investor for default risk.
Rating Companies: Firms such as Moody’s, Standard & Poor’s, and Fitch Ratings which estimate default risk and rate bonds' creditworthiness.
Rating Categories:
  - Investment Grade: Bonds rated BBB or Baa and above, indicating lower risk.
  - Speculative Grade: Bonds rated BB or Ba and below, indicating higher risk and higher yield to maturity.
  - Junk Bonds: Bonds that have been downgraded, offering higher risk, higher yield to maturity, and lower liquidity.

Government Bonds

Treasury Bills (T-Bills)
   - Short-term debt obligations issued by the U.S. government.
   - Used to cover budget deficits and refinance maturing debts.
   - Main tool of the Federal Reserve for monetary policy.
   - Denomination: Commonly $10,000.
   - Maturity: 4, 13, 26, or 52 weeks.
   - Liquidity: High.
   - Default Risk: None.
   - Interest Type: Discount.
   - Principal repaid at maturity.
Treasury Notes and Bonds
   - Long-term debt obligations issued by the U.S. Treasury.
   - Utilized to finance national debt and government expenditures.
   - Denomination: Commonly $1,000.
   - Maturity: Notes range from 1 to 10 years; Bonds are over 10 years.
   - Coupon Rates: Set at intervals of 0.125% (1/8 of 1 percent).
   - Liquidity: High.
   - Interest Type: Coupons paid semiannually.
Special Government Bonds:
- STRIPS: Separates interest payments from the principal that are issued in zero-bond format to immunize against interest rate risk.
- TIPS: Treasury Inflation-Protected Securities, provide returns adjusted to the inflation rate (CPI) with semiannual coupon payments and inflation index adjustments.

Municipal Bonds

Purpose: Issued by state and local governments to fund imbalances between expenditures and receipts, and to finance long-term capital projects.
Repaid using tax receipts or generated revenue from projects.
Types:
- General Obligation (GO) Bonds: Backed by the full faith and credit of the issuer (the municipal government’s ability to tax).
- Revenue Bonds: Fund specific revenue-generating projects, backed by their cash flows.
Risk: Not default-free (e.g., Orange County, California). Less liquidity when compared to Treasury securities.

Corporate Bonds

Definition: Long-term obligations issued by corporations.
Typical Face Value: $1,000 (though some may have $5,000 or $10,000).
Interest Payments: Usually, they pay interest annually or semi-annually.
Redeemability: Cannot be redeemed anytime by the issuer unless they have a call option.
Risk Variation: The required interest rate varies with the level of risk across different bonds, even from the same issuer.

Special Corporate Bonds

Callable Bonds: Bonds that may be repurchased by the issuer at a specified call price during a designated period.
Convertible Bonds: Allow bondholders to exchange them for a set number of common stock shares.
Puttable Bonds: Offer holders the option to exchange them for par value or extend for a specified number of years.
Floating-Rate Bonds: Coupon rates that periodically reset according to specified market data, thus the interest payments fluctuate over time.

Bond Terminology

Face Value (Par Value or Principal): The maturity value of a bond that is repaid at maturity.
Coupon Interest Rate: The stated annual interest rate on a bond, usually fixed, used to compute coupon payments.
Coupon Payment: Amount of promised interest payments on a bond.
Yield-to-Maturity (YTM): The return if the bond is purchased and held until maturity; it serves as the discount rate to value a bond.
Current Yield: The return of the bond for the current year based on its current price.
Coupon Payment Formula:
$\text{Periodic Coupon Payment} = \text{Coupon Rate} \times \text{Face Value} \times \text{Number of Payments per Year}$
Current Yield Formula:
$\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Price}}$

Bond Payments

Coupon Bonds: These bonds make regular coupon interest payments (annual or semiannual) and pay face value at maturity. Examples include Treasury Notes and Bonds, as well as most corporate bonds.
   - Return on a coupon bond includes:
     - Difference between the purchase price and the face value.
     - Periodic coupon payments.
Zero-Coupon Bonds: These do not make regular coupon interest payments and pay only face value at maturity. Examples include Treasury Bills, often termed Pure Discount Bonds.
- Return is derived from the difference between the purchase price and the face value.

Bond Valuation (Pricing)

Formula: The price of a bond is the present value of all expected future cash flows:
$P = PV(Coupons) + PV(Par Value)$
Components:
  - Let $P$ = Price of the Bond, $C$ = Periodic Coupon (or Interest) Payment,
  - $T$ = Number of Periods until Maturity,
  - $R$ = Periodic Yield-to-Maturity (YTM) or Periodic Discount Rate.
Pricing Calculator: Excel function = PRICE (settlement, maturity, coupon rate, yield to maturity, redemption value, frequency, basis).
Observation: As interest rates increase, bond prices decrease and vice versa.

Clean Price vs. Full (Dirty) Price

Bond prices fluctuate in a sawtooth pattern, especially around coupon payment times.
  - Accrued Interest: The interest that accrues between coupon payments.
  - Clean Price: The quoted price of a bond that does not include accrued interest.
  - Full Price: Includes the accrued interest; compensates the seller for interest accumulated since the most recent coupon was paid.
Accrued Interest Formula:
$\text{Accrued Interest} = \frac{\text{Periodic Coupon} \times \text{Days Since Last Coupon Payment}}{\text{Days in Coupon Period}}$
Full Dirty Price Formula:
$\text{Full Price} = \text{Clean Price} + \text{Accrued Interest}$

Yield-to-Maturity (YTM)

Definition: The discount rate that sets the present value of promised bond payments equal to the market price of the bond.
Calculation: Finding YTM often requires trial and error or financial calculators with PV, FV, PMT, and N keys.
Interpretation: If a bond is bought at the current price and held until maturity, that would be the YTM.

Bond Prices and YTM

Relationship: Bond prices and discount rates are inversely related.
Effect of Interest Rates: If yields are very high, the bond’s value will drop; conversely, if yields approach zero, the bond's value approximates the total of cash flows.

Bond Pricing Scenarios

At Par: Price equals Par Value, the bond yields return equal to the current yield and YTM.
Discount Bond: Price is less than Par Value, yielding lower coupon rate compared to current market requirements.
Premium Bond: Price exceeds Par Value, with the coupon rate being higher than market requirements.

Pricing Changes Over Time to Maturity

As time to maturity shortens, the bond price increases, reflecting the proximity of cash flows from the bond.
The price typically decreases right after coupon payment, maintaining an oscillating pattern throughout the bond's life.

Yield-to-Call (YTC)

Definition: Represents the annualized rate of return for a bondholder if the bond is held until the first call date.
Calculation Adjustments: Use time until the call instead of maturity time, and the call price instead of the par value.
Characteristic: Premium bonds are more likely to be called before maturity than discount bonds.

The Term Structure of Interest Rates

Definition: Compares market yields of securities with the same characteristics, except maturity.
Yield Curve: A graphical representation of the relationship between yield and maturity, which can take on different shapes.

Unbiased Expectations Theory (UET)

Concept: At a given time, the Yield Curve reflects the market's expectations of future short-term rates. Investing in long-term bonds should yield returns equivalent to investing in short-term bonds consecutively.
Shapes of Yield Curve:
  - Upward Sloping: Indicating that future 1-year rates are expected to rise.
  - Downward Sloping: Suggesting an expectation of declining future rates.
  - Flat Yield Curve: Indicating that future 1-year rates are expected to remain unchanged.
Formula for Return:
$\frac{1}{R_N} = \frac{1}{1+R_1} \times \frac{1}{1+E_2 r_1} \times \ldots \times \frac{1}{1+E_N r_1}$
(geometric averages of current and expected future rates).

Liquidity Preference Theory (LPT)

Concept: Investors will only invest in long-term securities if offered at a premium, compensating for future uncertainty (risk) increasing with asset maturity.
Liquidity Premium: A proposed extra expected return for bearing the risk associated with long-term bonds; tends to increase with maturity.
Formula for LPT:
$\frac{1}{R_N} = \frac{1}{1+R_1} \times \frac{1}{1+E_2 r_1 + L_2} \times \, \ldots \times \frac{1}{1+E_N r_1 + L_N}$
(including liquidity risk premium).

Yield Curves - Comparison Between UET and LPT

Yield to Maturity Comparison:
- Upward-Sloping for UET
- Inverted for LPT
Term to Maturity visual representation of yield dynamics is highlighted in contrasting shapes across theories.

Forward Rate

Definition: An expected or “implied” rate on a short-term security to be originated in the future.
Derivation: Based on existing rates on currently traded securities using UET, allowing for the calculation of the implied one-year forward rate.
Forward Rate Formula:
$Nf_1 = \frac{(1+R_N)^N}{(1+R_{N-1})^{N-1}} - 1$
Where $Nf_1$ is the expected one-year rate for year N.

Term Spread Example

Analysis: Yields compared between 10-Year Treasury Bonds and 90-Day T-Bills, noting different points of interest rates over time, showing substantial spread between long-term and short-term securities.

Conclusion

Next Focus: Managing Bond Portfolios. Suggested reading includes Chapter 11 from the textbook to delve deeper into the concepts explored throughout the course.