Bonds
Overview of Bonds
Overview of Investment Types
Three primary types of investments include:
Bonds: Involves loaning money to an organization in exchange for fixed interest payments until maturity.
Stocks: Represents ownership in a company, which can involve varying levels of risk and reward based on the company's performance.
Derivatives: Instruments derived from the value of other underlying assets; discussion on derivatives is noted as advanced and is not included in this course.
Bond Terminology
Definitions and Components
Bond: A financial security representing a loan from an investor to a borrower (typically corporate or governmental).
Issuer: The entity (corporation or government) that is borrowing the money through the bond.
Bondholder: The investor who lends money to the issuer by purchasing the bond.
Issued: Refers to the date the bond loan is made, also known as the offering date or first settlement date.
Maturity: The specified date on which the bond's principal amount is due to be repaid.
Principal: The total amount borrowed, which must be repaid at maturity.
Face Value: The stated value of the bond as printed on its face, also known as par value.
Interest: The compensation for lending money, which compensates the lender for the delay and uncertainty in repayment.
Coupon Rate: The annual interest rate that the borrower pays to the bondholder.
Coupon Frequency: The intervals at which interest payments are made (e.g., annually, semi-annually).
Coupon Payment: The actual interest payment made by the issuer to the bondholder.
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Example of a Bond
Issue Date: The date the bond is issued.
Maturity Date: The date the bond matures.
Coupon Rate: The annual interest rate on the bond.
Frequency: How often interest is distributed (e.g., annually or semi-annually).
Face Value: The bond’s principal amount.
Example Timeline of a Bond Payment Schedule
In this illustration, a bond has:
Maturity of 30 years
Coupon Rate of 2.650%
Frequency of semi-annual payments
Face Value of $1,000.
The cash flows over years may look as follows:
Years 0, 0.5, 1, 1.5: Coupon payments of $13.25 are made.
At maturity (Year 30): The bondholder receives the face value $1,000 plus the final coupon payment, culminating in $1,013.25 total.
Bond Valuation
Bond Valuation Formula
To calculate the present value (PV) of cash flows for bonds, the following formula is applied:
PV = rac{C1}{(1 + r)^1} + rac{C2}{(1 + r)^2} + rac{C3}{(1 + r)^3} + … + rac{Cn}{(1 + r)^n} + rac{FV}{(1 + r)^n}
Where:
C = Coupon payment per period
FV = Face Value of the bond
r = the required rate of return for discounting cash flows to present value
n = total number of periods
Yield to Maturity (YTM)
Definition: Yield to maturity is the total return expected on a bond if held until maturity, including all coupon payments and the repayment of principal.
Components: Evaluates the annual return under the assumption that all interest payments are made without default and that all coupon payments are reinvested at the same yield.
Bond Valuation Practice
Steps for Bond Valuation
Convert five pieces of information into the key components required for time value of money (TVM) calculations.
Aspects to Remember During Calculations
Rate of Return (I/Y): Divide the annual interest rate by the number of compounding periods per year.
Number of Periods (N): Multiply the number of years until maturity by the number of compounding periods per year.
Coupon Payment (PMT): This should be calculated by dividing the annual payment (calculated as face value times coupon rate) by the frequency.
Intrinsic Value vs. Market Price
Every input required for bond valuation is publicly available, thus the intrinsic value (true value) of a bond tends to align closely with its market price.
Bond Price and Yield Relationship
Coupon Rate: Fixed % that represents the cost to the borrower and corresponds to the total payments made during the bond’s life.
Yield to Maturity: The fluctuating rate representing profits from the lender's perspective based on current costs to borrow.
Inverse Relation between Prices and Yields
When interest rates rise, bond prices decline and vice versa; this principle requires constant monitoring for investors.
Bond Returns
Definitions
Current Yield: The income (interest) from a bond divided by its current market price.
Yield to Maturity (YTM): Expected return if the bond is held to maturity and assumes all interest payments are reinvested at the same rate.
Realized Yield: The actual return received factoring all interest payments, principal repayments, reinvestment income, and any capital gains or losses.
Formulas
Current Yield:
Current Yield = rac{Annual ext{ }Interest ext{ }Payment}{Market ext{ }Price ext{ }of ext{ }Bond}Realized Yield:
Realized ext{ }Yield = rac{Total ext{ }Interest + Principal + Reinvestment ext{ }Income + Capital ext{ }Gain - Price ext{ }Paid}{Price ext{ }Paid}
For class purposes, reinvestment income is assumed as zero and capital gain as zero if the bond matures without sale.
Practice Problem
Consider purchasing a bond valued at $1,000 face value with a 5.00% coupon rate at the current market price of $920 with 5 years until maturity. The realized yield should be calculated based on semi-annual payments.
Bond Risks
Breakdown of Rate of Return
The overall return on a bond includes compensation for:
Delay: Compensation for the duration before repayment.
Uncertainty: This is split into components:
Default Risk: The risk that the bond issuer fails to make payments.
Interest Rate Risk: The risk linked to fluctuating market interest rates affecting bond prices.
Default Risk
Definition: Risk of issuer failure to repay principal or interest (known as credit risk).
Default Premium: Compensation embedded in the bond yield reflecting default risk.
Credit Rating Agency: Organizations evaluating the creditworthiness of borrowers.
Interest Rate Risk
Definition: Risk where bond prices and reinvestment incomes fluctuate with changing interest rates.
Term Premium: Component of yield compensating for interest rate fluctuations.
Price Yield Curve: A graphical representation showing how bond prices vary with changes in interest rates.
Bond Characteristics
Interest Payments: Bonds typically pay semi-annual interest.
Liquidity: Many bonds have low liquidity, making them challenging to buy or sell without influencing their market price.
Types of Bonds
By Issuer
Corporate Bond: Bonds issued by private companies.
Treasury Bond: Bonds issued by the U.S. government.
Municipal Bond: Bonds from local or state governments.
By Characteristics
Plain Vanilla Bond: Has a standard coupon rate.
Floating Rate Bond: Coupon rate varies over time.
Zero Coupon Bond: Does not pay periodic interest.
By Rating
Investment Grade Bond: Rated BBB- or higher, indicating low risk.
Speculative Grade Bond: Between investment-grade and junk.
Junk Bond: Rated CCC or below, indicating high risk.
By Price
Premium Bond: Sells above face value (Coupon Rate > YTM).
Par Bond: Sells exactly at face value (Coupon Rate = YTM).
Discount Bond: Sells below face value (Coupon Rate < YTM).
Investing in Bonds in Practice
To engage with bonds in real-world scenarios, you can utilize bond search tools, investment dashboards, and updated listings available from financial institutions. Understanding terms and processes is critical in assessing the suitability of bond investments.
Resources and Tools
Spreadsheets for calculations and modeling.
Access to bond calculators and bond market insights.
Conclusion
To have a comprehensive understanding of bonds, you should familiarize yourself with bond terminology, cash flow visuals, pricing dynamics, yield calculations, risk assessment, and types of bonds. This knowledge is crucial in the bond investment landscape.