💰Finance Unit 6 – Bonds and Bond Valuation

What Are Bonds?

• Financial instruments that represent a loan made by an investor to a borrower, typically a corporation or government entity
• Bonds are debt securities where the issuer owes the holder a debt and is obligated to pay interest (coupon) and/or repay the principal at a later date (maturity)
• Investors buy bonds to receive regular interest payments and the return of their principal investment upon maturity
• Bonds are considered less risky than stocks but generally offer lower potential returns
• Issuers use bonds to finance projects, operations, or other expenses without diluting ownership by issuing stock
• Bonds are traded on the secondary market, allowing investors to buy and sell them before maturity
• Credit rating agencies (Moody's, Standard & Poor's, Fitch) assign ratings to bonds based on the issuer's creditworthiness and ability to repay the debt

Types of Bonds

• Government bonds
  • Issued by national governments (U.S. Treasury bonds) and considered low-risk investments
  • Municipal bonds are issued by state and local governments to fund public projects (infrastructure)
• Corporate bonds
  • Issued by companies to raise capital for various purposes (expansion, acquisitions)
  • Higher risk than government bonds but offer higher yields to compensate investors
• High-yield (junk) bonds
  • Issued by companies with lower credit ratings and higher risk of default
  • Offer significantly higher yields to attract investors willing to take on more risk
• Zero-coupon bonds
  • Bonds that do not pay regular interest but are issued at a discount and redeemed at face value upon maturity
• Convertible bonds
  • Bonds that give the holder the option to convert the bond into a predetermined number of shares of the issuer's common stock
• Callable bonds
  • Bonds that give the issuer the right to redeem the bond before maturity at a predetermined price
• Puttable bonds
  • Bonds that give the holder the right to sell the bond back to the issuer at a predetermined price before maturity

Bond Characteristics

• Face value (par value)
  • The amount the bondholder will receive when the bond matures
  • Typically $1,000 per bond
• Coupon rate
  • The annual interest rate paid by the bond issuer on the bond's face value
  • Expressed as a percentage (5% coupon rate means $50 annual interest on a$1,000 bond)
• Coupon frequency
  • How often interest payments are made (annually, semi-annually, quarterly)
• Maturity date
  • The date on which the bond issuer must repay the bondholder's principal investment
  • Bonds with longer maturities generally offer higher interest rates to compensate for the increased risk
• Credit rating
  • An assessment of the bond issuer's creditworthiness and ability to repay the debt
  • Higher ratings (AAA) indicate lower risk, while lower ratings (BB) indicate higher risk
• Yield to maturity (YTM)
  • The total return an investor can expect to receive by holding the bond until maturity
  • Accounts for coupon payments, principal repayment, and the time value of money
• Callable or puttable provisions
  • Features that allow the issuer (callable) or the investor (puttable) to redeem the bond before maturity under certain conditions

Bond Pricing and Valuation

• Bond prices are quoted as a percentage of the bond's face value
  • A bond quoted at 98 means it is trading at 98% of its face value ($980 for a$1,000 bond)
• Bond prices are inversely related to interest rates
  • When interest rates rise, bond prices fall (existing bonds become less attractive)
  • When interest rates fall, bond prices rise (existing bonds become more attractive)
• The present value of a bond is the sum of the present values of all future coupon payments and the principal repayment at maturity
  • Calculated using the bond's yield to maturity as the discount rate
• The basic bond valuation formula is:
  • $Bond Price = \sum_{t=1}^{n} \frac{Coupon Payment}{(1+r)^t} + \frac{Face Value}{(1+r)^n}$
  • Where $r$ is the yield to maturity, $n$ is the number of periods until maturity, and $t$ is the period number
• Duration measures a bond's sensitivity to interest rate changes
  • Longer duration bonds are more sensitive to interest rate changes than shorter duration bonds
• Convexity measures the curvature of the relationship between bond prices and interest rates
  • Bonds with higher convexity experience larger price increases when interest rates fall and smaller price decreases when interest rates rise

Yield and Interest Rates

• Coupon yield
  • The annual interest payment divided by the bond's face value
  • $Coupon Yield = \frac{Annual Coupon Payment}{Face Value}$
• Current yield
  • The annual interest payment divided by the bond's current market price
  • $Current Yield = \frac{Annual Coupon Payment}{Current Bond Price}$
• Yield to maturity (YTM)
  • The total return an investor can expect to receive by holding the bond until maturity
  • Accounts for coupon payments, principal repayment, and the time value of money
  • Calculated using an iterative process or approximated using the bond's price, coupon rate, and time to maturity
• Nominal yield
  • The stated interest rate on a bond, not adjusted for inflation
• Real yield
  • The nominal yield adjusted for inflation
  • $Real Yield = Nominal Yield - Inflation Rate$
• Term structure of interest rates (yield curve)
  • The relationship between bond yields and their maturities
  • Normal yield curve: longer maturities have higher yields than shorter maturities
  • Inverted yield curve: shorter maturities have higher yields than longer maturities, often signaling an impending recession

Bond Risks

• Interest rate risk
  • The risk that changes in interest rates will cause bond prices to fluctuate
  • When interest rates rise, bond prices fall, and vice versa
• Credit (default) risk
  • The risk that the bond issuer will fail to make coupon payments or repay the principal
  • Higher for lower-rated bonds (junk bonds) and lower for higher-rated bonds (investment-grade)
• Inflation risk
  • The risk that the purchasing power of the bond's coupon payments and principal repayment will be eroded by inflation over time
  • More significant for long-term bonds and during periods of high inflation
• Liquidity risk
  • The risk that an investor may not be able to sell a bond quickly or at a fair price due to low trading volume or market conditions
• Call risk
  • The risk that a callable bond will be redeemed by the issuer before maturity, potentially forcing the investor to reinvest at lower interest rates
• Reinvestment risk
  • The risk that an investor will have to reinvest coupon payments at lower interest rates than the bond's original yield
  • More significant when interest rates are falling
• Foreign exchange risk
  • The risk that changes in currency exchange rates will affect the value of a bond denominated in a foreign currency

Trading and Investing in Bonds

• Bonds can be bought and sold on the secondary market through brokers or electronic trading platforms
• Bond prices are quoted as a percentage of the bond's face value (par value)
  • A bond quoted at 98 is trading at 98% of its face value ($980 for a$1,000 bond)
• Accrued interest
  • The interest earned on a bond since the last coupon payment, paid by the buyer to the seller when a bond is traded between coupon payment dates
• Bond mutual funds and exchange-traded funds (ETFs)
  • Pooled investment vehicles that hold a diversified portfolio of bonds, providing investors with exposure to the bond market without having to purchase individual bonds
• Laddering
  • A bond investment strategy where an investor purchases bonds with different maturities to minimize interest rate risk and reinvestment risk
• Immunization
  • A bond investment strategy where an investor matches the duration of their bond portfolio to their investment time horizon to minimize interest rate risk
• Bond arbitrage
  • A trading strategy that seeks to profit from price discrepancies between related bonds or between a bond and a derivative security (bond futures)

Real-World Applications

• Governments issue bonds to finance public projects, infrastructure, and budget deficits
  • U.S. Treasury bonds are considered a risk-free benchmark for other investments
• Corporations issue bonds to raise capital for expansion, acquisitions, or other expenses without diluting ownership
  • Bond issuance allows companies to access funding at lower costs than equity financing or bank loans
• Investors use bonds to generate steady income, diversify portfolios, and preserve capital
  • Bonds are often used to balance the risk of equity investments, particularly for risk-averse investors or those nearing retirement
• Central banks (Federal Reserve) use monetary policy tools to influence interest rates and bond yields
  • Quantitative easing involves central banks purchasing government bonds to lower interest rates and stimulate economic growth
• Bond market indicators (yield curves, credit spreads) provide insights into economic conditions and market sentiment
  • An inverted yield curve (short-term rates higher than long-term rates) often precedes a recession
• Pension funds and insurance companies heavily invest in bonds to match their long-term liabilities and ensure stable returns
  • Liability-driven investing strategies aim to align bond portfolios with the duration and cash flow characteristics of an organization's liabilities