💹Financial Mathematics Unit 8 – Fixed Income Securities

What Are Fixed Income Securities?

• Financial instruments that provide investors with a predictable stream of income payments over a specified period
• Represent a contractual obligation for the issuer to make fixed payments to the investor on predetermined dates
• Include debt securities such as bonds, notes, and debentures issued by corporations, governments, and other entities
• Offer a lower-risk investment compared to equities, as they prioritize income payments over capital appreciation
• Provide portfolio diversification benefits when combined with other asset classes (stocks, real estate)
  • Help to mitigate overall portfolio risk by reducing exposure to market volatility
• Attract investors seeking stable income, capital preservation, and lower risk tolerance
• Play a crucial role in capital markets by enabling issuers to raise funds for various purposes (infrastructure projects, business expansion)

Key Types of Fixed Income Instruments

• Government bonds
  • Issued by national governments and backed by the full faith and credit of the issuing country
  • Considered low-risk investments due to the government's ability to raise taxes and print money to meet obligations
  • Examples include U.S. Treasury bonds, U.K. Gilts, and German Bunds
• Corporate bonds
  • Issued by companies to raise capital for business operations, expansions, or acquisitions
  • Offer higher yields than government bonds due to increased credit risk
  • Creditworthiness of the issuer is a key factor in determining the bond's yield and price
• Municipal bonds
  • Issued by state and local governments to fund public projects (schools, highways, hospitals)
  • Offer tax advantages, as interest income is often exempt from federal and state taxes
• Asset-backed securities (ABS)
  • Backed by a pool of underlying assets such as mortgages, auto loans, or credit card receivables
  • Provide investors with a claim on the cash flows generated by the underlying assets
• Mortgage-backed securities (MBS)
  • A type of ABS backed by a pool of mortgages
  • Issued by government-sponsored enterprises (Fannie Mae, Freddie Mac) or private financial institutions
• Collateralized debt obligations (CDOs)
  • Complex structured products that pool together various debt obligations (bonds, loans)
  • Divided into tranches with different risk and return profiles to cater to various investor preferences

Valuation Basics: Time Value of Money

• The concept that money available today is worth more than an identical sum in the future due to its potential earning capacity
• Reflects the opportunity cost of holding money, as funds could be invested to generate returns over time
• Depends on factors such as interest rates, inflation, and the time horizon under consideration
• Present value (PV)
  • The current worth of a future sum of money or stream of cash flows, given a specified rate of return
  • Calculated by discounting future cash flows back to the present using an appropriate discount rate
• Future value (FV)
  • The value of an asset or cash flow at a specified date in the future, based on an assumed rate of growth or return
  • Calculated by compounding the present value forward using an appropriate interest rate
• Annuities
  • A series of equal payments made at regular intervals over a specified period
  • Can be classified as ordinary annuities (payments occur at the end of each period) or annuities due (payments occur at the beginning of each period)
• Perpetuities
  • A type of annuity that continues indefinitely, providing a constant stream of cash flows without an end date
  • The present value of a perpetuity is calculated by dividing the periodic cash flow by the discount rate

Bond Pricing and Yield Calculations

• Bond pricing
  • Determined by discounting the bond's future cash flows (coupon payments and principal repayment) to the present using an appropriate discount rate
  • Influenced by factors such as the bond's coupon rate, maturity, credit quality, and prevailing market interest rates
• Yield to maturity (YTM)
  • The internal rate of return earned by an investor who buys a bond at the market price, holds it until maturity, and receives all scheduled coupon payments and the principal repayment
  • Represents the total return an investor can expect to receive by holding the bond to maturity
• Current yield
  • The annual coupon payment divided by the bond's current market price
  • Provides a simple measure of the bond's annual cash flow relative to its price, but does not account for capital gains or losses
• Yield curve
  • A graphical representation of the relationship between bond yields and their maturities
  • Reflects market expectations about future interest rates and economic conditions
  • Normal yield curve (long-term yields higher than short-term yields) indicates expectations of economic growth and rising interest rates
  • Inverted yield curve (short-term yields higher than long-term yields) may signal an impending recession or economic downturn

Interest Rate Risk and Duration

• Interest rate risk
  • The risk that changes in market interest rates will adversely affect the value of a bond or bond portfolio
  • When interest rates rise, bond prices generally fall, and vice versa
  • Longer-term bonds are more sensitive to interest rate changes than shorter-term bonds
• Duration
  • A measure of a bond's sensitivity to changes in interest rates
  • Expressed in years and represents the weighted average time to receive a bond's cash flows
  • Modified duration
    • A refined measure of duration that accounts for the bond's yield to maturity
    • Estimates the percentage change in a bond's price for a 1% change in interest rates
  • Effective duration
    • An extension of modified duration that accounts for embedded options in a bond (callable or putable bonds)
    • Provides a more accurate measure of interest rate sensitivity for bonds with contingent cash flows
• Convexity
  • A measure of how the duration of a bond changes as interest rates change
  • Represents the curvature of the relationship between bond prices and interest rates
  • Positive convexity (bond prices rise more when interest rates fall than they fall when interest rates rise) is generally desirable for investors

Credit Risk and Bond Ratings

• Credit risk
  • The risk that a bond issuer may default on its obligation to make timely coupon payments or repay the principal at maturity
  • Depends on the issuer's financial health, cash flows, and ability to service its debt obligations
• Credit spread
  • The difference in yield between a corporate bond and a government bond of similar maturity and currency denomination
  • Reflects the additional compensation investors require for assuming the credit risk associated with corporate bonds
• Bond ratings
  • Assigned by credit rating agencies (Moody's, Standard & Poor's, Fitch) to assess the creditworthiness of bond issuers
  • Range from AAA (highest credit quality) to C or D (default or near-default)
  • Investment-grade bonds (rated BBB- or higher) are considered lower-risk than high-yield or "junk" bonds (rated BB+ or lower)
• Credit analysis
  • The process of evaluating a bond issuer's financial health, business prospects, and ability to meet its debt obligations
  • Involves examining factors such as the issuer's financial statements, industry trends, competitive position, and management quality
• Credit enhancements
  • Techniques used to improve the credit quality of a bond issue and reduce the risk of default
  • Examples include bond insurance, letters of credit, and collateral backing

Fixed Income Trading Strategies

• Buy and hold
  • Purchasing bonds with the intention of holding them until maturity
  • Suitable for investors seeking a predictable income stream and who are not concerned with short-term price fluctuations
• Laddering
  • Constructing a portfolio of bonds with different maturities to minimize interest rate risk and reinvestment risk
  • As bonds mature, the proceeds are reinvested in new bonds at the longer end of the maturity spectrum
• Bullet strategy
  • Concentrating bond investments in a specific maturity range to target a particular point on the yield curve
  • Can be used to express a view on future interest rate movements or to match a specific liability stream
• Barbell strategy
  • Dividing a bond portfolio between short-term and long-term maturities while avoiding intermediate-term bonds
  • Aims to balance the stability of short-term bonds with the higher yields of long-term bonds
• Immunization
  • Structuring a bond portfolio to match the duration of the investor's liabilities
  • Helps to minimize the impact of interest rate changes on the portfolio's value relative to the liabilities
• Yield curve strategies
  • Positioning a bond portfolio to benefit from expected changes in the shape of the yield curve
  • Examples include bullet strategies (concentrating in a specific maturity range) and barbell strategies (overweighting short-term and long-term maturities)

Market Trends and Current Issues

• Low interest rate environment
  • Central banks worldwide have maintained low or negative interest rates to stimulate economic growth following the 2008 financial crisis and the COVID-19 pandemic
  • Low rates have driven investors to seek higher-yielding assets, including corporate bonds and emerging market debt
• Rising inflation concerns
  • As economies recover from the pandemic, there are growing concerns about rising inflation pressures
  • Higher inflation can erode the real value of fixed income investments and lead to higher interest rates
• Environmental, Social, and Governance (ESG) investing
  • Increasing investor focus on incorporating ESG factors into fixed income investment decisions
  • Green bonds, social bonds, and sustainability-linked bonds have gained popularity as a means of financing projects with positive environmental and social impacts
• Liquidity challenges
  • Reduced market liquidity, particularly in corporate bond markets, has raised concerns about potential difficulties in buying or selling bonds during periods of market stress
  • Regulators and market participants are exploring ways to improve bond market liquidity and transparency
• Technological advancements
  • The growth of electronic trading platforms and the use of algorithmic trading have transformed fixed income markets
  • Innovations such as blockchain technology and digital currencies may have implications for the future of fixed income investing
• Geopolitical risks
  • Political events, trade disputes, and global conflicts can impact fixed income markets by affecting economic growth, inflation, and investor sentiment
  • Diversification across geographies and sectors can help mitigate the impact of geopolitical risks on bond portfolios