Bonds: Raising Long-term Capital

Bonds

• Bonds are used to raise long-term capital by corporations and governments
• When you invest in bonds, you pay the initial cost and receive coupon (interest) periodically, and the face value of the bond when it matures
• Types of bonds:
  • Zero-coupon bonds: no coupon payments, only receive face value at maturity
  • Convertible bonds: can be converted into a predetermined number of stocks in the future
  • Indexed bonds: coupon rate is related to movements in inflation
  • Callable bonds: issuer can buy the bond back from the investor in the future
  • Perpetual bonds: last forever
  • Treasury bonds: issued by the federal government
  • Municipal bonds: issued by state governments or government agencies

Bond Pricing and YTM

• YTM (Yield to Maturity) reflects the market's required return on the bond
• If the market requires a higher return than the bond's coupon rate, the bond's price will drop (discount)
• If the market requires a lower return than the bond's coupon rate, the bond's price will increase (premium)
• Interest rate changes affect YTM: when market interest rates rise, YTM increases, and bond prices fall; when market interest rates fall, YTM decreases, and bond prices rise

Characteristics of Bonds

• Par value bond: coupon rate = YTM
• Discount bond: coupon rate < YTM
• Premium bond: coupon rate > YTM

Strips

• Separate trading of registered interest and principal securities
• Investors can sell components of their bonds
• Common in Treasury bonds
• The total PV of interest and principal cashflows should equal the bond's face value price

Arbitrage

• If PV Bond = PV of all strips, no arbitrage opportunities present
• If PV Bond > PV of all strips, arbitrage opportunities are present
• If PV Bond < PV of all strips, arbitrage opportunities are present

Risks

• Reinvestment risk: occurs when interest rates go down, and investors can reinvest coupons at a lower market yield
• Price risk: occurs when interest rates go up, and investors are subject to price risk if they need to sell before maturity
• Inflation risk: inflation causes bond prices to decrease, decreasing the return of bonds
• Liquidity risk: occurs when investors need to sell their bonds before maturity and cannot get a reasonable price

Pure Expectations Theory

• Assumes the current yield curve reflects investors' expectations of future short-term interest rates
• Predicts future short-term rates based on current long-term rates
• If the market expects short-term rates to increase, the yield curve will slope upwards; if the market expects short-term rates to decrease, the yield curve will slope downwards

Yield Curve Shape

• Normal (upward-sloping): short-term yields are lower than long-term yields
• Inverted (downward-sloping): short-term yields are higher than long-term yields
• Flat: rarely seen, only when the economy is changing

Discount Factors, Spot Rates, and Forward Rates

• Discount factor: determined from the market price and cashflows of a bond
• Spot rate: market price and cashflows of a bond
• Forward rate: market expectations of interest rates in the future
• Use forward rates to hedge risk and indicate what the market thinks will happen in the future

Arbitrage Opportunity - Negative Rates

• A negative rate implies mispricing
• Buy the underpriced bond and sell the overpriced bond

Interest Rates

• High interest rates: decrease in bond prices
• Low interest rates: increase in bond prices
• The shape of the yield curve is determined by participants' expectations of future movement in interest rates

Liquidity Preference Theory, Market Segmentation Theory, and Preferred Habitat Theory

• Liquidity Preference Theory: investors are compensated for time but get extra if they invest for longer
• Market Segmentation Theory: investors will never change their preference, supply and demand shift the yield for each market segment
• Preferred Habitat Theory: investors have preferred time maturity to bonds, but if they see other opportunities, they may take it

Macaulay's Duration and Modified Duration

• Macaulay's Duration: measures the sensitivity of a bond's price to changes in interest rates
• Modified Duration: adjusts Macaulay's Duration for the bond's yield
• Implications of Duration:
  • Positive relationship between a bond's duration and price sensitivity to interest rate changes
  • Positive relationship between Time to Maturity and Duration
  • Negative relationship between the coupon rate and duration
  • Two bonds with the same Modified Duration have the same percentage price change sensitivity to yields

Convexity

• Measures the sensitivity of a bond's duration to changes in interest rates
• Captures the non-linear relationship between a bond's price and yield
• Properties:
  • Convexity is higher for bonds with lower coupon rates
  • Convexity is higher for bonds with lower YTM
  • Convexity is higher for bonds with higher Time to Maturity
• Using convexity with duration can provide a more accurate estimate of price changes in response to interest rate movements

Duration and Convexity Summary

• Duration and Convexity have a positive relationship
• Convexity is good: gives you more gains when yields decrease and gives you less losses when yields increase
• Duration is not good: when duration increases, you have more interest rate risk; when duration decreases, you have less interest rate risk

Active and Passive Trading Strategies

• Active Trading Strategies: require investors to forecast yield curve changes or divest depending on the prediction
• Passive Trading Strategies: require little from the investor, aiming to Buy & Hold bonds until maturity
• Duration Management: increase or decrease portfolio duration based on forecasted changes in rates