Bonds: Raising Long-Term Capital

Bonds

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

Bond Pricing and YTM

• YTM reflects the market's required return on the bond
• If market required return > coupon rate, bond price decreases (discount)
• If market required return < coupon rate, bond price increases (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
• Relationship between YTM, coupon rate, and time to maturity:
  • If coupon rate > YTM, bond is sold at a premium
  • If coupon rate < YTM, bond is sold at a discount
  • As time to maturity decreases, bond price decreases
  • As time to maturity increases, bond price increases

Strips

• Separate trading of registered interest and principle securities
• Investors can sell components of their bonds
• Common in Treasury bonds (federal government)
• PV of strips 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 decrease
• Price risk: occurs when interest rates increase
• Inflation risk: causes bond prices to decrease
• Liquidity risk: difficulty selling bonds before maturity at a reasonable price

Pure Expectations Theory

• Yield curve reflects investors' expectations of future short-term interest rates
• Forward rates are market expectations of interest rates in the future
• Pure Expectations Theory predicts future short-term rates based on current long-term rates
• 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: rare, occurring when the economy is changing

Discount Factors/Spot Rates/Forward Rates

• Discount factor is determined from the market price and cashflows of a bond
• Forward rates are market expectations of interest rates in the future
• Spot rate curve: a curve that shows the yield or discount rate for different maturities
• Forward rate curve: a curve that shows the expected future short-term interest rates

Macaulay's Duration

• Measures the sensitivity of a bond's price to changes in interest rates
• Duration looks at price risk: if yields increase, price decreases
• Properties:
  • Dmac is less than or equal to TTM
  • Dmac is higher for bonds with lower Crate (all else equal)
  • Dmac is higher for bonds with lower YTM (all else equal)
  • Dmac is higher for bonds with higher TTM (all else equal)

Modified Duration

• Modified version of Dmac, adjusting for the bond's yield
• Dmod represents a percentage change in a bond's price
• Implications of duration overall:
  • Positive relationship between a bond's duration and price sensitivity to interest rate changes
  • Positive relationship between TTM and duration
  • Negative relationship between coupon rate and duration

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 Crate (all else equal)
  • Convexity is higher for bonds with lower YTM (all else equal)
  • Convexity is higher for bonds with higher TTM (all else equal)

Active and Passive Trading Strategies

• Active management: forecast yield curve changes or divest depending on the prediction
• Passive management: little involvement from the investor, aiming to buy and hold bonds until maturity
• Duration management: increase or decrease portfolio duration based on forecasted changes in rates
• Rollover strategy: invest in a bond with a shorter period than the investment time horizon, expecting interest rates to increase
• Riding the yield curve: invest in a bond with a longer TTM than the investment time horizon, expecting to benefit from falling yields

Bonds

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

Bond Pricing and YTM

• YTM 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)
• Changes in market interest rates affect YTM and bond prices

Relationship Between YTM, Coupon Rate, and Time to Maturity

• If coupon rate is higher than YTM, the bond is sold at a price above face value (premium)
• If coupon rate is lower than YTM, the bond is sold at a price below face value (discount)
• As time to maturity decreases, bond price decreases (premium) or increases (discount)
• When YTM decreases, the bond price increases, and when YTM increases, the bond price decreases

Characteristics of Bonds

• Par Value Bond: coupon rate = YTM
• Discount Bond: coupon rate is less than YTM
• Premium Bond: coupon rate is greater than YTM

Strips

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

Arbitrage

• If PV Bond = PV of all Strips, no arbitrage opportunities are present, and the market is efficient
• If PV Bond > PV of all Strips or PV Bond < PV of all Strips, arbitrage opportunities are present, and the market is inefficient

Reinvestment Risk

• Occurs when interest rates go down
• Good for investors if yields increase, and bad if yields decrease
• Price risk and reinvestment risk are negatively related

Price Risk

• Occurs when interest rates go up
• Good for investors if yields decrease, and bad if yields increase

Inflation Risk

• Inflation will cause bond prices to decrease, ultimately decreasing the return of bonds
• Good for investors if yields decrease, and bad if yields increase

Liquidity Risk

• Occurs when investors need to sell their bonds before maturity
• Good for investors if yields decrease, and bad if yields increase

Pure Expectations Theory

• Assumes the current yield curve solely reflects investors' expectations of future short-term interest rates
• Predicts future short-term rates based on current long-term rates
• If the market anticipates short-term rates will increase, the yield curve will slope upwards
• If the market anticipates short-term rates will 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: obtained from the discount factor
• Forward Rate: market expectations of interest rates in the future
• If the forward rate is higher than the spot rate, the market expects interest rates to increase
• If the forward rate is lower than the spot rate, the market expects interest rates to decrease

Arbitrage Opportunity - Negative Rates

• A negative rate implies mispricing
• Bond X's yield is too high relative to Bond Y, indicating rate is too high, price must be under-priced
• Bond Y's yield is too low relative to Bond X, indicating rate is too low, price must be over-priced

Interest Rates

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

Liquidity Preference Theory

• Investors are compensated for time but get extra if they invest for longer
• You are taking more risk
• Reinvestment risk is an issue if you don't have to sell
• Price risk is an issue if you must sell

Market Segmentation Theory

• Investors will never change their preference
• Supply and Demand will 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
• Preference such as investment duration, price risk, or tolerance

Macaulay's Duration

• Measures the sensitivity of a bond's price to changes in interest rates
• Duration looks at price risk
• Properties:
  • Dmac is less than or equal to TTM
  • Dmac is higher for bonds with lower Crate
  • Dmac is higher for bonds with lower YTM
  • Dmac is higher for bonds with higher TTM

Modified Duration

• Modified version of Dmac adjusting for the bond's yield
• Dmod represents a percentage change in a bond's price
• 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 Dmod have the same exposure to interest rate risk

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 Crate
  • Convexity is higher for bonds with lower YTM
  • Convexity is higher for bonds with higher TTM
• Implications of convexity:
  • More convexity is good, gives more gains when yields decrease and less losses when yields increase

Active and Passive Trading Strategies

• Active management: forecast yield curve changes or divest depending on the prediction
• Passive management: buy and hold bonds until maturity

Duration Management

• Increase or decrease portfolio duration based on forecasted changes in rates
• Investors can modify their portfolio allocation to increase or decrease its duration

Rollover Strategy

• Invest in a bond for a shorter period than your investment time horizon
• Expect interest rates to increase
• Roll into a new investment that gives you a higher return

Riding the Yield Curve

• Invest in a bond with a longer Time to Maturity
• Take advantage as the bond's time decreases
• Sell before maturity for a capital gain

Barbell and Bullet

• Barbell: invest in low-risk, low-maturity bonds and high-risk, high-maturity bonds
• Bullet: invest in bonds all with similar maturity dates
• Butterfly: combine the bullet and barbell strategies