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Questions and Answers
What happens to the bond price when interest rates decrease?
What happens to the bond price when interest rates decrease?
What type of bond is sold at a price below face value?
What type of bond is sold at a price below face value?
What is the result when the PV of the bond is greater than the PV of all strips?
What is the result when the PV of the bond is greater than the PV of all strips?
What happens to the bond price when the investor is subject to price risk?
What happens to the bond price when the investor is subject to price risk?
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According to the Pure Expectations Theory, what determines long-term interest rates?
According to the Pure Expectations Theory, what determines long-term interest rates?
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What is the implication of an inverted yield curve?
What is the implication of an inverted yield curve?
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What type of bond does not offer periodic coupon payments to the investor over the life of the bond?
What type of bond does not offer periodic coupon payments to the investor over the life of the bond?
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What is the effect on the bond price when the market interest rates rise?
What is the effect on the bond price when the market interest rates rise?
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What is the characteristic of a bond that is issued by a state government or government agency?
What is the characteristic of a bond that is issued by a state government or government agency?
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What happens to the bond price when the yield to maturity (YTM) decreases?
What happens to the bond price when the yield to maturity (YTM) decreases?
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What type of bond gives the investor the option to convert the bond into a pre-determined number of stocks in the future?
What type of bond gives the investor the option to convert the bond into a pre-determined number of stocks in the future?
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What is the relationship between the coupon rate and the yield to maturity (YTM) when a bond is sold at a premium?
What is the relationship between the coupon rate and the yield to maturity (YTM) when a bond is sold at a premium?
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What is the implication of a negative forward rate in the bond market?
What is the implication of a negative forward rate in the bond market?
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What is the main difference between spot rates and forward rates in bond yield curves?
What is the main difference between spot rates and forward rates in bond yield curves?
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According to the liquidity preference theory, what is the primary reason for the upward slope of a yield curve?
According to the liquidity preference theory, what is the primary reason for the upward slope of a yield curve?
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What is the relationship between Macaulay's duration and the term to maturity of a bond?
What is the relationship between Macaulay's duration and the term to maturity of a bond?
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What is the primary factor that affects the shape of a yield curve?
What is the primary factor that affects the shape of a yield curve?
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What is the implication of a downward sloping yield curve?
What is the implication of a downward sloping yield curve?
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What is the primary condition for Riding the Yield Curve to be effective?
What is the primary condition for Riding the Yield Curve to be effective?
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What is the primary benefit of riding the yield curve?
What is the primary benefit of riding the yield curve?
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Which strategy is most profitable when interest rates are expected to increase?
Which strategy is most profitable when interest rates are expected to increase?
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What is the main reason why the Barbell strategy tends to be more successful than the Bullet strategy?
What is the main reason why the Barbell strategy tends to be more successful than the Bullet strategy?
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What is the primary difference between the Barbell and Bullet strategies?
What is the primary difference between the Barbell and Bullet strategies?
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What is the result of combining the Bullet and Barbell strategies?
What is the result of combining the Bullet and Barbell strategies?
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What is the implication of a positive relationship between a bond's duration and price sensitivity to interest rate changes?
What is the implication of a positive relationship between a bond's duration and price sensitivity to interest rate changes?
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What is the impact of a 1% increase in yield on a bond's modified duration?
What is the impact of a 1% increase in yield on a bond's modified duration?
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Which of the following is a characteristic of a bond with high convexity?
Which of the following is a characteristic of a bond with high convexity?
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What is the main goal of an active trading strategy in bond management?
What is the main goal of an active trading strategy in bond management?
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What is the main advantage of a rollover strategy in bond management?
What is the main advantage of a rollover strategy in bond management?
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What is the relationship between duration and convexity in bond management?
What is the relationship between duration and convexity in bond management?
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What is the primary condition required for the 'Riding the Yield Curve' strategy to be effective?
What is the primary condition required for the 'Riding the Yield Curve' strategy to be effective?
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What is the primary benefit of 'Riding the Yield Curve'?
What is the primary benefit of 'Riding the Yield Curve'?
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What is the primary difference between the Barbell and Bullet strategies?
What is the primary difference between the Barbell and Bullet strategies?
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What happens to the bond's time to maturity as you 'Ride the Yield Curve'?
What happens to the bond's time to maturity as you 'Ride the Yield Curve'?
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What is the primary advantage of the Barbell strategy over the Bullet strategy?
What is the primary advantage of the Barbell strategy over the Bullet strategy?
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What is the result of combining the Bullet and Barbell strategies?
What is the result of combining the Bullet and Barbell strategies?
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What is the primary reason why the Barbell strategy is more profitable than the Bullet strategy when interest rates are expected to increase?
What is the primary reason why the Barbell strategy is more profitable than the Bullet strategy when interest rates are expected to increase?
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What is the primary benefit of the Bullet strategy?
What is the primary benefit of the Bullet strategy?
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What is the primary goal of 'Riding the Yield Curve'?
What is the primary goal of 'Riding the Yield Curve'?
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What happens to the bond's yield as you 'Ride the Yield Curve'?
What happens to the bond's yield as you 'Ride the Yield Curve'?
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Study Notes
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
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Description
Learn about bonds, a type of long-term capital investment, including how they work, coupon payments, and face value. Discover the difference between regular bonds and zero-coupon bonds.
