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Questions and Answers
What is the main benefit of riding the yield curve?
What is the main benefit of riding the yield curve?
Which of the following strategies is most likely to benefit from increasing interest rates?
Which of the following strategies is most likely to benefit from increasing interest rates?
What is the primary reason for the barbell strategy's success?
What is the primary reason for the barbell strategy's success?
What is the purpose of investing in bonds with a longer TTM than the investment time horizon?
What is the purpose of investing in bonds with a longer TTM than the investment time horizon?
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What is the main difference between the barbell and bullet strategies?
What is the main difference between the barbell and bullet strategies?
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What is the result of a parallel shift in the yield curve?
What is the result of a parallel shift in the yield curve?
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What is the primary advantage of the butterfly strategy?
What is the primary advantage of the butterfly strategy?
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What is the assumption required for riding the yield curve to be successful?
What is the assumption required for riding the yield curve to be successful?
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What is the primary goal of investing in bonds with a longer TTM than the investment time horizon?
What is the primary goal of investing in bonds with a longer TTM than the investment time horizon?
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What is the key characteristic of an upward sloping yield curve?
What is the key characteristic of an upward sloping yield curve?
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What is the underlying principle behind the idea of riding the yield curve?
What is the underlying principle behind the idea of riding the yield curve?
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What happens to the price of a bond as its time to maturity decreases, assuming yields are stable?
What happens to the price of a bond as its time to maturity decreases, assuming yields are stable?
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Which of the following strategies involves investing in bonds with different maturity dates?
Which of the following strategies involves investing in bonds with different maturity dates?
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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 happens to the yield curve when interest rates increase?
What happens to the yield curve when interest rates increase?
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What is the primary goal of the butterfly strategy?
What is the primary goal of the butterfly strategy?
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What is the assumption required for the barbell strategy to be successful?
What is the assumption required for the barbell strategy to be successful?
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What is the primary benefit of selling a bond before its maturity date?
What is the primary benefit of selling a bond before its maturity date?
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What is the primary difference between the bullet and barbell strategies?
What is the primary difference between the bullet and barbell strategies?
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What happens to the price of a bond as its yield increases, assuming the time to maturity remains the same?
What happens to the price of a bond as its yield increases, assuming the time to maturity remains the same?
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What is the primary reason for selling a bond before its maturity date when riding the yield curve?
What is the primary reason for selling a bond before its maturity date when riding the yield curve?
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What is the shape of the yield curve that riding the yield curve strategy is most beneficial for?
What is the shape of the yield curve that riding the yield curve strategy is most beneficial for?
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What happens to the bond's yield as its TTM decreases, assuming the yield curve remains the same?
What happens to the bond's yield as its TTM decreases, assuming the yield curve remains the same?
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What is the primary benefit of investing in bonds with a longer TTM than the investment time horizon?
What is the primary benefit of investing in bonds with a longer TTM than the investment time horizon?
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What is the assumption required for riding the yield curve to be successful?
What is the assumption required for riding the yield curve to be successful?
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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 price as its TTM decreases, assuming yields are stable?
What happens to the bond's price as its TTM decreases, assuming yields are stable?
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What is the primary advantage of riding the yield curve over a buy-and-hold strategy?
What is the primary advantage of riding the yield curve over a buy-and-hold strategy?
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What is the primary risk associated with riding the yield curve?
What is the primary risk associated with riding the yield curve?
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What is the primary advantage of riding the yield curve over a laddered portfolio?
What is the primary advantage of riding the yield curve over a laddered portfolio?
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Study Notes
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
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
Bonds
- Bonds raise long-term capital for corporations and governments.
- Characteristics:
- Par Value Bond: Coupon rate = YTM
- Discount Bond: Coupon rate < YTM
- Premium Bond: Coupon rate > YTM
- Types of bonds:
- Convertible bonds: can be converted into a predetermined number of stocks
- Indexed bonds: coupon payments are related to inflation
- Callable bonds: seller can buy the bond back from the investor
- Perpetual bonds: last forever
- Treasury bonds: issued by the federal government
- Municipal bonds: issued by state governments or agencies
- Bond pricing and YTM:
- YTM reflects the market's required return on the bond
- If market requires a higher return than the bond's coupon rate, the bond's price will drop (discount)
- If market requires a lower return than the bond's coupon rate, the bond's price will increase (premium)
- Interest rate changes:
- When market interest rates rise, YTM increases, and bond prices fall
- When market interest rates fall, YTM decreases, and bond prices rise
Strips
- Strips are separate trading of registered interest and principal securities
- Investors can sell components of their bonds
- Total PV of interest and principal cash flows 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: occurs when investors need to sell before maturity
Pure Expectations Theory
- Assumptions:
- Investors are indifferent between holding short-term or long-term securities
- Market's expectation of future short-term interest rates determines long-term interest rates
- Yield curve shapes:
- 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, indicates changing economy
Discount Factors, Spot Rates, and Forward Rates
- Discount factor: determined from market price and cash flows of a bond
- Spot rate: used to obtain the yield curve
- Forward rate: market expectations of interest rates in the future
- Forward rate vs. spot rate: indicates market expectations of future interest rates
Macaulay's Duration and Convexity
- Macaulay's Duration:
- Measures sensitivity of a bond's price to changes in interest rates
- Looking at price risk: if yields increase, price decreases
- Properties:
- Dmac ≤ 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: adjusted version of Dmac, represents percentage change in bond price
- Convexity:
- Measures sensitivity of a bond's duration to changes in interest rates
- Accounts for non-linear relationship between bond 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 prediction
- Passive management: buy and hold bonds until maturity
- Duration management: modify portfolio allocation based on forecasted changes in rates
- Rollover strategy: invest in a bond with TTM less than investment time horizon, then roll into a new investment with a higher return
- Riding the yield curve: invest in a bond with a longer TTM, then sell before maturity to capture a capital gain
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Description
This quiz covers bonds, a type of long-term capital raised by corporations and governments. Learn about bond investments, coupon payments, and face value returns. Understand the differences between regular bonds and zero-coupon bonds.
