20 Questions
What does Macaulay's Duration measure?
A bond's sensitivity to interest rate changes
What is the relationship between Duration and Coupons?
There is an inverse relationship between Duration and Coupons
What is Modified Duration?
A modified version of Macaulay's Duration adjusting for the bond's yield
What is the relationship between a bond's duration and price sensitivity to interest rate changes?
There is a positive relationship between a bond's duration and price sensitivity to interest rate changes
What does Convexity measure?
The sensitivity of a bond's duration to changes in interest rates
What is the relationship between Time to Maturity (TTM) and Duration?
There is a positive relationship between TTM and Duration
What happens to a bond's duration as yields decrease?
Duration increases
What is the relationship between Duration and YTM?
There is an inverse relationship between Duration and YTM
What do two bonds with the same Modified Duration have in common?
The same percentage price change sensitivity to yields
What is the relationship between Duration and Coupon rate?
There is an inverse relationship between Duration and Coupon rate
What is the primary benefit of convexity for investors?
It provides a more accurate estimate of price changes in response to interest rate movements.
What happens to a bond's modified duration for every 1% increase in yield?
It decreases by 1%.
What is the relationship between duration and convexity?
Positive, as duration increases, convexity increases.
What is the primary goal of the rollover strategy?
To invest in bonds with shorter TTM to benefit from expected interest rate increases.
What is the assumption behind the riding the yield curve strategy?
An upward sloping yield curve.
What is the benefit of selling a bond before maturity in the riding the yield curve strategy?
To capture a capital gain.
What is the characteristic of a barbell strategy?
Investing in low-risk, low-maturity bonds and high-risk, high-maturity bonds.
What happens to the yields of a barbell and bullet strategy under a parallel shift?
The yields change by the same rate.
What is the impact of convexity on the price change of a bond?
It decreases the price change when yields increase.
What is the relationship between convexity and TTM?
Convexity is higher for bonds with longer TTM.
Study Notes
Macaulay's Duration
- Measures a bond's price sensitivity to interest rate changes (yields)
- As yields increase, price decreases
- Duration increases as Time to Maturity (TTM) increases, exposing the bond to more interest rate risk
Properties of Macaulay's Duration
- Dmac ≤ TTM
- Dmac is higher for bonds with lower coupon rates (all else equal)
- Dmac is higher for bonds with lower Yield to Maturity (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
- Represents a percentage change in bond price
- Example: Dmod of 2.23 means a 1% yield increase will decrease bond price by approximately 2.23%
Implications of Duration
- Positive relationship between duration and price sensitivity to interest rate changes
- Positive relationship between TTM and duration
- Negative relationship between coupon rate and duration
- Two bonds with same Dmod have same percentage price change sensitivity to yields
Convexity
- Measures sensitivity of a bond's duration to changes in interest rates
- Accounts for non-linear relationship between bond price and yield
- Increasing (decreasing) yields decrease (increase) duration
- Convexity provides a more accurate estimate of price changes in response to interest rate movements
- Higher convexity means more curvature and less price change when yields increase
Properties of Convexity
- Convexity is higher for bonds with lower coupon rates (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)
Rollover Strategy
- Invest in a bond for a shorter period than investment time horizon, expecting interest rates to increase
- Roll over into a new investment with a higher return when rates increase
Riding the Yield Curve
- Invest in a bond with a longer TTM than investment time horizon
- Sell the bond before maturity, taking advantage of the upward sloping yield curve
Barbell and Bullet Strategies
- Bullet: Invest in bonds with similar maturity dates
- Barbell: Invest in low-risk, low-maturity bonds and high-risk, high-maturity bonds
- Barbell tends to be more successful due to convexity benefits
Learn about Macaulay's Duration, a measure of a bond's price sensitivity to interest rate changes, and its properties.
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