20 Questions
What is the primary purpose of Macaulay's Duration?
To measure the sensitivity of a bond's price to changes in interest rates.
What is the relationship between Macaulay's Duration and Time to Maturity?
Positive relationship
What is the effect of an increase in yield on a bond's Macaulay's Duration?
Decreases the Macaulay's Duration
What is the primary difference between Macaulay's Duration and Modified Duration?
Modified Duration is adjusted for the bond's yield
What is the implication of two bonds having the same Modified Duration?
They have the same exposure to interest rate risk
What is the purpose of Convexity?
To capture the non-linear relationship between a bond's price and yield
What is the effect of an increase in interest rates on a bond's duration?
Decreases the duration
What is the relationship between a bond's duration and its price sensitivity to interest rate changes?
Positive relationship
What is the implication of a bond having a higher Macaulay's Duration?
The bond is more sensitive to interest rate changes
What is the effect of an increase in a bond's coupon rate on its Macaulay's Duration?
Decreases the Macaulay's Duration
Which of the following statements about convexity is false?
Convexity is higher for bonds with lower TTM.
A bond has a modified duration of 8. If the yield increases by 1%, the modified duration will approximately decrease by what percentage?
0.8%
Which investment strategy is best suited for an upward-sloping yield curve?
Riding the Yield Curve
What is the main advantage of the Rollover Strategy?
It provides a higher return when interest rates increase.
What happens to the bond's price when yields decrease and convexity is high?
The bond's price increases more than if convexity was low.
Which statement about the Barbell Strategy is true?
It protects against short-term rates declining.
What happens to the bond's TTM when an investor uses the Riding the Yield Curve strategy?
It decreases over time.
What is the main difference between the Barbell and Bullet strategies?
The Barbell strategy involves investing in bonds with different maturity dates, while the Bullet strategy involves investing in bonds with similar maturity dates.
What is the relationship between duration and convexity?
They are positively correlated.
What is the benefit of having higher convexity for an investor?
It provides a higher return when interest rates decrease, and a lower loss when interest rates increase.
Study Notes
Macaulay's Duration
- Measures the sensitivity of a bond's price to changes in interest rates (yields)
- Longer duration means higher exposure to interest rate risk
- Properties:
- Dmac ≤ TTM
- Dmac is higher for bonds with lower coupon rates (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)
- Inverse relationship between Dmac and coupons/YTM: higher yield, lower Dmac
- Positive relationship between Dmac and TTM: higher TTM, higher Dmac
Modified Duration
- Modified version of Dmac, adjusting for the bond's yield
- Dmod represents a percentage change in bond price
- Example: Dmod of 2.23 means a 1% increase in yield means a 2.23% decrease in bond price
Implications of Duration
- 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
- Two bonds with the same Dmod have the same exposure to interest rate risk, but not necessarily the same dollar price sensitivity
Convexity
- Measures the sensitivity of a bond's duration to changes in interest rates
- Captures non-linear relationship between bond price and yield
- Properties:
- 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)
- Positive relationship between convexity and duration
- Convexity is desirable: gives more gains when yields decrease and less losses when yields increase
Rollover Strategy
- Invest in a bond with a shorter TTM than the investment time horizon
- Reinvest in a new bond with a higher return when yields increase
- Only works if interest rates are forecast to increase
Riding the Yield Curve
- Invest in a bond with a longer TTM than the investment time horizon
- Take advantage of the bond's decreasing TTM and sell before maturity for a capital gain
- Only works for upward sloping yield curves
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 benefiting from extra convexity
Learn about Macaulay's Duration, a measure of bond price sensitivity to interest rate changes, and its relationship with yield to maturity and coupon rate.
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