Macaulay's Duration: Bond Price Risk

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Questions and Answers

What is the primary purpose of Macaulay's Duration?

To measure the sensitivity of a bond's price to changes in interest rates. (correct)

To estimate the expected return on investment of a bond.

To measure the sensitivity of a bond's yield to changes in interest rates.

To calculate the credit risk of a bond issuer.

What is the relationship between Macaulay's Duration and Time to Maturity?

Positive relationship (correct)

Inverse relationship

No correlation

Negative correlation

What is the effect of an increase in yield on a bond's Macaulay's Duration?

Increases the Macaulay's Duration

Has no impact on the Macaulay's Duration

Depends on the bond's coupon rate

Decreases the Macaulay's Duration (correct)

What is the primary difference between Macaulay's Duration and Modified Duration?

Modified Duration is adjusted for the bond's yield Signup and view all the answers

What is the implication of two bonds having the same Modified Duration?

They have the same exposure to interest rate risk Signup and view all the answers

What is the purpose of Convexity?

To capture the non-linear relationship between a bond's price and yield Signup and view all the answers

What is the effect of an increase in interest rates on a bond's duration?

Decreases the duration Signup and view all the answers

What is the relationship between a bond's duration and its price sensitivity to interest rate changes?

Positive relationship Signup and view all the answers

What is the implication of a bond having a higher Macaulay's Duration?

The bond is more sensitive to interest rate changes Signup and view all the answers

What is the effect of an increase in a bond's coupon rate on its Macaulay's Duration?

Decreases the Macaulay's Duration Signup and view all the answers

Which of the following statements about convexity is false?

Convexity is higher for bonds with lower TTM. Signup and view all the answers

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% Signup and view all the answers

Which investment strategy is best suited for an upward-sloping yield curve?

Riding the Yield Curve Signup and view all the answers

What is the main advantage of the Rollover Strategy?

It provides a higher return when interest rates increase. Signup and view all the answers

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. Signup and view all the answers

Which statement about the Barbell Strategy is true?

It protects against short-term rates declining. Signup and view all the answers

What happens to the bond's TTM when an investor uses the Riding the Yield Curve strategy?

It decreases over time. Signup and view all the answers

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. Signup and view all the answers

What is the relationship between duration and convexity?

They are positively correlated. Signup and view all the answers

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. Signup and view all the answers

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

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Description

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.