Macaulay's Duration and Bond Risk

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Questions and Answers

What does Macaulay's Duration measure?

A bond's sensitivity to interest rate changes (correct)
A bond's liquidity risk
A bond's price to change in yields
A bond's credit risk

What is the relationship between Duration and Coupons?

There is a positive relationship between Duration and Coupons
Duration is unaffected by Coupons
There is an inverse relationship between Duration and Coupons (correct)
There is no relationship between Duration and Coupons

What is Modified Duration?

A modified version of Macaulay's Duration adjusting for the bond's TTM
A modified version of Macaulay's Duration adjusting for the bond's credit rating
A modified version of Macaulay's Duration adjusting for the bond's coupon rate
A modified version of Macaulay's Duration adjusting for the bond's yield (correct)

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 (A) Signup and view all the answers

What does Convexity measure?

The sensitivity of a bond's duration to changes in interest rates (C) Signup and view all the answers

What is the relationship between Time to Maturity (TTM) and Duration?

There is a positive relationship between TTM and Duration (D) Signup and view all the answers

What happens to a bond's duration as yields decrease?

Duration increases (C) Signup and view all the answers

What is the relationship between Duration and YTM?

There is an inverse relationship between Duration and YTM (B) Signup and view all the answers

What do two bonds with the same Modified Duration have in common?

The same percentage price change sensitivity to yields (B) Signup and view all the answers

What is the relationship between Duration and Coupon rate?

There is an inverse relationship between Duration and Coupon rate (A) Signup and view all the answers

What is the primary benefit of convexity for investors?

It provides a more accurate estimate of price changes in response to interest rate movements. (D) Signup and view all the answers

What happens to a bond's modified duration for every 1% increase in yield?

It decreases by 1%. (C) Signup and view all the answers

What is the relationship between duration and convexity?

Positive, as duration increases, convexity increases. (D) Signup and view all the answers

What is the primary goal of the rollover strategy?

To invest in bonds with shorter TTM to benefit from expected interest rate increases. (A) Signup and view all the answers

What is the assumption behind the riding the yield curve strategy?

An upward sloping yield curve. (A) Signup and view all the answers

What is the benefit of selling a bond before maturity in the riding the yield curve strategy?

To capture a capital gain. (B) Signup and view all the answers

What is the characteristic of a barbell strategy?

Investing in low-risk, low-maturity bonds and high-risk, high-maturity bonds. (A) Signup and view all the answers

What happens to the yields of a barbell and bullet strategy under a parallel shift?

The yields change by the same rate. (D) Signup and view all the answers

What is the impact of convexity on the price change of a bond?

It decreases the price change when yields increase. (B) Signup and view all the answers

What is the relationship between convexity and TTM?

Convexity is higher for bonds with longer TTM. (D) Signup and view all the answers

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