IA Week 10

What does bond duration measure conceptually?

A bond’s sensitivity to changes in interest rates

Why is duration a measure of risk and not time?

Because it captures how much price changes when yields change

How do bond prices move when interest rates rise?

Bond prices fall

How do bond prices move when interest rates fall?

Bond prices rise

What type of risk does duration capture?

Interest rate risk

What does higher duration imply?

Greater sensitivity of bond price to interest rate changes

How does maturity affect duration?

Longer maturity generally increases duration

How does coupon size affect duration?

Lower coupons increase duration

Why do zero coupon bonds have high duration?

Because all cash flows are received at maturity, making the bond’s price very sensitive to interest rate changes.

What is the duration of a zero coupon bond relative to maturity?

It equals its maturity because all cash flow is received at the end

What is Macaulay duration conceptually?

The weighted average time when a bond’s cash flows are received, with more weight on larger and earlier payments.

What does modified duration measure?

The approximate percentage change in a bond’s price for a small change in yield.

Why is modified duration more useful than Macaulay duration?

It directly links yield changes to price changes

When is duration approximation most accurate?

When interest rate changes are small.

Why does duration become less accurate for large rate changes?

The price yield relationship is curved not linear

What is convexity intuitively?

describes how curved the bond price–yield relationship is
With higher convexity, bond prices fall less when yields rise and rise more when yields fall.

Why is convexity beneficial to bondholders?

Prices rise more when rates fall than they fall when rates rise

How is portfolio duration calculated?

As the weighted average of individual bond durations

Why is portfolio duration useful?

It estimates how the entire portfolio responds to rate changes

What is duration gap?

The difference between asset duration and liability duration

Why does duration gap matter for banks?

It explains how equity value changes when interest rates move

What happens to bank equity if assets are more rate sensitive than liabilities?

Equity becomes more sensitive to rate changes

What does a duration gap close to zero achieve?

It stabilizes the value of equity against interest rate changes

Why did rising rates hurt banks with long duration assets?

Asset values fell faster than liability values