FINM2003 Study Guide - Final Guide: Interest Rate Risk, Interest Rate, Yield Curve
Convexity
- The notion that the relationship b/w the % change in price against % change in yield
is not exactly linear , but that it is convex
- The curvature in the price-yield curve is
known as the bond’s convexity , the rate at
which the slope of the curve changes scaled
by the bond’s price
- It is a more precise measure of change and
matters less for smaller yield changes
-it is the second derivative of the price-
yield curve
- the greater the convexity, the greater the curvature
Further modification
Important
Convexity is an attractive feature for investors because:
1. Bonds with greater curvature enjoy greater price gains when yields fall than suffer
price falls when yields rise
2. But bonds with greater convexity are more expensive and offer lower YTM
Duration and Convexity for Callable Bonds
1. When r is high, the price-yield curve is positively
convex
2. When r is low, the price-yield curve is negatively
convex, sitting below the tangency line and
3. The negative convexity part of the price-yield
curve is a result of the fact that the bond cannot
have a value greater than its call price
4. Future Cash Flows are no longer known
a. If a bond is called early, its Face Value repaid earlier and so subsequent CF’s
would not be paid. Macaulay’s duration might not be appropriate in
ascertaining the sensitivity of bond prices to changes in yields
b. Industry practice estimates effective duration :
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Document Summary
The notion that the relationship b/w the % change in price against % change in yield is not exactly linear , but that it is convex yield curve. The curvature in the price-yield curve is known as the bond"s convexity , the rate at which the slope of the curve changes scaled by the bond"s price. It is a more precise measure of change and matters less for smaller yield changes it is the second derivative of the price- the greater the convexity, the greater the curvature. Convexity is an attractive feature for investors because: bonds with greater curvature enjoy greater price gains when yields fall than suffer price falls when yields rise, but bonds with greater convexity are more expensive and offer lower ytm. If a bond is called early, its face value repaid earlier and so subsequent cf"s would not be paid.
