9.3) Convexity Flashcards
What is convexity? (2)
- Relationship between bond price and yield is not linear.
- Convexity is the curvature of the price/yield relationship
_____ of the increase in bond price resulting from a given decrease in yield is _____________ than the _________ in
price resulting from a similar increase in yield.
Size
greater
drop
What does high convexity imply? (2)
- That bond has got high interest rate risks
- It will experience the greatest price appreciation when yields fall
o It will also experience the lowest price depreciation when yields increase
o Outperform in all situations
What is the formula for convexity?
For relatively ________ changes in yield, duration is a _______ approximation. For large changes in yield, duration is ______ an accurate measure.
small
good
not
Thus, what is a more accurate measure to calulate the price change?
Why do we add (not subtract) the convexity term?
Duration always underestimates
What happens to the convexity term when the yield change is too small?
The convexity becomes insignificant in distorting the price as duration is accurate for small changes in yield
What is the value of convexity?
Holding yield and duration constant, higher convexity bond has a higher price than a lower convexity bond, regardless of whether yields increase or decrease
What factors affect convexity? (3)
-
Size of the coupon payments.
o Coupon Rate: ↓ Coupon Rate ↑ Convexity -
The time to maturity of the bond.
o Time to Maturity: ↑ Maturity ↑ Convexity -
The current yield to maturity.
o Yield to Maturity: ↓ YTM ↑ Convexity
What are the properties of convexity? (2)
- As required yield increases (decreases) the convexity of a bond decreases (increases)
a. i.e., ‘positive convexity’. - For a given YTM, the lower the coupon, the greater the convexity of the bond.
How come some investors don’t worry much about convexity sometimes ? (2)
- It drains down their returns
- It does not benefit them
o Interest rates are stable
