9.3) Convexity

Question 1

What is convexity? (2)

Answer 1

• Relationship between bond price and yield is not linear.
• Convexity is the curvature of the price/yield relationship

Question 2

_____ 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.

Answer 2

Size
greater
drop

Question 3

What does high convexity imply? (2)

Answer 3

• 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

Question 4

What is the formula for convexity?

Answer 4

Question 5

For relatively ________ changes in yield, duration is a _______ approximation. For large changes in yield, duration is ______ an accurate measure.

Answer 5

small
good
not

Question 6

Thus, what is a more accurate measure to calulate the price change?

Answer 6

Question 7

Why do we add (not subtract) the convexity term?

Answer 7

Duration always underestimates

Question 8

What happens to the convexity term when the yield change is too small?

Answer 8

The convexity becomes insignificant in distorting the price as duration is accurate for small changes in yield

Question 9

What is the value of convexity?

Answer 9

Holding yield and duration constant, higher convexity bond has a higher price than a lower convexity bond, regardless of whether yields increase or decrease

Question 10

What factors affect convexity? (3)

Answer 10

• 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

Question 11

What are the properties of convexity? (2)

Answer 11

1. As required yield increases (decreases) the convexity of a bond decreases (increases)
   a. i.e., ‘positive convexity’.
2. For a given YTM, the lower the coupon, the greater the convexity of the bond.

Question 12

How come some investors don’t worry much about convexity sometimes ? (2)

Answer 12

• It drains down their returns
• It does not benefit them
  o Interest rates are stable