Module 46.3: Convexity and Yield Volatility

Question 1

What is convexity? What is the formula?

Answer 1

a measure of the curvature of the price-yield relation. can improve the estimates from duration.

Formula is - V1 + V2 -2V0 / (change in YTM)^2 * V0

V1 = lower price driven by increase in yield
V2 = higher price driven by decrease in yield
V0 = current price

Question 2

What is effective convexity? What is the formula?

Answer 2

Similar to effective duration, effective convexity must be used to determine the convexity for bonds with embedded options

Same formula as approximate convexity except the change in the curve is used rather than change in YTM.

Question 3

Is the convexity of an option free bond always positive? is that the same for a bond with options?

Answer 3

Yes, always positive. No, the convexity of a callable bond can be negative at low yields.

Question 4

What is the formula for change in full bond price given annual modified duration and convexity?

Answer 4

= - annual modified duration * change in YTM + 1/2 * annual convexity * change in YTM^2

Question 5

What is the duration gap? What does positive / negative signify?

Answer 5

the difference between a bond’s macaulay duration and the bondholders investment horizon.

positive - exposes the investor to market price risk from increasing interest rates

negative - exposes the investor to reinvestment risk from decreasing interest rates.