Effect of Yield Curve shift on convexity (question 8, part D in the 2013 morning session)

Hi guys,

I’m hoping to clarify something from question 8, part D in the 2013 morning session exam

Case facts:

-Durations of assets and liabilities are matched

-Convexity of assets remain higher than the liabilities

-The yield curve shifts upward in a parallel move

Question: Explain the effect of the yield curve shift on the economic surplus

Answer: "Because the duration of the assets equals the duration of the liabilities, changes in value due to duration will be equal. As a result of the yield curve shift, there is no change in economic surplus due to duration effects.

In this case, however, the convexity of the liabilities is less than the convexity of the assets. Therefore, the decline in value of the liabilities as a result of the yield curve shift will be greater than the decline in value of the assets, thus increasing economic surplus."

My understanding is that:

if duration of the liab < duration of the assets, then yield curve has a upward paralled shift --> decline in value of the liabilities < decline in value of the assets

So why is the decline in value of the liabilities > the decline in value of the assets after an upward yield curve shift when convexity of the liabilities < convexity of the assets?

Convexity works in the opposite way to duration

Remember the formula:

Total Price change = - (duration x change in yield x 100) + (C x change in yield squared x 100)

Thank you!!! I needed to confirm if it was the opposite of duration because I thought that they both measured the same thing

When yield curve shift upwards, bonds with higher convexity less affected than bonds with lower convexity.

Only for positive changes in yield.

Look at the formula.

Is this due to negative convexity?

So for:

  1. upward shift in yields = bonds with higher convexity are less affected vs. bonds with lower convexity

  2. downward shift in yields = bonds with higher convexity are more affected vs. bonds with lower convexity

  3. upward shift in yields = bonds move opposite to duration

  4. downward shift in yields = bonds move the same as duration

So if convexity of the liabilities < convexity of the assets and the yield curve shifts DOWNWARD in a parallel move: value of assets > value of liabilities?

so to confirm, when they question answer say the decline in value of liability as a result of yield curve shift is greater for liability is because the add on price difference due to convexity is smaller? when yield goes up convexity related price difference is positive, is that right?