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Convexity

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Published: 13th July 2012 by William Webster

As interest rates fall bonds become more sensitive to further changes in yield.

This is what happens to the basis point value of a $10m bond position at different interest rates:

 

BPV

1%

  7,457.40

2%

  6,917.02

3%

  6,421.23

4%

  5,965.94

5%

  5,547.47

6%

  5,162.52

7%

  4,808.11

8%

  4,481.53

9%

  4,180.35

10%

  3,902.37

In simple terms as interest rates fall the bond becomes much more price sensitive to changing interest rates.

How important is this? Let's see.

  1. Currently interest rates are at historically low levels.
  2. Furthermore many commentators think things will remain like this for a long time.
  3. But sooner or later rates will rise.
  4. When this happens any firm with an unhedged portfolio will lose money.
  5. But because interest rates are relatively low the amount lost will be commensurably larger.
  6. Put another way when interest rates are low interest rate risk limits designed for higher rate environments are potentially a lot riskier.
  7. The message is simple. When did you last review your limit structure?

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17th February 2010

Convexity is often used to describe how the value of a fixed coupon bond alters with respect to interest rates. This explanation of convexity considers the value of a bond with a principal amount of $10,000,000, a coupon of 5% and a maturity of 10 years. This bond pays the investor $500,000 every year and returns the principal at maturity. The market value of the bond is the sum of its discounted cash flow values. If different interest rates are used to discount those cash flows the value of the bond will change. The higher the interest rate the lower the value of the bond becomes. Let's look at this bond's value at interest rates between 0% and 10%.