Negative convexity is a rare pattern on a yield curve where interest rates decrease as maturity time increases. Mortgage-backed securities and callable bonds are common forms of debt with negative convexity, and a more concave yield curve means less sensitivity to changes in interest rates.
Negative convexity is a characteristic of a loan best represented by a remarkably unusual pattern on a yield curve. This feature reverses the normal situation that the longer a debt has to run, the higher the interest rate. Mortgage-backed securities are one of the most common forms of debt that can have negative convexity.
The yield curve is a graph that compares the time a debt has left before repayment, known as time to maturity, with prevailing interest rates. An example of the usual form of this relationship comes with savings in a bank, which is effectively a loan from the client to the bank. The bank will generally pay a higher interest rate for a savings account where the money must be left in the bank for a fixed period of time than it would for a checking account where the money can be withdrawn quickly. Similarly, a company that borrows money by issuing a bond will generally pay a higher annual interest rate if the bond has a longer life span. In both examples, the higher rate is effectively the price of the guarantee of having the money longer.
This relationship means that, in most cases, a yield curve graph shows a convex curve, which means that the interest rate slopes up before leveling off. This is because, for example, the difference between a 1-year loan and a 2-year loan is much more significant than between a 24-year and 25-year loan. In situations with negative convexity, the curve is partially or fully concave. That is to say that at some points the interest rate decreases as the maturity time increases.
When looking at the negative convexity of bonds, economists and investors usually look at the issue from the other perspective. Instead of looking at how the length of a loan affects interest rates, they look at how interest rates affect the length of a loan. In general, it is believed that the more concave a yield curve is, the less sensitive is the price people will pay for bonds to changes in interest rates.
A common area where a debt can have negative convexity is in callable bonds. These are bonds where the issuing company, which is effectively the borrower, has the right to repay the bond before the agreed maturity date. If interest rates drop, the company may find it better to take out a new loan at a lower rate and use that money to pay off the bond early.
Another area with negative convexity is mortgage-backed securities. This is because the mortgages themselves are often based on variable mortgage rates. When interest rates drop, homeowners are more likely to pay off the loan faster and pay it off sooner. This means that the interest rate cut has shortened the life of the loan. Owners of mortgage-backed securities will often seek to hedge against this fluctuation by buying or selling long-term assets, such as treasury bills that cannot be repaid early.
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