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Tuesday, May 17, 2011

What is Negative Convexity?

Investors today are scrambling for yield, and one place they are looking is at funds of mortgage-backed securities. An example is MBB, a popular exchange traded fund, which is comprised of GNMA and FNMA mortgage-backed securities whose principal and interest payments are guaranteed by the U.S. Treasury.

Do-it-yourself investors know to consider the yield-to-maturity of funds along with the duration. These reveal the interest rate risk of a particular fund, and the key question is whether the yield compensates for the underlying risk.

This process is a bit trickier in the case of mortgage-backed securities because of negative convexity. Although ominous sounding, it is easy to understand.

Let's begin with the very first concept learned about bonds:  that yields and prices move in opposite directions. How much prices move when rates drop is determined by duration. The greater the duration, the greater the price volatility for given swings in yield. All of this depends on the coupon interest payment and the maturity of the bonds in the fund. But here's the kicker:  mortgage-backed securities don't have a maturity - they have an average life. And the average life changes as yields change. This is the callability feature of bonds in spades!

You may not have thought about this before, but you very likely have contributed to negative convexity by refinancing your mortgage. Because homeowners refinance when mortgage rates fall and hold on to mortgages longer when mortgage rates rise, the average life varies inversely with yields. In essence, you are buying bonds and not knowing their maturities! As a result, mortgages are considered to have an average life of 12 years.

The bottom line of all of this is that a fund of mortgage-backed securities will be paid off quickly as mortgage rates fall (in other words you have a portfolio of shorter term mortgages than you bargained for) and will extend in average life when interest rates rise. As a result, mortgage-backed securities tend to do well when yields stay within a given band (in other words, prepayment surprises are minimal) and under-perform when there are significant changes in rates.

Should you buy mortgage-backed security funds? It depends on whether you think mortgage rates will stay fairly stable or if you think they will go off on a trend upwards or downwards. It is very likely that many investors will be surprised if interest rates trend meaningfully higher over the next few years, as many observers think likely.

For the math geeks - duration is the first derivative of price change related to yield changes, and negative convexity is the second derivative.


  1. Nice explanation Robert! I didn't realize till I looked at MBB, that they pay monthly and not quarterly dividends.

    But considering current market conditions, there is too much uncertainty.

  2. Thank you. Tremendous insight. What do you think about MLP's for income?