Bonds: Negative vs. positive convexity (bond, fund, mortgage, investment)

[ncole1]

Do negative convexity bonds (such as mortgage bonds) correlate less with the stock market, or more with the stock market, than positive convexity bonds like Treasury securities?

What are the implications of this on investment strategies?

[mathjak107]

bogleheads wiki had this to say "

In addition to the normal risks of bonds, mortgage-backed securities exhibit negative convexity. This negative convexity results from contraction risk--the tendency of homeowners to refinance as interest rates fall--and from extension risk--the tendency of homeowners to delay pre-payments as interest rates rise.
Determining the exact extent of this negative convexity is impossible, as it depends on how mortgagors behave. In general, this behavior is non-linear: small changes make little difference in homeowner behavior but large changes cause homeowners to overcome the hassle and to refinance in larger numbers. The extent of negative convexity can be approximated with statistical modeling, although behavior with large interest rate changes is relatively hard to predict. Bondholders are compensated for this risk by the "option-adjusted spread," which can be interpreted as the market's assessment of the size of prepayment risk.

there is some question as to whether the option-adjusted spread has historically been enough to compensate investors for the increased risk of MBS'

Holding MBS's as a part of a diversified bond portfolio is unlikely to lead to ruin, and over time investors are likely to be compensated for the increased risk of negative convexity with higher yield. Therefore, investors are justified in investing in MBS's, either directly or through a total bond market fund (which typically are about one-third MBS), provided they understand that they are assuming a moderate amount of additional risk. Investors who do not wish to assume the risk of negative convexity or who are interested in lowering the correlation between the bond component of their portfolio and the equity component are equally justified in sticking to bonds that lack embedded options.

[Wells5]

Would "negative convexity" be equivalent to concavity?