# MBS and Convexity

Value (MBS)=Value (Treasury)-Value of prepmt option (CFAI page 166 Reading 31) I don’t understand why when int rates increase, the value of MBS decreases less than the value of a comparable-duration security. The reason that CFAI gives is “the value of the prepmt option offset part of the depreciation”. Does this mean that the values of prepmt option become negative? If so, why would it become negative? I thought minimum value would be zero. I am confused. Any input is appreciated. Thanks

value of prepayment option reduces… not becomes negative. No one wants to prepay their MBS loans in a rising interest rate environment. Neither will there be any refinancing occurring. [two of the prepayments available]. so when you subtract a lower # from the Value(Treasury) the value now becomes higher… so it decreases LESS.

Yes, I agree with your first stmt, but then I get confused. When int rates increase, the value of prepmt option decreases (but remains positive, minimum value is zero). We have to subtract that cost, so the value of an MBS should decrease MORE than the price of a comparabe duration treasury. What am I getting wrong?

The prepayment option is priced in , i.e. it is offered by the issuer to the investor. But its value reduces when rates rise ( i.e. it is market-directional ) , because of what CP said above

Looking at the equation, the only way that the V(MBS) > V(T) when rates rise is that the V(prepmt) is negative (to the investor, so add the value of prepmt option to the V(T)). When int rates decrease, then the value of option is positive (to the investor), so the V(MBS)

You are right that the prepayment option is deducted in determining the value; however, since in a rising rate environment it is now worth less the deduction is smaller. Not looking for the lower value. The change is what we are measuring.

Humm, yeah. But I still think that the prepmt option is positive (to homeowner) when rates decrease and negative (to homeowner) when rates increase. Since the MBS investor sold that option. It’s the opposite to a callable option. In fact, on 172 under “volatility risk”, CFAI states that when volatility increases, OAS widens. So the option cost must be negative in that case. (OAS=Zspread - Option Cost)

To the homeowner the option is worth more as rates decrease, and less (bound by 0) as rates increase. The option can’t be negative to them.

Yes, not to the homeowner, but to the MBS investor. If rates decline, the pre-pmt option is “ITM” for the homeowner, so positive for it but negative for the MBS investor (since he sold that option). When rates decline, the option is “OTM” for homeowner, so zero to them, but positive for the MBS (since they sold it to get extra yield). That is what I am arguing. So in my first post, I asked whether the option cost ever becomes negative (to the MBS investor). I think it does when rates decline, but it’s positive when rates increase. V(MBS)=V(T)-V(prepmt option), V(prepmt option)=V(T)-V(MBS) When rates rise, V(MBS)V(T) so option cost negative Sorry if I keep bugging withn this stuff but I need to get it.

The option cost will never be positive to the MBS investor (as it is the opposite of the value to the homeowner and is bound by zero on one side). As it becomes more OTM for the homeowner, the value of the MBS converges toward the comparable security. (when i say positive i mean that it will never be added to the comparable…it is a cost)

Just started SS11 on equities, can I get through the whole course by April 16, leaving me 7 weeks revision

Example: r=5%, Value treasury =100, Value option = 20 => Value MBS = 80 Now interest rates go up, r = 7% so the value of re-financing decreased which is similar as a decrease in the value of the ‘embedded’ option. So now: Value treasury = 80, value option = 5, and therefore Value MBS = 80 - 5 =75. Which proves the statement.