MBS : Unchanged PSA Vs Changed PSA : Rate increase impact on Price?

[rajeshtr]

Hi David, Question regarding the highlighted statement in the attachment: When PSA reduces from 165 PSA to 150PSA on a rate increase situation --> my understanding is that the prepayment cash flow decreases and the bond should be valued more just using the cash flow pricing approach. (i.e. More cash flow is expected in the 150 PSA situation).

Kindly clarify why Bond Price (Mortgage Value) is dropping more in the Reduced PSA - Rate increase situation compared to Constant higher PSA (165 PSA) rate increase situation.

 

[David Harper CFA FRM]

Hi @rajeshtr Great question, very instructive! What's the source? (at first glance, the zero convexity is incongruous; constant PSA in general still tends to imply nonzero convexity). I copied below Fabozzi's own explanation of contraction risk (from the newly published Handbook of MBS, 7th Edition). I looked at my MBS model (it's from previously assigned Veronesi who is very good on this, here is a copy https://www.dropbox.com/s/jth83x3ovkrgu7d/1227-mbs-convexity.xlsx?dl=0 ) and here is what is happening: the lower PSA, by definition, increases the duration of the security; this is effectively discounting principal repayments further into the future. By analogy, a 6-year zero coupon bond is cheaper than the same 5-year zero coupon bond: F*exp(-6y) < F*exp(-5), but the analogy only here refers to incrementally deferred principal payments of course. In my MBS model, decreasing the PSA (eg, from 165 to 150) yet ceteris paribus everything else does increase duration and lower price, therefore I am suspicious of the lower duration (5.34) under the Changed PSA scenario, as it makes sense to me only for the higher PSA shock.

While it is true that the introduction of variable PSA decreases the duration (i.e., at 7.50% the duration decreases from 5.49 years under static 165 PSA to 5.24 years under variable PSA), the dynamic refers to the price behavior at 7.75% (i.e., 7.50% + 25 bps) where the point is that, ceteris peribus, given the 7.75% rate level, a decrease in the PSA (from 165 to 150) increases the duration which contributes a price decrease component.

Fabozzi on Extension Risk: "Extension Risks: When investing in a mortgage passthrough security, an investor is exposed to prepayment risk— the uncertainty about the cash flow due to prepayments. But prepayment risk can be decomposed into contraction risk and extension risk.

Contraction risk is the risk that an MBS life will be shorter than expected when the security was purchased because prepayments are faster than expected. There are two adverse consequences that an investor who faces contraction risk encounters. First, the price of an option-free bond will rise when interest rates decline. But in the case of a mortgage passthrough security, the rise in price will not be as large as that of an option-free bond because a fall in interest rates increases the borrower’s incentive to prepay the loan and refinance at a lower rate. This results in the same adverse consequence faced by holders of callable corporate and municipal bonds. The effect is that the upside price potential of a mortgage passthrough security is truncated because of prepayments, a bond attribute referred to as negative convexity. The second adverse consequence is that since an MBS will realize faster prepayments when mortgage rates decline, the receipt of principal repayment must be reinvested at a lower interest rate (i.e., the investor faces reinvestment risk).

Now consider what happens when interest rates rise. The price of a mortgage passthrough security will decline when interest rates rise. However, it will decline more because the higher rates will tend to slow down the rate of prepayment, in effect increasing the amount invested at the coupon rate, which is lower than the market rate. Of course, this is just the time when investors want prepayments to speed up so that they can reinvest the prepayments at the prevailing interest rate. This adverse consequence of rising mortgage rates is called extension risk. Some institutional investors are concerned with extension risk when they invest in a mortgage passthrough security while others are more concerned with contraction risk. Fortunately, redirecting cash flows from a mortgage passthrough security to various bond classes makes it possible to redistribute prepayment risk for investors who want to reduce their exposure to the particular form of prepayment risk for which they are concerned. Because the collateral’s prepayment risk will not be changed by redirecting the cash flows, other investors must be found who are willing to accept the unwanted prepayment risk." -- Frank J. Fabozzi. The Handbook of Mortgage-Backed Securities, 7th Edition (Kindle Locations 6467-6486). OUP Oxford. Kindle Edition.

 

[rajeshtr]

Hi David,
Thanks for the detailed explanation : Ofcourse the duration is extending because of hte delayed payments.. I didn't correlate that Duration increase (delay in payments) will decrease the cost of the bond. Now i am able to correlate. Thanks.

Source : Financial Risk Manager Handbook, 6th Edition by Philippe Jorion

Best Regards,
Rajesh TR.