Prepayment effect on bond prices and causes of prepayment.

[jdg123]

I understand that as interest rates go down, homeowners are likely to prepay and thus, holding an MBS is worse than holding a regular treasury bond. However, I am trying to understand why it is worse to hold an MBS than a regular treasury bond when interest rates rise. In my mind, an MBS holder is short a call option on bond price. However, as bond prices go down (yields rise), that call becomes worth less and less. I don't see how this hurts the MBS holder.

Also, I am trying to understand how increases in housing prices would cause an increase in prepayments. If the borrower takes out additional equity, isn't that the opposite of a prepayment?

 

[David Harper CFA FRM]

Hi jdg123,

It's a great point, I struggle with the dynamics of mortgage/MBS at higher yields, where the negative convexity seems far less intuitive. I don't pretend to have this mastered. I think the "worse than" comparison is complicated by the definition of what exactly we are comparing to. I see three perspectives:

1. I think the bald assertion is illustrated by, for example, my question 105. In the MBS pricing model, we easily achieve a negative convexity at higher yields (lower bond price) simply by decreasing the prepayment assumption from 100% PSA to 50% PSA. A study of the pricing model (Veronesi's Table 8.3), for me, really clarified this: if you increase the yield and lower the PSA, you discount more future principal (less prepayment) at higher discount rates. Here is Fabozzi's explanation of the same:

"Since prepayments increase as bond prices rise and market yields are declining, mortgages shorten in average life and duration when the bond markets rally, constraining their price appreciation. Conversely, rising yields cause prepayments to slow and bond durations to extend, resulting in a greater drop in price than experienced by more traditional (i.e., option-free) fixed income products. As a result, the price performance of mortgages and MBS tends to lag that of comparable fixed maturity instruments (such as Treasury notes) when the prevailing level of yields increases. This phenomenon is generically described as “negative convexity.” The effect of changing prepayment speeds on mortgage durations, based on movements in interest rates, is precisely the opposite of what a bondholder would desire. (Fixed income portfolio managers, for example, extend durations as rates decline, and shorten them when rates rise.) The price performance of mortgages and MBS is, therefore, decidedly nonlinear in nature, and the product will underperform assets that do not exhibit negatively convex behavior as rates decline." -- FRM assigned (2012) Fabozzi MBS Chapter 1

2. On the other hand, financially sub-optimal prepayments (i.e., behavioral, prepayments are driven by also by housing turnover) reward investors. This turnover (i.e., not refinancing) influence acts in the opposite direction and supports your point. So far then, we have sub-optimal prepayments due to housing turnover (favorable to the investor) outweighed by extended duration hit due to fewer prepayment. Tuckman explains this counter-force:

"According to the figure, the price of the pass-through is above that of the nonprepayable mortgage when rates are relatively high. This phenomenon is due to the fact that housing turnover, defaults, and disasters generate prepayments even when rates are relatively high. And when rates are high relative to the existing mortgage rate, prepayments benefit investors in the pass-through: A below-market fixed income investment is returned to these investors at par. Therefore, these seemingly suboptimal prepayments raise the price of a pass-through relative to the price of a nonprepayable mortgage. These prepayments are only seemingly suboptimal because it may very well be optimal for the homeowner to move. But, from the narrower perspective of interest rate mathematics and of investors in the MBS, turnover prepayments in a high-rate environment raise the value of mortgages." Tuckman Chapter 21

3. Just to include it on a technicality as it would manifest in a M2M trading context: to the extent the prepayment risk is the investor writing a short option, we might keep in mind that the short option is short gamma (convexity) and this is generally "unfavorable" to the short option writer; i.e., if I write you an option with a strike price equal to your mortgage balance, as the fair value of the mortgage decreases, the option value is decreasing (my intrinsic value = -max[0,S-K] while K is fixed and S drops, so a negative becoming less negative) but the negative gamma/convexity refers not to my gain per se, but the decreasing rate of change (the curvature) in my gain. Put another way, as bond prices drop, the call becomes worth less and less to you, but the decrease is decelerating and constraining your M2M loss. We could arguably defend the assertion on these grounds alone; i.e., negative position gamma of the embedded short option.

Re: "how increases in housing prices would cause an increase in prepayments."
I'm not recognizing that assertion, sorry? Source? I think historically there has been an inverse correlation between interest rates and turnover because: lower rates --> higher prices, which in turn correlates to higher turnover (i.e. , more sales --> more prepayments) but IMO, to agree with you, the wealth effect would be ambivalent.

I hope that's a start

 

[jdg123]

In Fabozzi, Introduction to Mortgage and MBS Markets, page 18. It says prepayments occur because of refinancing. It then goes on to say a driver of cash-out refinancing is home price appreciation. Does taking out a home equity loan or an additional loan on a house count as refinancing and also as prepayment? I would have thought if one had a home worth 200K and had 25K outstanding on the loan, if she then took out an additional 50K, it wouldn't be re-financing but simply adding to the loan (or just a new loan).

In response to the short embedded call argument. If one is long a stock and short a call, he would effectively lose if the stock price appreciated a lot (analogous to yield declining and bond prices going up), however, as the stock goes down, he would get longer delta exposure (due to the negative gamma) but never get longer than a pure long stock holder. At worst, if the option is worth zero, then the exposure is equivalent to a long stock holder. That's why I don't understand the analogy that a person who holds a security with prepayment risk would do "worse" than a pure treasury as yields go up. To me, the worst the exposure would be would be the same as a pure treasury without the prepayment option. (although clearly, on the upside, the prepayment risk is very large as yields decrease). Perhaps there is some argument I'm missing related to duration.

I also would think that the negative convexity would turn to no convexity once yields are high enough. Lastly, I would think that the pure treasury would decrease in value more as rates rise, as it started out at a much higher point. With yields very low, the MBS is worth much less than a treasury but as yields go up, they become more equal, so although negatively convex, the starting point is much different and the treasury would fall by a greater amount.

Anyway, perhaps I need to really think about this for a while. It's still somewhat unclear for me.

 

[David Harper CFA FRM]

I think it depends on whether the home equity loan is a second mortgage. I had understood that home equity loans were generally second mortgages that do not necessarily payoff the first ... (although I don't have post crisis knowledge; I am not current) as opposed to cash out-refi that necessarily paid off the first in order to pull out cash.Fabozzi seems to be say that: higher home prices --> greater tendency to cash-out refinance (I don't see him saying "home equity" but rather refinance).

Re: the option: your argument (in my opinion) comports with Tuckman. Please note, unlike Fabozzi, Tuckman has the MBS outperforming (without negative convexity) its non prepayable analog at high yields. Why? Turnover triggers some (non optimal) prepayments which benefit the investor.

But, with respect to the option, I think it's hard to be precise about what comparison we are talking about. A written option itself has negative position gamma. When you say, "as the stock goes down, he would get longer delta exposure," I think this is a bit wrong. If you are the investor, you might be long 100 shares (position delta = +100) and hedged with a short position in 200 options each with percentage delta of +0.5 (option position delta = -200* +0.5 = -100). You are delta neutral: if stock drops by $1, a $100 share loss is offset by a 200*0.5 = +100 option gain. But when the stock drops, then delta drops also (percentage gamma is always positive). Say it drops to 0.40. Now a $1 price decrease only "hedges" the $100 share loss by 200*0.4 = +$80. But that's not exactly what's happening in an MBS anyway: you are initially compensated for the embedded option with a higher yield. And i think the point is: as an isolated component, the negative position gamma of the embedded written option has a lose/lose component, in addition to any duration (first order), if bond prices change. You sold (in part) an option. (Visually, I would tend to think of the option as an additional tweak to the vanilla P/Y curve). If bond prices go up, it gets called to your obvious detriment; if price goes down, diminishing delta mutes your valuation gain.

So, if we think of negative position gamma as a lose/lose component, then the comparison (maybe) is something like. You have a $100 to invest, you can buy either:

• $111 face of vanilla bond (100/90, price of $90), or
• $125 face value of bond with embedded option (100/80, price of $90)

i.e., both have $100 par, but you are compensated initially with the high yield. The price of this includes the lose-lose component that manifests as unfavorable bend in the P/Y curve.

After I re-built Veronese's Table 8-3 model, I understood that varying the prepayment assumption overwhelms the above. It's really more like a basket option which can be exercised at various tranches (50% PSA, 150% PSA). In the true pricing model, the negative convexity at high yields is mostly a function of the lower prepayment assumption extending the duration (to hurt the investor).

 

[jdg123]

Thanks for the replies. I appreciate it.