American Capital Agency Corp. - Book Value Resilience In The Face Of Rates Back-Up

Treasury yields and mortgage rates have backed up massively over the past few weeks. Mortgage-backed securities (MBS) prices have fallen, some by 5 or 6 points. And agency mortgage REITs have been killed, the implicit logic being that leverage of 7 or 8 times on something falling like a rock can't be good. American Capital Agency Corp. (NASDAQ:AGNC), in that respect, is the poster child of the entire mortgage REIT market.

Many investors and analysts have followed this simple logic, (leverage x MBS price drop) modulo some fudge factor, in order to estimate book value losses on mREITs. Analyzing the drivers of agency mortgage REIT value (MBS, TBAs, specifieds, repos, swaps, swaptions, caps, floors, etc.) is complicated -- it takes many years of intense daily focus for people in these various fixed-income and derivatives markets to really understand the way they operate and interact. It's natural that those without the appropriate tools and framework should resort to what is perceived as reasonable approximations.

However, this approach leads to materially wrong conclusions. Mortgage REITs are a leveraged difference: long MBS, short hedges, times a lot of leverage. What accuracy can we expect if we take an approximation, subtract another approximation, and multiply all that by a leverage of 8?

In stable market conditions, making such extreme approximations is not necessarily a huge issue, because the prior quarter is probably not a bad estimate for the current quarter. In such conditions detailed analysis can to some extent help with better precision (some REIT's assets could be marginally better than some other REIT's, for example). But when large market movements occur, significant non-linearities develop, and one cannot just extrapolate anymore, proper analysis is essential.

Based on the non trivial analysis I lay out below, I derived an estimation that AGNC's BV as of the 20th close is about $27.25 per share before dividend payment, reflecting a significant loss on the assets, and compensating gains on the hedges. This implies that the current market price puts it at a significant discount to book.

In this article I am not going to define terms that can be found on Wikipedia. If you do not already know what effective duration, OAS, swaps, swaptions, negative convexity are you should read up. As a random example for MBS, the University of Minnesota has some course material here. I really think it is not a good idea to make investment decision on mREITs without understanding these concepts.

Analyzing mortgage REITs. For real.

Now, what do I call proper analysis? Quite simply, pricing and analyzing all the moving parts inside a REIT (and in particular inside AGNC), the same way they would be analyzed and priced by the REIT itself, or by a major broker/dealer. Pricing complex instruments always implies making some form of approximation from a yield curve spline to fitting a volatility surface. My design goal here was that these proxies should be close enough to market practice.

In other words, I want to be able to say where book value is projected to be, as a function of market conditions at any point in time. In addition, I want to be able to measure that BV's exposure to a wealth of different risks. What happens if rates move up by some amount, in parallel? What if the curve steepens? What if the basis widens? What if swaption implied volatilities decline?

However, as astute readers should be quick to point out, agency mREITs do not give investors a detailed view of their positions, line by line. They do, however, provide hundreds or thousands of individual data points. For example, take AGNC's quarterly report, or quarterly presentation. There is detailed information on each MBS coupon they hold (amount, characteristics like average LTV, age, etc), on each swap maturity, rate, notional, etc. Hence my approach has been that every single piece of information such as these must somehow be reflected in the analysis.

The overall logic is to build a portfolio of representative positions (MBS, swaps etc.) such that all of their characteristic, whether in aggregate, for various subsets, or for certain individual lines, match the data points obtained from the quarterly report or presentations as closely as possible. This is done through a complex mathematical optimization. The main point here is to realize this is a quantitative problem, not black magic. Big computers are all that's required. For my analysis of AGNC, I used about 200 separate types of mortgage-backed securities, and solved for the optimal weights among these that best captured AGNC's book as of the end of Q1. The non-automatic and painful aspect in this part of the process is to take each data point (each relevant number in the quarterly), and turn that into a constraint in a modeling sense.

On the derivatives or hedges side, it is in fact easier, because these products are more standardized, so their pricing does not have to be so customized as for MBS. They are also listed in slightly aggregated form in the quarterly presentation.

Now, how do I "properly" value all these different elements? The main idea is to build an entire pricing system, just like the ones the larger banks use in their fixed-income businesses, but with some adjustments that make them more adapted to analyzing mortgage REITs.

Here are some of the typical products that we need to value, and I explain the main ideas.

Swaps

Swaps are the simpler of these different products, and their valuation is tedious but not very complicated. At a market close, one can see swap rates for certain standard maturities (see for example the WSJ's site). Based on these rates, and certain theoretical constraints, one can build an entire "curve", that will say where any swap would be priced, using a standard so-called "spline" method that interpolates unknown points in a smooth way.

Note that we do not model swap rates per se, but rather forward swap rates, and in particular forward spot swap rates: the rate, agreed upon today, at which you would do an extremely short swap starting at some future point in time. This Seeking Alpha article explains some of the relationships between forward rates and commonly understood interest rates.

The pricing of a swap is then simply the difference between the present value of its receiving leg, and the present value of its paying leg, where these present values are taken at the forward spot rate. A standard swap, at the date when it is written, will have a value of 0. Over time, as its maturity becomes shorter, and the entire curve moves around, its value will change by (very approximately) 0.9 x (maturity in years) x notional x change in swap rate in %.

An example of actual valuation is the $3.2bb notional of 10-year swaps that AGNC had at the end of Q1, 2.17% payer, which at that date would be valued -30.8mm, and would now be at +146.7mm. (Logically up since swap rates went up).

Swaptions

Swaptions are options to enter swaps. Stock options, that most people are familiar with, are quoted in price. Swaptions are quoted in implied volatility, typically in a 3-dimensional matrix (hence called a "vol cube") as a function of maturity (for how long the option lives), tenor (how long will the swap be that the swaption gives a right to), and moneyness (depending on the rate of the swap the swaption gives a right to).

Building a swaption pricer is more complicated than a pricer just for swaps, but is a fairly well known process. Textbooks and research articles cover the subject in detail (just type "swaption pricing" in Google). First, one needs a stochastic interest rate model -- that is some logic that generates random future interest rates according to certain parameters. Then, we solve for the parameters in question so that the value of the swaptions given by the market coincides with the values that would be derived from the model with these parameters. Then, "inside" that calibrated model we can reprice any swaption pretty well. Of course in reality the true value of any derivative will only be given by a hard bid from a market counter-party to unwind that trade. But following the same modeling approach as most banks, we should be pretty close.

One example: the $5bb notional swaptions with a 2.5 years maturity, ~8 years tenor and 3.42% strike would be priced at $86mm at the end of Q1, and $205m now - significantly up as it gets closer to the money, and with higher implied volatilities.

Generic MBS or TBAs

Then let's address the more generic parts of the MBS market. There are daily, and even intraday prices on these products so they are very important inputs in our analysis.

While swaps and swaption pricing in spite of their complexity, can be found in textbooks, MBS are one notch above in terms of complexity. Their valuations starts the same: we use the calibrated interest rates dynamic processes mentioned earlier.

On top of that we need to model mortgage rates. This is done by modeling the relationship between the swap rate curve and mortgage rates. There are a few different approaches used across the Street for these relationships, we take the simplest -- a non-linear function, statistically estimated. Then we naturally obtain projected mortgage rates (in a fashion theoretically consistent with swaption prices). Some banks use an endogenous approach where future rates are indirectly determined by the theoretical future fair value of MBS, which allows for more precise valuations on IOs, inverse IOs and other levered products. This added complexity is not worth it for us, since we are not looking to value very levered mortgage derivatives (these products are seldom found on mREITs' balance sheets).

At that point, we get to the more difficult aspect of MBS modeling: prepayments. Again, following standard Street modus operandi we use several years of historical prepayment data across all products (about 60k data points) and fit a fairly basic non-linear prepayment model (by Street standards). This model relates prepayment speeds to a large number of pool variables, such as the rate paid by borrowers, how far that is from the prevailing market rate (knowing there is a lag between being exposed to a lower market rate, and when the refinancing is effectively processed), LTV, loan size, credit characteristics (FICO scores), and many other variables interacting in various ways.

Using the calibrated simulated interest rates and mortgage rates processes, for every possible MBS of interest (defined by its characteristics such as coupon, origination date, rate paid by the borrower, etc) we can generate projected prepayments. With these prepayments and other product characteristics we can then generate cash flows. Then, we solve for the spread added to spot rates so that the present value of these cash flows equals the market price. This spread is the Option Adjusted Spread. A very good reality check of the model at this point was to compare these OASs at different points in time with Street OASs, and they all fell within a few basis points across the board, with the typical patterns of tight OASs on lower coupons and increasing OASs on less liquid higher coupon TBAs.

So what we have here is an analytical method that relates interest rates, mortgage rates, swaption volatilities, and certain MBS in a consistent fashion. Hence, we can look at what happens if we tweak certain inputs. How would such and such MBS be affected by a change in rates? Easy, we move the rate in question, and recalculate everything all the way down to the MBS price fixing the OAS (which is the most invariant inputs of all), and see what the resulting price impact is on the MBS.

A valuation example is shown below: the OAS on FNMA 4s over the past few days. The jump on 6/13 is likely due to the change in settlement date of TBAs. Overall, we can see that it has not really moved much until Thursday's close. This means that in spite of everything that has happened, the relative value of these MBS has not moved around that much. They are not particularly cheaper or richer in general. FNMA 4s did richen eventually, since they are becoming the purchase coupon of choice, since with mortgage rates above 4% they will become the main origination coupon.

Also shown is the duration. Clearly, it has extended, which is naturally a consequence of the higher interest rates all over.

Date	FNMA 4s OAS	FNMA 4s duration
6/7/2013	2	3.9
6/11/2013	-1	3.9
6/12/2013	1	4.0
6/13/2013	10	4.1
6/14/2013	8	4.0
6/17/2013	5	4.0
6/18/2013	5	4.0
6/19/2013	1	4.3
6/19/2013	-8	4.4

Click to enlarge

Specified or off-the-run MBS

In order to do a comparable analysis on more esoteric pools (like HARPs, low FICOs, Investors, etc.) the prepayment models are further refined so that they can explain the differences in prepayment behavior due to certain particular borrower characteristics. These specified pools' values are not as easy to obtain on a daily basis as TBAs, since they are not as liquid and disseminated.

For these products, we carry out a pricing at month end, and intra month use (again, a fairly generic approach in this business) the changes in OASs from more liquid coupons in order to effect a change in OAS on the specifieds. From that, we can entirely reprice them.

Determining or computing the characteristics of all the various specifieds is important also in figuring out the optimal representation of AGNC's book, since some of the information provided (such as average LTV, or average loan size etc) must be matched to these characteristics.

Computing book value

Determining the change in book value is not simply based on a change in value on these products. We also need to account for carry. An MBS or derivative position generates cash through coupon payments for example. But actual prepayments also create a loss on premiums, and a gain on discounts. We hence compute these cash flows using either the historical observed prepayments on the representative cohorts, or projected prepayments when they are not yet reported. Principal returns are reinvested in the same products at the then market price.

Our logic also tells us what book value would be, without any active management. One could expect that proper management will actually add value over what we estimate. But this is not always necessarily the case. The same approach, applied between Q4 2012 and Q1 2013 on AGNC led us to project a drop in book value by about 6%, instead of the 8% and change they reported. The difference did not seem, however, related to changes to portfolio composition (or "management") but rather to certain derivatives valuations. Still, we were in the ballpark.

Looking at AGNC's Q1 book, as of 20th close (hence stale by a day), we obtain the following numbers:

- A drop in asset value by $2.9bb (over 3 points of face value), plus income of $780mm, and a loss of premium around 153mm (due to prepays), for a total economic value added on the asset side of -2.28bb

- Derivatives carry and repo cost total of 245m, but a gain on derivatives and hedges (swaps, swaptions, short Treasurys) of $2.0bb, for a total derivative, financing and hedge contribution of 1.83bb

So a net of -520m, which including management fees would be about -570mm. This is a drop of roughly 5%, and would put book value per share around 27.25 before dividend payment.

A curve steepener by 50bps or a parallel move by the same amount would result in an additional loss of 190m and 275m respectively. So the net book, conservatively assuming no particular adjustments would have been made since Q1, does not have a very strong duration or convexity exposure. This is the positive result of massive swaption positions, whose positive convexity and vega exposure (benefit from increases in implied volatility) largely compensate the negative aspects inherent in MBS.

Thanks to the mechanics of derivative hedges, as they are intended to work, movements in rates have some impact, but it is not very significant. The true risks lie in the relative value of mortgages. For example, if all OASs widened by 50bps (and mortgage rates also increased in direct relation), BV would be $2.5bb lower.

The conclusions are naturally dependent on the many assumptions going into these calculations. There are too many detailed assumptions and caveats going into these calculations to list them here, but I'd summarize as follows: don't trade what you don't understand, and do your own analysis.

Conclusion

This analysis here is not arguing that AGNC is a perfect investment, or that they could weather all storms. As a matter of fact they are quite exposed to many risks, just not the ones people seem to focus on.

So, what are these "real" risks? The main one that I would worry about is basis risk.

If mortgages cheapen relative to swaps and swaptions (we say the basis widens), then lower / middle coupons will suffer directly in a manner that mREITs will not be able to hedge. Only higher coupons or a combination of middle coupons and IOs would help in such a situation, and these are generally not found on REITs' balance sheets (not in size in any case). My analysis on AGNC tells me that each basis point of OAS widening is a little less than 0.5% drop in book value.

I think that mortgages will not cheapen up for some time, probably until the Fed really starts its tapering by not reinvesting pay-downs. But I monitor it regularly, since it could have so much bearing on book value.

Disclosure: I am long AGNC. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.