Interest rate risk is the largest risk and return factor for Agency Mortgage Real Estate Investment Trusts ("AMREITS"). In particular, AMREITS that invest primarily in fixed rate MBS are presumed to have large amounts of interest rate risk exposure; however, there seems to be an inconsistent view of what drives AMREIT interest rate risk, the role of hedging and how that impacts return. This article seeks to define and explain the sources of interest rate risk for MREITS and relate them to economic return. This article also applies these concepts to American Capital Agency to explain the trends in net spread and return.

**MBS Valuation: Decomposing MBS Value and Yield**

Before we define the types of interest rate risk, we'll need a basic understanding of mortgage-backed securities ("MBS") valuation. This supplemental background is helpful in that it aids in building an understanding around why certain hedges are used and how MBS are impacted by interest rates.

MBS are valued by discounting stochastic cash flows relative to a market discount rate. This means that MBS cash flows are discounted across multiple scenarios to arrive at a value. The reason for this is the underlying mortgages within a MBS are allowed to prepay. Specifically, mortgage borrowers prepay when interest rates fall below their current mortgage rate to provide them a payment savings in excess of their closing costs. This prepayment option has positive value to the borrower and negative value to the MBS holder.

As a result, interest rate scenarios need to be determined for valuation. The base interest rate scenario is determined from the shape of the yield curve today. The other interest rate scenarios for MBS valuation are determined using interest rate options, which are priced based on an expectation on future interest rate volatility. An expectation of volatility around the base interest rate scenario simulates possible interest rate moves that may trigger the prepayment option exercise.

Once the interest rate scenarios are defined, a prepayment model is used to estimate the cash flows across each scenario and the cash flows are discounted. The discount rate is calculated as a rate off of the yield curve plus a MBS spread plus an option cost spread. The reason for this discount rate build up is that MBS exhibit the risk of several market instruments, including a fixed rate bond and a prepayment option (interest rate option).

Â· The market yield curve is the yield for a comparable risk free bond of a similar duration or term.

Â· The MBS spread is due to MBS requiring a yield higher than the market yield curve due to the incremental liquidity, credit and other non-interest rate risk factors embedded in MBS.

Â· The option cost spread is the additional yield to compensate the MBS holder fairly for the prepayment option risk.

Once the present values are determined for each scenario, the average value is calculated as the market value for an MBS.

**Figure 1: Fixed Rate MBS Valuation Process**

*Key Takeaways from MBS Valuation*

Based on the MBS valuation process we can make several key takeaways:

1) MBS Yield (Discount Rate) = Market Yield Curve + Option Cost + MBS Spread

a. The yield for the Fixed Rate Bond portion of MBS = Market Yield Curve

b. The yield for the Prepayment Option portion of MBS = Option Cost

c. The yield for the Non-Interest Rate Risk Factors of MBS = MBS Spread

2) MBS Value = Fixed Rate Risk Free Bond Value - Prepayment Option Value - Non-Interest Rate Risk Factors Value

Incidentally, interest rate derivatives and repo agreements are valued in the same fashion as MBS. Interest Rate Swaps and Repos can be compared to the fixed rate risk free bond portion of MBS. Interest Rate Options such as Swaptions can be compared to the prepayment option portion of MBS. AMREITs actively decompose the risk factors that make up MBS and offset them with interest rate derivatives. Essentially, they are then able to tactically choose the risk exposures they like and offset the exposures that they do not like.

**AMREIT Interest Rate Risk 101**

As discussed, MBS value and yield can be decomposed into several components. This same attribution can also be applied to the entire balance sheet. As it turns out, the value and yield components are driven off of the factors that make up interest rate risk. By attribute the different interest rate risk factors an AMREIT is taking, we can also attribute how they generate their returns. The first interest rate risk factor is yield curve risk, which drives the yield of the fixed rate bond portion of MBS. The second interest rate risk factor is option risk, which directly relates to the mortgage prepayment option and swaptions. The third interest rate risk factor is basis risk which is related to MBS spreads. The total of these three interest rate risk factors make up total yield and total interest rate risk. Figure 2 below illustratively shows how each component of an AMREIT's balance sheet adds or reduces each interest rate risk exposure.

**Figure** **2: AMREIT Balance Sheet and Interest Rate Risk Factors**

__Yield Curve Risk__

Investing and borrowing on different points of the yield curve creates yield curve risk. This risk is measured by using the duration metric. A duration of an asset or liability can be thought of as the weighted average investment or borrowing on the yield curve. For example, a 5-year bond will have a duration of roughly 5 and the yield due to yield curve risk will be roughly the 5-year rate on the yield curve. Duration can also be used to measure price sensitivity to interest rates, where duration indicates the inverse percentage sensitivity to a change in interest rates. Using the same 5-year bond example, a 5 year duration and 1% increase in interest rates will result in a 5% decline in market value.

Yield Curve Risk manifests itself when the duration of assets and liabilities are mismatched to result in a large duration gap. A large positive duration gap may occur if an AMREIT invests in long duration MBS and funds using short duration repo. A large positive duration gap generates positive income due to the spread between a long rate on the yield curve and a short rate on the yield curve, but is exposed to rising rates as short rates re-price, while long rates stay constant.

In reality, AMREITs do not maintain a large duration gap. The use of hedges, specifically interest rate swaps offset this risk. A pay-fixed and receive-float interest rate swap effectively convert an AMREITs short-term repo funding into longer-term fixed rate funding to match the duration of MBS. Shown in figure 3, MBS funded by repo and hedged using interest rate swaps results very little yield curve risk.

**Figure 3: Investment, Borrowing and Hedging on the Yield Curve**

__Option Risk__

This risk is driven by the embedded prepayment option in MBS. Prepayment option risk manifests itself in the form of higher prepayments as interest rates decline to cause reinvestment at lower yields or lower prepayments as interest rates rise to result in an increase in duration and a valuation decline. The latter is currently the most widely discussed concern and is often referred to as extension risk.

AMREITs actively hedge option risk. However, they further decompose option risk into two components. The first option risk component is __negative convexity__, which refers to the rate at which duration changes as prepayments and interest rates change. A simple way to think of this is if the duration of MBS increases from 4 years to 6 years when interest rates increase 100bp, the 2 years of extension is due to negative convexity. The second option risk component is __volatility__, which refers to the length of time at which the option can be exercised. This is important as an option that is available to exercise for longer of periods of time will benefit from future volatility as it increases the potential that the option will be exercised.

AMREITs partially hedge both components of option risk with swaptions, which are options to enter into an interest rate swap at a certain price. An example of the use of swaptions would be if rates increased and the duration of MBS extended, swaptions would serve as a contract to enter into a longer swap at a rate lower than market to prevent a duration mismatch.

A large swaption position directly addresses negative convexity; however if the expiration term of the swaptions are short, volatility remains unhedged. This is typically the case with AMREITs, in which swaptions are used to offset a large portion of negative convexity, but the expiration terms of the swaptions are much sooner than the terms of the mortgage prepayment option. This leaves open the risk that interest rate volatility increases in the future to result in the increase in the cost of swaptions, which will reduce economic return if AMREITs continue to want to hedge prepayment option risk. However, by not entirely hedging volatility the option cost collected from MBS exceeds the hedge cost of using swaptions to enhance spread income.

__Mortgage Basis Risk__

This risk is defined as changes in MBS spreads, which is the spread (excluding option cost) between MBS and the market yield curve. Agency MBS spreads are typically very tight and might range from 0-50bps for liquid fixed rate MBS. The tight spreads reflect the incremental non-interest rate risk above government bonds, which usually focus around liquidity. Changes in MBS spread or the "mortgage basis" results in valuation impacts that are not be offset by interest rate derivatives.

The unique aspect of basis risk is that most AMREITs currently __do not__ extensively hedge this risk. The reason for this is that there aren't many easily available and liquidly traded offsets. Without getting into detail, products such as IO strips and mortgage options are available, but are very costly. Another option is MSRs, which I plan to discuss in a future article. In any case, this represents a material risk for AMREITs, particularly as Fed tapering and issues in the bank space could potentially cause the MBS basis to widen and cause valuation declines that will not be offset by interest rate derivatives.

**AMREIT Interest Rate Risk Conclusion**

The yield on MBS, funding and hedges can be attributed due to different interest rate risk factors. Increasing exposure to these risk factors enhances yield and net spread. AMREITs hedge some of these factors such as yield curve risk, which results in no incremental spread. Other factors such as option cost are somewhat left unhedged and generate the bulk of an AMREITs spread and profitability. Simply put, AMREIT net spread is a function of the level of interest rate risk exposure and the specific interest rate risk exposures that AMREITs take are deliberate and tactical.

**Evaluation of American Capital Agency's Interest Rate Risk Exposures**

Based on the wide array of information provided by American Capital Agency ("AGNC"), we can conduct a simple review of the changes in their risk exposures and net spread. From Q2 to Q3 AGNC experienced a decrease in net spread despite a stable book value. This has sparked some concern over the sustainability of the current dividend level as well as the future prospects for AGNC. However, based on the stable book value and analyzing the change in AGNC's balance sheet the reduction of spread can be explained by a tactical shift in AGNC's risk exposures. This shift to reduce certain interest rate risk factors results in lower net spread and expected ROE, but does not prevent AGNC from repositioning back to past risk levels to increase potential ROE in the foreseeable future. Below I compare the changes in AGNC's key risk factors to illustrate how the reduction in spread is accompanied by a reduction in the overall level of interest rate risk. I use comparison from Q1 to Q3 as these periods reflect the tactical shift in AGNC's interest rate risk positioning.

**Yield Curve Risk**

Exposure: Low-Moderate (From Low in Q1 2013)

Contribution to Expected ROE: Low-Moderate (From Low in Q1 2013)

As of Q3, AGNC's mortgage asset duration of 4.8 is offset by their liability and hedge duration of -3.9 to arrive at a duration gap of 0.9, which is up from 0.5 in Q1 2013. For illustrative purposes, we can simplify this by saying AGNC's weighted average investment is on the 5-year part of the yield curve, while their weighted average borrowing is on the 4-year part of the yield curve. Based on this, we can say that AGNC is taking on slightly more yield curve risk, which should slightly increase net spread and expected ROE.

**Option Risk - Negative Convexity**

Exposure: Low (From High in Q1 2013)

Contribution to Expected ROE: Low (From High in Q1 2013)

AGNC's Q3 duration extension for a 200bps increase in interest rates is 0.2 years, which is down from 2 years on 4/30/2013. This is a significant reduction in negative convexity, which is due to the reduction of 30-year MBS and TBAs in favor of 15-year MBS. MBS with shorter remaining terms have less negative convexity due. This reduction in negative convexity results in the collection of less option cost spread from AGNC's MBS and significantly reduces net spread and expected ROE.

Source: Pg. 14 of Q1 2013 and Q3 2013 Investor Presentations

**Option Risk - Volatility**

Exposure: Moderate (From High in Q1 2013)

Contribution to Expected ROE: Moderate (From High in Q1 2013)

AGNC's Q3 swaption position remained fairly unchanged from Q1. The majority of swaption expiry terms are within 1 year compared to the longer prepayment option terms of MBS to indicate very little volatility risk offset. However, volatility was reduced on the asset side as 30-year MBS and TBAs were reduced in favor of 15-year MBS. The allocation shift increased 15-Year MBS from roughly 30% of MBS market value in Q1 to over 50% of MBS market value in Q3. The shorter remaining term on 15-year MBS result in lower volatility risk as the prepayment option exercise is available for a short period of time relative to 30-year MBS. This reduction in volatility results in the collection of less option cost spread from AGNC's MBS and significantly reduces net spread and expected ROE.

Source: Pg. 23 and 28 of Q1 2013 Investor Presentation and Pg. 11 and 26 of Q3 2013 Investor Presentation

**Mortgage Basis Risk**

Exposure: Moderate (From High in Q1 2013)

Contribution to Expected ROE: Low (From Low in Q1 2013)

AGNC's mortgage basis risk is slightly reduced with the reduction of 30-year MBS and TBAs in favor of 15-year MBS. This is due to 15-year MBS being less sensitive to changes in spreads. However, this risk still does not have a hedge offset and represents one of the larger exposures for AGNC.

**AGNC Interest Rate Risk Conclusion**

AGNC slightly increased their duration gap since Q1, which incrementally enhances spread and will result in additional income if rates stay range bound. However, by moving from 30-year MBS to 15-year MBS AGNC gave up a significant amount of spread income due to option cost in order to reduce both negative convexity and volatility option risks. The reduction in option risk better positions AGNC for future interest rate volatility and large shifts in interest rates. The shift from 30-year MBS to 15-year MBS also reduced mortgage basis exposure. In sum, AGNC gave up spread income to position itself for future interest rate volatility and spread widening based on the expectation of Fed tapering. Once this passes and they put risk back on the table their net spread and dividend should eventually follow. Until then we should expect a more stable book value and a temporarily smaller net spread.

**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.