Interest rates have been increasing at a rapid pace over the past few months and this past Friday's positive surprise in Non-Farm Payrolls helped long rates reach a multi-year high. Consecutively, investors punished mREITs by pushing prices to an all-time low. I can only speculate on the rationale for the sell trade, but some of the sentiment of many individuals seems to focus around concern that book value has and will continue to erode under the increase in interest rates. Contrary to stock price performance, American Capital Agency (NASDAQ:AGNC) has not expressed the same fear as its investor base. And what support do I have for that statement? They hedge.

I'm definitely not the first to point this out, but it seems odd that there is very little focus on a critical aspect of AGNC's strategy. Perhaps it is because hedging appears to be a black box or an esoteric concept that does not apply to reality, but it is used in the real world from the most sophisticated of investors to your small local community bank. In each of AGNC's formal presentations they makes an effort to highlight the net exposure of their assets, liabilities and hedges to changes in interest rates. They use a metric called duration gap to highlight how much of their exposure is hedged. In addition, AGNC also simulates the impact of their NAV for a given change in interest rates. Both metrics estimate an impact that is significantly less than the change in stock price. My goal is to use AGNC's provided data to illustrate that they structure their hedging activities to offset interest rate risk and the margin of error that AGNC's hedges must have to justify the current stock price is large and unlikely.

## How Does AGNC View the Expected Performance of Its Hedges?

The concept of duration gap touches on the net sensitivity of AGNC's assets, liabilities and hedges to interest rates. To understand this, let's review the concept of duration. The actual computation of duration can become complex when it comes to MBS, but the simple definition of duration is the % change in price for a 100bps change in interest rates. Duration can also be roughly interpreted as the weighted average investment or borrowing on the yield curve. Applying this understanding to AGNC's duration gap we can see that as of 4/30/2013 the duration gap of -0.2 (slide 14 of Q1 presentation) implied that assets are invested roughly 0.2yrs shorter than liabilities and hedges. This also implies that for a 100bps increase in interest rates AGNC's market value as a % of total assets should increase by 0.2%. Shown below is an illustrative example of how to interpret duration gap.

*click to enlarge images *

However, duration gap only highlights some of the interest rate risk. Looking at the same table as the 4/30/2013 duration gap, we can see that duration gap shifts from -0.2 to positive 1.2 under a 100bps interest rate increase. The table shows that the duration gap increase is due to mortgage assets increasing in duration, while being partially offset by swaptions. This is the concept of negative convexity or extension risk being hedged by swaptions. We can see that the entire risk is not being hedged, so an increase in interest rates should have an impact on BV. The change in duration gap as interest rates change provides us with valuable information on how MV sensitivity to rates switches from a benefit to a cost as interest rates rise. Illustratively we can see below what price sensitivity would look like if duration gap shifted instantaneously at +50bps.

In reality mortgages do not extend instantaneously at a single rate point, so we can assume that mortgage extension and the increase in duration gap occurs continuously. Using some basic calculus and textbook finance concepts we can approximate the price impact if the change in duration gap were continuous based on the following formula:

MV Change as % of Total Assets = (Duration Gap)*(Δ in Interest Rates)/100*(MV of Total Assets)-(Δ in Duration Gap +100bps)*(Δ in Interest Rates)^2/100*(MV of Total Assets)

For a 100bps increase in rates, the price impact would now be +0.2% due to the initial duration gap of -0.2 and a -1.4% due to the change in duration gap to 1.2. The net result is a -1.2% impact to Market Value as a % of total assets. Shown below, we can illustratively view the price sensitivity as duration gap changes.

So far, based on the risk levels estimated and provided by AGNC, the impact of higher rates is significantly lower than that implied by the current stock price. For example, the duration gap and change in duration gap provided by AGNC as of 4/30/2013 would imply a value decline of 1.2% of total assets and adjusted for leverage of ~8x a decline of 9.6% of common equity. This implies that AGNC should not be overly concerned about higher interest rates as they believe that they are well hedged.

## Accounting for Risk Exposure Not Offset by Hedges

The risk exposure that AGNC does not actively hedge is the spread between MBS and Swap rates. An example of this risk would be when MBS yields increase relative to swap rates. We can think of the MBS yield as the discount rate for MBS and when discount rates increase asset values fall, among other impacts. Therefore if the spread between MBS and swap rates widen, asset values will decline relative to hedges and liabilities regardless of the duration gap. To get a feel for this exposure we can look to the AGNC's mortgage asset duration of 3.6 as of 4/30/2013, which would imply a 3.6% decline in MV as percent of total assets for a 100bp widening in MBS yields relative to swap rates. A common way to roughly estimate the change in MBS spread is to compare MBS yields to 10-year swap rates. MBS yields can be calculated by interpolating the coupon of MBS bonds trading above par and below par to arrive at the theoretical yield for a par bond.

Other risks such as volatility and curve positioning exist, but are not as large of an exposure as the discussed risks and are beyond the scope of what is explained in this article.

## Combining the Key Risks to Illustrate BV Sensitivity

We've established that AGNC hedges their MBS portfolio and if correct should be for the most part protected from interest rate increases. We also know that they are exposed to spread risk as mentioned above and discussed in their presentations and financial releases. With this understanding of AGNC's risk exposure was the recent decline in stock price reasonable?

We can conduct a back of the envelope analysis using the concepts above to test the market hypothesis implied by the current stock price. Assuming that AGNC's risk metrics are reasonable we can illustrate how BV could have changed and build intuition around the dynamics of their balance sheet. Duration gap, change in duration gap and mortgage durations can be used to estimate sensitivity to recent increases in interest rates. In order to keep this illustration simple we need to make a few high level assumptions.

- The 10-year swap rate is a reasonable proxy for the change in interest rates
- The difference between 30-year MBS Par Yields to 10-year swap rates is representative of mortgage spreads
- AGNC does not rebalance their position between horizon dates in our illustrative simulation (the horizon dates are based on dates with reported risk metrics from AGNC)
- Exclude effects such as volatility, interaction between spread risk and extension risk, carry, and change in value of pay-ups on specified pools
- 3/31/2013 EOP shares outstanding are estimated based on Common Equity/BV Per Share
- Shares outstanding remain unchanged

Despite the simplifying assumptions a level of conservatism is maintained. For example AGNC employs active management/hedging and most likely would rebalance their position in light of increasing rates, thus experiencing a lower amount of risk exposure vs. the risk due to periodic rebalancing at the time horizons shown below.

In the tables below duration gap, change in duration gap, mortgage durations and market rates are tracked for periods in which risk data was provided by AGNC. 1) In a similar fashion as discussed above, changes in 10-year swap rates were applied to duration gap and duration gap change metrics to estimate periodic impacts to MV as a % of total assets. 2) A similar calculation is applied to mortgage durations using the change in Mtg. spreads to estimate basis impact as a % of total assets and also using MBS yields to estimate the MV of total assets in each horizon period. 3) Each of the impacts as a % of total assets were converted to dollar amounts based on the estimate MV of total assets and then applied to common equity over each period. 4) Common equity is then divided by shares outstanding to arrive at BV per share.

## Illustrative Application of AGNC's Risk Metrics

## Data Sources and Calculations

The back of the envelope estimate of BV illustrates the effectiveness of hedges and alludes to the idea that the recent decline in stock price is overblown and irrational. Notwithstanding the simplistic nature of this analysis and the potential for AGNC's risk metrics to have some error, the margin of error must be fairly large to justify a price of $20.75 (7/5 Closing).

In order to quantify the margin of error, I stressed the duration gap and duration gap +100 estimates provided by AGNC to arrive at a BV near last Friday's closing price. To be conservative I applied the stress to the horizon points after 3/31/2013 to stress only periods of rising rates. Based on this, duration gap, duration gap change and mortgage durations would have to be off by 1.3 to justify a $20.75 BV. Due to the predictable duration of repos, swaps, swaptions and treasury futures this implies that the error would be in the firm's MBS, which I find hard to believe given the expertise and resources available to AGNC. To put into perspective there are estimates of MBS durations readily available by all major broker dealers, Bloomberg and historical observations in the market place (one could calculate historical price sensitivity to interest rate changes). Based on this, I find it hard not to believe that AGNC is trading well below book.

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