In this article, I explain why, to a large extent, reasonably hedged mortgage REITs should not be affected by the shape of the curve. Yes, that's right, a REIT that uses derivatives for hedging purposes in a standard manner should not be concerned, at the first order, by the shape of the yield curve. The level of interest rates should not affect them, and a strongly inverted yield curve should not be an issue either. As counterintuitive as that might sound to some, it is a rather direct consequence of putting hedges in place.

Before going into how hedges work, it is important to distinguish the carry, that is how much monthly cash (positive or negative) a position generates, from the gains or losses from changes in market value. Both are strongly correlated, because a product with a very large positive carry will normally tend to compensate that with market value losses over time, and a product with negative carry will normally generate market value gains.

I only address here what could be described as duration hedging, not convexity, which is a bit more complicated.

## Swaps

A swap is a contract between two counterparties by which someone pays a certain fixed percentage (the swap rate) of a reference amount (the notional) over time (until the swap's maturity) in exchange for receiving a payment indexed on a floating rate (the swap index rate, such as Libor). In fact, the actual payment between the two parties is just that of the difference of these two payments.

The swap rate quoted by the market is such that the swap has a value of 0 at the time when it is entered. For example, say today a 10-year swap on 3-month Libor trades at a rate of 2.4%. This means that if I enter such a swap on 10m notional, I do not pay anything and I do not receive anything initially but over time I will have to pay 60k every quarter (2.4% / 4 of 10m) and I will receive (3-month Libor at that time / 4 times notional). When 3m Libor is quite low, say about 0.2% for example, I will only receive 5k leaving me with a net outflow of 55k per quarter. So that is a fair amount of negative carry on this swap.

How come a swap could be so unfair? By quoting the 10 year swap at 2.4% the market is saying in a sense that the average of 3-month Libor over the next 10-years will be 2.4%. Hence, if Libor is very low now it implies that the market expects Libor to be higher than 2.4% at some point. If the yield curve was inverted, it would be the contrary, the fixed rate paid on the swap would be lower than what I collect based on Libor, with the market-implied expectation that this would revert at some point in the future.

By market convention, swaps are not always quoted as a rate, like my 2.4% example, but also as spreads to Treasurys. For example, if the 10-year reference Treasury trades at a yield of 2.25%, then the "10-year swap spread" is 2.4% - 2.25% = 0.15% = 15 basis points. The reason why people think in "spread" rather than in "rate" is that usually, broad movements in the fundamental Treasury yield curve are the main drivers behind swap rates. In other words, the spreads move less than the rates. Still, in times of credit crises (for example back in 1998), swap spreads could gap out massively, even though Treasury yields would not move, or even tighten.

Now how would we reprice a swap over time? Let's say that I have my 10-year swap at 2.4%, but at the end of the week, the market for 10-year swaps is 3%. If I were to do a swap for 10 years minus one week, I'll assume I have the exact same rate for simplicity. Hence, I could write a swap in the opposite direction on $10m, for free, where I get paid 3%. If I did that what would I have?

1 - My prior swap's paying leg where I pay 2.4%

2 - My prior swap's receiving leg where I get 3-month Libor

3 - My new swap's paying leg where I pay 3-month Libor (therefore canceling line 2)

4 - My new swap's receiving leg where I get 3%.

Therefore, after swap rates have moved to my advantage, I could, for free, turn my existing swap into a guaranteed payment at a rate of 0.6% (3% - 2.4%) over 10 years. I would need to compute the present value of these cash flows, but it's intuitive enough to see that this will be around 0.6% times notional times 10 times some present value discounting. In practice on such a swap, this discounting is about 90% of the full value. So due to the market movement I have made about $540k.

Relative to the swap's notional of $10m, I would have made approximately 5.4% of that. Another way to look at this is to say that this swap hedge brings a negative duration of about -9. For each increase in rates by 1%, one gains approximately 9% of the notional amount.

Now, how do these swaps work as good hedges for MBS? There are two essential ways: as financing hedges, and as duration hedges.

## A financing hedge

As we have seen above, a swap written as a hedge pays me some market index, like 1 or 3-month Libor. This index reflects banks funding costs (when not manipulated of course). As thus, it is a natural reference points for banks and broker dealers when establishing repo funding costs. In other words, in normal market conditions (as in no credit crunch or banking system blow up), repo rates are some kind of small spread over Libor.

Therefore, If the total notional amount of swaps I have in place matches the total amount of repos I am using, then the interest rate sensitivity of these repos will be fully taken care of by the swaps. If Libor rates increase, and repos cost me more when they are renewed in 30 or 60 days, the higher payment on the swaps will compensate for that. Also, if repos become cheaper because rates are declining, I am not going to benefit because I will get less money from the swaps.

The financing hedge comes from the floating-rate leg of the swap (the part of the swap where I receive a market index).

## A duration hedge

The second way in which swaps will act as hedges is through their fixed leg.

By being long a sizeable amount of MBS, just like with any other fixed-income instrument, I am exposed to interest rate risk. If rates go up it means that the fixed coupon on my assets will look less attractive that previously, and their value will go down. And reciprocally. This has been quite clear with the recent back up in Treasury yields, swap rates, and mortgage rates. MBS prices on lower coupons went from around 103 to around 98.

As we've seen, in such a situation, a swap that was entered as a hedge would see its value rise significantly, compensating the loss on the assets more or less depending on its notional and duration.

## Balancing the right amount of swaps

Since the leverage provided by a swap on the level of interest rates is a direct function of its maturity there are many ways in which to construct a hedge portfolio. Schematically, 5 years of duration on the assets could equivalently be hedged with 5 years swaps, a lot more of 2 years swaps, or half the amount in 10-year swaps. Various maturities can also be mixed, for example some 2, 5, 7 and 10-year swaps resulting in an average duration of 5 years.

Another constraint is that the total notional amount of swaps should be close to the total amount of repos, so that the financing hedges work as intended.

## Why rates are irrelevant to a reasonably hedged REIT

At the first order, the shape and level of the yield curve are irrelevant for a REIT. This might sound very counterintuitive. How on Earth could a REIT make money if it borrows 2 points higher than the yield on its assets? Let us consider an actual example, with some simplifications.

Let's first describe a presumably good environment for leveraged investing where Libor is at 0.5%, the 10-year swap rate at 3%, and 30-year MBS yield 4.2% (120bps over swap rates). We're considering that these are low coupon MBS with little convexity exposure and long durations so we'll just need 10-year swaps to hedge them. Repo rates are 0.7%, that is about 20bps over Libor. Some people would think that mREITs here would get 4.2%, minus 0.7% in financing cost, hence 3.5% of net spread. But we need to factor in the negative carry on the swaps. So the swaps would cost (3% fixed payment minus 0.5% Libor) = 2.5%. Hence, a net income of 1%. It's not very large but remember I am assuming we're long MBS with very little negative convexity.

Now, let's consider the environment where mREITs could not possibly survive. Libor is at 5%, repos are at 5.2% (no reason to consider there is a particular credit crunch), 10-year swaps are at 2% and MBS yields at 3.2%. We need to invest, so the plan is to borrow at 5.2%, and invest at 3.2%, for a straight loss of 2%. Oh but we also must enter swaps. How do these work? We pay the swap rate of 2%, and receive Libor of 5%. So yes, that is a positive carry of 3%. All in, the negative carry on the MBS is compensated by the positive carry on the hedges. That is the whole notion in using hedges.

Bottom line, the shape of the curve is irrelevant at the first order, what matters is the spread of MBS over swaps (the 120bps in the above example) and the spread of repos over Libor (20bps in the example).

Note that I am not describing here what happens if all of the sudden we go from a very steep curve to a very inverted curve. These swap hedges work at the first order (duration), but that does not address negative convexity. Negative convexity will negatively affect a long MBS / short swaps position whether rates go up or down. It has to be hedged with different tools, namely swaptions.

I'd say that swaps hedge where the yield curve is, and swaptions hedge how fast it is moving. Here I am only addressing the level / shape of the curve, but it really is the most fundamental thing to understand, before looking into convexity, implied volatility etc.

## Things to watch out for

We have seen enough here to conclude that proper swap hedges need to be built with both financing hedges in mind (the short end of the curve) and duration hedges in mind (the longer end of the curve).

For the first part, an easy way to get a handle on how a REIT is hedging, is to compare swap notional with the amount of repo used. One step further, one can also look at whether the swap indices (1-month Libor vs. 1-year Libor) match the maturity of the repos.

For duration hedges, one needs to compare the overall weighted average (by notional) duration on the hedges (as a double check, the rule of thumb is duration = .9 x maturity) with that of the MBS assets. These numbers are provided in the quarterlies in most cases.

Partial durations could be calculated on the swaps, but they are a lot more difficult to obtain on MBS without real models. But at least, checking financing and duration hedging still is a lot more than many people do, which leads them to materially wrong conclusions when analyzing the rate exposure of mREITs.

**Additional disclosure:** I am long several mortgage REITs.

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