Posted tagged ‘interest rates’

Fannie and Freddie: Some Facts to Keep in Mind

July 12, 2008

Well, Fannie and Freddie’s troubles have prompted this post (interrupting my work on the upcoming first installement of Build an Investment Bank). Basically, what I’ve bee hearing is that Freddie and Fannie are in trouble. Interesting. Here are some things to keep in mind about Fannie and Freddie…

1. Fannie and Freddie essentially securitize mortgage loans. This is complicated, but here’s the story in their own words:

Mortgage lenders … deliver pools of mortgage loans to us in exchange for Fannie Mae MBS backed by these loans. After receiving the loans … we place them in a trust that is established for the sole purpose of holding the loans separate and apart from our assets… Upon creation of the trust, we deliver to the lender (or its designee) Fannie Mae MBS that are backed by the pool of mortgage loans in the trust and that represent a beneficial ownership interest in each of the loans. We guarantee to each MBS trust that we will supplement amounts received by the MBS trust as required to permit timely payment of principal and interest on the related Fannie Mae MBS. We retain a portion of the interest payment as the fee for providing our guaranty. Then, on behalf of the trust, we make monthly distributions to the Fannie Mae MBS certificateholders from the principal and interest payments and other collections on the underlying mortgage loans.

(emphasis mine).

The essential point here is that Fannie and Freddie take on the entire risk of the mortgage defaulting in exchange for an ongoing fee (generally 50 bps per annum). The fee they charge for this type of transaction is small, generally less than 1/2 of 1/32nd of one percent of the principal balance of the loans they are guarenteeing. Also, Fannie and Freddie retain any risk of hedging their exposure. Part of this is meant to imply that the fees they collect offset the losses they expect to endure, but there’s also a lot of expense to hedging these exposures. I won’t pretend to understand all the complexities of this process, but they have to manage duration risk and interest rate risk (note that in mortgages, these are linked, but not exactly the same thing: lots of factors, including interest rates, affect a borrower’s decision to prepay their mortgage and changes in interest rates affect the future cashflows from fees). This is more art than science as it is very dependent on odd accounting rules and complex models–models that are a best guess at an uncertain future. Read their risk management section (and keep in mind that O.A.S. models are just lots of iterations run over another set of models… so, two layers of models… and we know how good those have performed) or this OFHEO report, specifically the sections on risk (Model Risk especially). The report I just linked to goes into, in depth, the various risk, accounting, and hedging issues at “the Enterprises.”

2. Fannie and Freddie are one of the largest, if not the largest, buyers of mortgage product. They buy their own mortgages (ones they have seen securitized) and hedge their massive portfolios. They issue bonds at extremely cheap levels to fund these activities. One former treasury official seems to think that this huge funding advantage seems to have translated into a bit of reckless purchasing on the part of the agencies. They even tout this–going back to the Fannie filings, we learn the following:

The U.S. Congress chartered Fannie Mae and certain other GSEs to help ensure stability and liquidity within the secondary mortgage market. In addition, we believe our activities and those of other GSEs help lower the costs of borrowing in the mortgage market, which makes housing more affordable and increases homeownership, especially for low- to moderate-income families.

(emphasis mine).

How noble! They lower the cost of a morgtgage by, well, buying lots of them and lowering rates. Why do they buy so much? so they can lower rates. Easy to understand, right? The reason they do this is to help increase home ownership. Interesting, then, that their business volume in 2007 had 11% investor properties or second/vacation home (see table 41, here). Also interesting, then, that 32% of their business was lending for cash-out refinancings (same table)–those don’t seem to be helping home ownership, and actually reflect a higher risk segment of mortgage loans. So, Fannie and Freddie own a huge amount of their own product, which is notoriously difficult to hedge, have bought a lot of product fore the sake of buying, and seem to have a portfolio composition that is slightly different from it’s purpose… Well, holdon. It gets even better!

3. Fannie and Freddie were the largest buyers of sub-prime mortgage bonds and commercial mortgage-backed securities. Look at any securitization, look at the AAA-rated portions, and if there is a class that is all loans considered “conforming balance” or have amounts that generally conform to the agencies’ maximum loan size limits, then you know those were purchased by an agency. At the end of 2007 Freddie owned $100 billion of these sub-prime securities (according to OFHEO, page 43, pdf) where 21% of loans were 60+ days delinquent. Fannie Mae has about 13% of it’s portfolio, which was an average of $725 billion during 2007 (from their filings), or $94 billion. Now, if regulators understood these products, they would understand that securitizations are structured in a way that Fannie and Freddie could be at risk for a decline in value of their own securities that occurs from the performance of the other assets–the ones that have nothing to do with their goals and charter. I would even challenge anyone who thinks that congress would agree with the programs that Fannie and Freddie use to support their mission … I’ve been on calls with people discussing how Fannie and Freddie merely need to be able to claim something passed the most cursory of tests to take on a $1+ billion loan. Providing the opportunity to afford housing to credit worthy indivisuals has nothing to do with buying CMBS and sub-prime RMBS.

What does all this point to? Seemingly a massive amount of “mission creep” for the agencies that lead them to be over-levered, in increasingly risky products, and in an accounting and hedging nightmare.

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Assume all Bonds are Spheres: Part I

February 14, 2008

This segment is a regularly occurring feature. It gets its name from a joke that is commonly made about technical people. Usually a very simple problem is presented about horses (or sometimes cows) and a physicist/engineer/mathematician is asked to provide a solution. The solution is made complex because incorporating the nuances of the animals in question is extremely difficult, hence the highly technical person is required. The solution then starts with the technical person saying, “I made two assumptions. The first assumption is gravity. The second assumption I made was that all horses are spheres.” The crux of the joke, which is often found in the markets, is that approximating is both easier and “accurate enough.” Hence the naming of this series on mathematical financial tricks and other interesting tidbits.

Loans are simple enough. I tell you that I would like to originate a loan, which I will securitize, and your interest rate on a loan is going to be 10%. Easy! You just send in 10% of the loan amount every year. Well, not really:

  • If I followed convention, I quoted you an Act/360 rate (it accrues yearly based on the actual days, but assumes a 360 day year)–the interest you pay is really 10.14% (~ 365/360 * 10%). (Note that the lower the interest rate, the lower the impact of converting to Act/360.)
  • If this was a 10 year loan, those 14 basis points (bps, 1/100th of a percent) are worth about 1.11% of the total notional of the loan (don’t forget, that’s 14 bps extra one pays per year, for 10 years–take the present value of all those cashflows).

Now, let’s look at what happens when I securitize the loan.

  • I monetize the 14 bps because the bonds I sell accrue on a 30/360 basis (market convention), so those extra days of interest never get paid to bondholders–I keep it.
  • Another nuance: The bonds are priced to the market convention, which is assuming a semi-annual yield. Investors will demand, say, a 10% coupon on their bonds. The bonds, though, match the loan–they pay monthly. What is the 10% worth on a monthly basis? About 9.80% (see below). What do I earn on arbitraging the difference? Well, about 20 bps per year, which, present valued, is worth about 1.59% of the loan amount.

Let’s review: I quoted you a loan at 10%. The 10% tuned out to be more than 10%. I then sold the loan using a completely different set of assumptions and, doing nothing at all, managed to pocket 2.7% of the loan amount. On $10 million dollars that’s $270,000 I made just for arbitraging various conventions and the difference in how bond investors think and how lenders generally think. Would you have been better off to take the 10.05% loan from the insurance company, quoted on a 30/360 basis? Yep. But the rate was lower … and all bonds are spheres.

————————–

The voodoo behind the 9.80% monthly equivalent coupon is easy. The first insight is to recognize that a yield is essentially a discount rate. To find a monthly equivalent to a semi-annual yield one needs only to find the interest rate that, when compounded twelve times a year, equals the yield that assumes compounding twice a year (the semi-annual yield).

We start by saying that an annualized yield, assuming compounding x times a year is

     (1 + i/x)^(x) – 1 = annualized yield       Formula that codifies the above intuition.

For our example of a 10% semi-annual yield, we get the following:

ann. yield (12 pmts.) = ann. yield (2 pmts)
(1 + (r/12))^12 – 1 = (1 + (10%/2))^2 – 1 
1+ (r/12)) = (1+5%)^(2/12)                      
Algebra… 😦
r/12 = (1.05)^(2/12) – 1
r = 12 * ((1.05)^(2/12) – 1)
r =  9.79781526%   
                                   Our answer!

And that’s how I arrived at that solution. I’m sure I’m missing something minor that excel would do for me, but you get the idea.