Thursday, July 12, 2007

The choice is yours but I warn you not to underestimate my power

Let's say you have to make a loan, and you have two applicants. Luckily, you happen to be the proud owner of a semi-functional crystal ball. While it cannot tell you the future exactly (always in motion the future is) but it can give you certain facts about your potential borrowers.

The first borrower is willing to pay a rate of 6.35% for a 10-year term. He will pay interest only until maturity but cannot pay principal early. According to your crystal ball, there is a 4.7% chance he defaults, and if he does default, his assets will be worth 36 cents on the dollar.

The second potential borrower will pay a rate of 6.25%, but your crystal ball shows there is no chance of default. He will pay principal monthly on a 30-year amortization schedule, but can also prepay principal at any time. Obviously the odds are good that the principal repayment will occur at a time when interest rates are lower than current levels.

The first exposes you to default risk but not reinvestment risk. The second exposes you to reinvestment risk but not default risk. Which would you rather take on?

It depends on how you feel about skewness. Bonds with default risk are said to be negatively skewed. Basically this means that there is a large chance of a small return, and a small chance of a large loss. The probability-weighted average return for the first loan is close to the stated rate (something like 5.94% depending on when the default occurs), but many investors are so adverse to the -64% loss scenario, that they are unwilling to accept the relatively attractive "average" return.

By contrast, the second borrower will return the stated rate, but in exchange for that certainty, we are allowing the borrower to play interest rates against us. Let's make a relatively simple assumption: if interest rates fall 75bps or more, the borrower will refinance the loan. Let's further say that the odds of rates falling by 75bps in year 1 is 10%, but the odds increase by 20% per year, so year 2 is 30%, year 3 is 50% and so on. This is roughly consistent with a normally distributed rate pattern. The odds that rates fall by at least 75bps at some point rises to 100% by year 5. Once rates eventually fall that 75bps, we assume reinvestment in another loan 75bps lower in yield (or 5.50%).

To make things simple, we'll measure yields and odds at the end of each year. For instance, since there is a 10% chance the loan is paid off after year 1, during year 2, you have a 10% chance of earning 5.50% and a 90% chance of earning 6.25%. In year 3, its 30% that you earn only 5.50% and 70% of 6.25%, etc.

Your weighted-average return (5.87%) is actually slightly less than loan #1 (5.94%). But notice that your worst-case scenario is your bond is called at the beginning of year 2. You'd earn 6.25% for one year then 5.50% for five years, or a total return of 5.60%.

As you've undoubtedly figured out, loan #1 is a corporate bond (with stats based on a Baa-rating), and loan #2 is an agency mortgage-backed security (MBS).

Obviously this analysis is simplistic. MBS don't pay off all at once, and you rarely buy them at par. So you really have a myriad of possibilities, and any kind of probability-weighted analysis gets very messy. But no matter how you draw up the rate possibilities, your worst case scenario is a minor impairment in your realized yield. With the corporate bond, you worst case scenario is you lose 60% of your investment.

Many investment managers eschew MBS or else manage the sector passively, choosing instead to focus on credit analysis. I think many are put off by the "myriad of possibilities" in MBS, while they believe they can control credit risk. I question this attitude. While there are infinite cashflow possibilities with MBS, many scenarios have very similar results. Its relatively easy to group your potential results together and come up with a manageable set of possibilities.

Meanwhile, the credit of a corporation is always a moving target. The company with consistent cash flow and modest leverage seems like a great credit, until they are purchased in a LBO. The company with conservative management seems like a great credit, until the CEO is replaced with someone more aggressive because the stock was lagging. The company with valuable hard assets seems like a great credit, until they pledge those assets to secure a bank line. The company with diversified lines of business seems like a great credit, until they do a series of spin-offs.

The global need for yield remains strong. With all this fear surrounding the economy, which would you rather own?


Anonymous said...

Intellectually, I have to agree, but my gut says you're SADLY mistaken, financially speaking. Perhaps if one has the fortitude to hang in, while the "baby is thrown out with the bath water", when a whole sector tanks, one might be ok...but I value my beauty sleep.

Anonymous said...

You highlight prepays and contraction, but what about extension risk? Let's say I've estimated prepays and figure a bond to have a particular bond to have a 2 year duration. Rates go up, no one prepays, and now I've got a ten year bond. How are my horizon returns affected in that situation?

Accrued Interest said...

Oh no, anonymous... I'm afraid it is you who are mistaken... about a great many things!

Seriously, though, do you think the agency MBS market is that bad? Even in the short-term?

Accrued Interest said...

Anon #2:

On extention... its similar, except that you have to assume other vehicles have the chance to reinvest at higher levels while you do not. In order to have made this comparison in my expample, I'd also have to assume the 10-year corp reinvests at year 10 while the MBS does not.

One problem I kind of glossed over is that MBS are likely to either extend or shorten every year you own them, and it will always occur in a way that goes against you. If rates remain relatively calm, like within +/- 50bps, you can usually out yield your benchmark over an extended period.