Tuesday, August 28, 2007

That's impossible, even for a computer!

The three most denounced words in the investing vernacular these days are "mark to model." But let me clue you in on something.

Every bond portfolio is marked to model. Every mutual fund. Every UIT. Every brokerage account. Every portfolio manager. Every pension. Every hedge fund. Every bond portfolio in the whole damn world is marked to model.

"Wait a minute," you're probably thinking, "surely you jest! After all, you can't tell me that open-end mutual funds, which have to redeem shares at NAV on demand, can get away with mark to fantasy figures! Besides, they are mostly invested in more simple bonds, like Treasuries, agencies, corporates, munis, etc."

No, I don't jest. All those portfolios are marked to model. Consider the following:

  • There are 152,732 different US dollar denominated corporate bonds outstanding as of today, according to Bloomberg.
  • Between Fannie Mae, Freddie Mac, Federal Farm Credit Bank, and Federal Home Loan Bank, there are 21,989 different issues outstanding.
  • There are 1,269,428 different municipal bond issues outstanding.

How many of those trade on a given day? A very small percentage. According to TRACE, which is a system for tracking corporate bond trading, about 4,300 TRACE eligible corporate issues trade each day. That's less than 3% of the total corporate universe. I note that trading activity in non-TRACE eligible bonds is not publicly reported. According to the MSRB, about 14,900
municipal bonds trade each day, or just over 1% of the universe.

Wait... It gets worse. Not only do a small percentage trade each day, but many don't trade at all for extended periods of time. Of the 4,300 bonds that trade each day, its often a few very liquid issues that trade over and over. Even many very large issues, for instance Washington Mutual 5.125 '15, which is a $1 billion issue, trade rarely. That bond has had only one trade of over $1 million during all of August.

So tell me how anyone can claim they've "marked to market" when a large percentage of their bonds have no recent trades. If there is no trade, there is no "market" price to use. And we know that using the last price wouldn't make sense. First of all, we know the general level of rates changes every day. Plus spreads move constantly as well. Again, take Washington Mutual. We know they are right in the middle of the sub-prime mess, so whatever you think of the company, you know the bonds are going to move significantly from day to day. So using a trade on August 16 to value the bond on August 31 makes no sense at all.

Some try to claim that getting dealer desks to value your portfolio is "marking to market" but let's think about the incentives for a moment. Bond dealer firms are sales organizations. They are run by sales people. They are not in the business of pissing their customers off by giving weak marks. So while many bond managers use dealer marks, it can be very dicey. I can say from first hand experience that sometimes sales people are all to happy to throw your ball back onto the fairway and assume you're OK with that.

So we're left with pricing matrices. These aren't perfect either. I have access to several matrices, and its not uncommon to find substantial differences from one model to another, even on relatively simple bonds. By virtue of the large variance in estimated prices, we know the models aren't perfectly reflecting reality.

Obviously there is a difference between an ABS CDO and a generic corporate. But as someone who deals with the reality of mark to model every day, I'm telling you, its no different. Only different in your mind. It's the difficulty to model CDOs that makes it problematic, not the concept of mark to model.


Anonymous said...

Sure. And that's why it's called price discovery.

I've spent half my life trying, essentially, to find holes in other people's mark-to-models.

Anonymous said...

Thanks for setting us innocent bystanders (read: civilians) straight . . . must be why I read you every day.

Meantime, how does the yield curve look to you now? What change might you expect if the Fed lowers Fed Funds rate in September? What change if they keep Fed Funds rate the same?

disclaimer: "might expect" does NOT mean "predict", much less "advise".

The Inscrutable Chicken said...

I'm sad....

...because one day you'll run out of quotes...and your blog will never be the same again.....

but until then, keep up the good work!

Accrued Interest said...

James is right. There is a ton of money to be made in coming up with a better price model.

Psychodave: Thanks for reading. I'm bearish on rates, which will soon be the subject of another post. I don't really think the Fed will cut more than 3-4 times.

Chicken: Never... I'll never stop quoting Star Wars.

Anonymous said...

I own numerous individual municipal bonds and I am always surprised at the valuation number my broker puts on them. (Muriel Siebert, but clears through NFS, like Fidelity does). Some are so far off I am forced to check the recent trades on investinginbonds.com to see if they can be true. Not even close. It must be tough for an investment advisor who gets paid a percentage of asset value of their clients account.

Anonymous said...

"If there is no trade, there is no "market" price to use. And we know that using the last price wouldn't make sense."

How about using the bid price? Stocks can go without trading for weeks, for instance, but there will always be some sort of underlying bid, even if it never trades down to that level.

Accrued Interest said...

Well, there is no public bid price. That's basically what people are trying to accomplish when they ask dealers to value their bonds. But I'm telling you that had a hedge fund asked for dealer quotes on A or better on most ABS CDO's at the end of May, the quote would have been very close to par.

flow5 said...

There's been a lot of hopping back & forth between different securities/maturities, but overall interest rates bottom in Oct. (the calculation is taken from Dr. Leland James Pritchard's formula, Ph.D, Economics, Chicago, 1933, MS, Statiistics, Syracuse). From that point, depending on how far the fed "eases" will determine the next rout.

Anonymous said...

simply put.... very true.

Accrued Interest said...

Dave M:

Municipals are great. I miss trading munis. Because that's such a murky market, and a smart trader can just rip bonds off left and right.

Anyway, the problem with MSRB data (who runs the website he mentioned) is that retail investors get routinely screwed. So you'll see a AAA-rated clean state GO bond trade at $107.526 and $109.125 on the same day. Why? Because one or the other of those guys got screwed.

Someday I'm going to quit my current job and start a muni arb fund. I'll do nothing but rip munis off and blog all day long.

Anonymous said...

You should start quoting from episodes I, II, & III.

Accrued Interest said...

I won't dignify that with a response.

venkat said...

I don’t think that there is any problem with the models as such (At least most of them). Most of the models do an admirable job of perfectly incorporating real word complexities. The problem is with us who provide the inputs to the models. Models always require inputs which do not have a universally accepted value. Take the simple B-S model for example. This model in my opinion is theoretically very sound. However, I wonder if any two persons will have similar numbers for the inputs which it requires such as volatility and even risk free rate. This model uses so many values which are readily observable, however a small disagreement over one of the two variables I mentioned before can provide drastically different numbers.

When a simple model like B-S can cause so much ambiguity, I can understand the problem that modeling a CDO can create. How can one up come up with a definitive number for Prepayment speed for example?

I would conclude saying that I think that it is actually the inputs that a model requires that are the source of much consternation rather than the creation of a model to price a CDO in this case. Please feel free to correct me.

Accrued Interest said...

I think a major problem with CDO modeling is the default and recovery rates plus the timing of defaults are all assumptions. And if you own a mezz piece, relatively minor changes in assumptions have a very large impact on the current estimated price.

I think both the street and academia focus too much on drilling down to an exact number when creating models. Investors really need models that indicate value. Layering on additional assumptions just so you can get the model to produce an exact dollar price probably reduces the model's utility.

DAB said...

This discussion brings to mind a meeting I had about six or seven years ago now. We were discussing marking to market highly illiquid long dated energy positions. We had various techniques for constructing forward curves and we always constructed a bid-mid-ask structure.

The lead external auditor (very high up in his firm, my company was considered an easy, plum job at that time) looked at us (me, my boss, his boss) and asks "ok, what do you do then".

"Well, we simply mark the long positions to the bid, and the short positions to the ask".

"Really?..." (confused look on his face) "You don't mark long positions to the ask?"

"Uh, no. That is clearly absurd..."

"Hmmm... Well, you are putting yourselves at a competitive disadvantage then. Your competitors all mark long positions to the ask since that would be the replicating position".

My boss looks at the auditor (and note that this was not an audit situation so him saying competitive disadvantage was not out of line...) and replies "Wow, we should all just go out and short energy stocks right now".

This was right before Enron fell (though it was on its death bed by then, must have been Nov 2001 timeframe), and never were more true words spoken (look at the charts of Reliant, Williams, Dynegy, El Paso, Calpine, AES from that day)...

To the best of my knowledge, none of us followed that advice (I know neither he nor I did).

Anonymous said...

Tom, I've been working in a hedge fund since 1991 and I've never marked to model. For bonds that did not trade, I'd mark to brokers bid (for my longs) and offer for the shorts. If you want to say that brokers give shitty markets, so be it, as for illiquid stuff you may have to mark to the bid or maybe under the bid - that is the illiquidity haircut. The value you have to give your investor on the portfolio is where would you be able to liquidate it on a given date if you had to.

With all due respect, "mark to model" is bullshit. I've never done it, but maybe its just me. I hated to ever be in a position of going to my investors and saying "last quarter's valuation was actually bullshit. sorry about that."

flow5 said...

Real-gdp was just revised to 4% for the 2qtr. Now it's the beginning of Sept. - so look out below.

Accrued Interest said...


I think an honest and ethical manager always marks to the most accurate mark s/he can. But the only way to really say you've marked to market is if the brokers in question are obligated to buy your bond at the level they give you.

If the trader who gave you the quote is unwilling to actually buy your position at that level, then he's making an estimation of the execution price. And maybe that's the most accurate possible price. But in the end the mark is just an expert opinion, not the market.

Look, I use dealer quotes too. But I also weed out anyone who seems to be to be marking my bonds too high. I'd say I have a bigger problem with quotes from dealers coming in too high than the opposite.

AND, if you use a pricing service for any bonds, then you are surely marking to model.

flow5 said...

The FOMC is inflexible. And the Fed's research staff's calculations are ex-post. And GDP doesn't move at the same rates-of-change.

Now the FOMC is going to get whipsawed.

Or maybe not, Bernanke's not talking. He's got the opportunity, and is going to take it, and will "squeeze" the rate-of-change in inflation until he "wrings" it out (right now).

Anonymous said...

Could the establishment of an exchange-traded market for corporates help liquidity? Would it even be feasible, given that so few of the products trade daily and that so many new issues come out every day? Would the big investment houses be willing to be, say, $5 million up on the bid-ask of the more popular issues, and maybe $1 million up on the less liquid stuff, at least to make some sort of a discoverable market?

Just throwing it out as an idea. I used to work at the CBOE and we had plenty of illiquid strikes and stocks listed with quotes for all of them. Granted, the size wasn't huge (I think each crowd guaranteed a 25-up market on any strike), but at least there were marks every day.

Accrued Interest said...

There are a few bonds that trade on an exchange. For whatever reason it never caught on.

Anonymous said...


B-S is theoretically sound? You're kidding me right?

No jumps.
Contiuously traded underlying.
Constant risk-free rate.
Constant volatility.

None of these are reasonable assumptions, yet the theoretical framework requires all of them for B-S.

As to the CDO models, all the copula models suck since no one has any clue what happens at the tail probabilities. This is an issue of data, I agree, but also of just people assuming normality without cause.

Accrued Interest said...


You are hitting the nail on the head. So many models (of all sorts) require an input we simply don't have or can't speculate on. Such as forward volatility. Or dynamic correlation in CDO models. The problem comes when we just decide to assume away the complexity so that we can get to a single answer. Why can't we build models which give less exact answers but don't rely on so many assumptions? That's how I build my trading models.