Back-of-the-Envelope: Making Sense of TARP

Suppose I told you that there was a crisis with a stock, say, GE. That the price of the stock had dropped around 75% in the past year. And you responded, “But the problem is solved; the prices of long-term Call Options (say, the January 2011 20s) has gone up, as has their Open Interest.

You will (rightly) point out that this won’t revitalise the assets themselves and I will (rightly) note that option markets rather saved the equity markets in 1987, for instance. You will note that I am too optimistic, and I will agree, holding up a Brad DeLong mask (since I’d rather have DeLong’s [relative to mine] abundant hair than Geithner’s abundant forehead).

Then I will drop the other shoe and say that the toxic (“legacy”) assets should be priced as if the Fed-supported trades were options, with the underlying current price worked out by Black-Scholes. (As I’ve noted before, B-S is specifically INappropriate for this exercise, as it will overvalue the option. And therefore anyone suggesting the toxic [“legacy”] assets should be priced—or carried on their books—at a level higher than that model will clearly be insane.)

Ladies and Gentlemen, welcome to The TARP Solution. Details beneath the fold.

TARP is the Treasury Department’s attempt to confront two realities: (1) it isn’t a “market” in any reasonable sense of the word if the Fed is putting up 85% of the cash. (People who tell us that this means firms are committing a “large amount” to the process either do not understand the English language,or are hedge fund managers trying to sell something.) So let’s put some random numbers together.

Those “legacy” assets are trading in the market around 30. The Big C and others are carrying them on their books around 80. Several people who should know better (Summers, Geithner, DeLong) have conflated “the market is underpricing the assets” with “the true price of the assets will make the banks solvent again.”*

So we know three things. (1) People are willing to pay 30% of their own money to buy these assets, (2) the Fed is only requiring them to pay 15%, and (3) the fair value is between 30 (the current market price) and 80, and probably closer to the former than the later.

So again, using back-of-the-envelope principles, let’s pretend that we think the recovery will be soon, that the defaults will slow (or at least that resales will be quick and frictionless), and that the market reaches that consensus quickly. And so fair value should be around 50.**

So let’s say the Fed offers to buy a MBS for 50. How, as an investor, do I make money off this? Three possible ways:

1. If I own securities for which I paid
2. If I own securities for which I paid >50, and which I cannot sell for 50 without revealing myself to be insolvent, I buy securities at 50 along with the Fed and “average in.” (This is the “how to stay solvent longer than the market can be rational” act.)
3. If the Fed is buying securities at 50 so that I can no longer buy them at 30—I buy a LONG-dated Call Option on the security.

It is that last that explains TARP. Effectively, the co-investors with the Fed will be buying a Call option at 7.5 on the security at 50.***

Of course, it may not be an at-the-money Call option. More likely, the hedge fund effectively will be buying an out-of-the-money option (say, a 49.5 Call for 8) where some portion of the purchase is put up by the government.

Now you will note that, technically, TARP requires the hedge fund to buy the asset. So you might argue that this is not an option. But let’s look at the generic payoff diagram to the hedge fund of the two scenarios.

Amazingly, you can’t tell the difference on the payoff diagram as the security gains.**** In both cases, the hedge fund manager has just gone long volatility.

Expect that to have a ripple effect—I’m guessing dampening, cet. par.—on other option volatility trades.

All that is left is to back out what actual value of the security was assumed by the hedge fund when they bought the option. Which I will also leave as an exercise to the reader, while suggesting that a fair indication is min[x, TotalFedContribution] s.t. x a.s. approaches TotalFedContribution.

Will this bring the markets back, or make bank balance sheets more stable? I’m still saying “No,” and hoping to be proved wrong.

But what it should do is reduce volatility buying, especially in the other debt markets, for the foreseeable future. So if any of those Bankrupt “legacy asset constrained” institutions has a long volatility position, there will be even more “Unintended Consequences.”

*In fairness to Brad DeLong, I don’t believe he believes this. As Dr. Black noted, George Voinovich “wants to see a pile of money in flames before he’s willing to vote for what’s necessary,” and DeLong therefore sees this as a necessary evil. Having seen no evidence from the Obama Administration that they Have a Clue, I am naturally suspicious that this particular idiocy will do anything other than waste time and money—both of which are in increasingly short supply—but, since Larry Summers has shown his brilliant foresight before and clear has no skin in the game, I am reassured that there is no Principal-Agent problem at work here, as they was when Christopher “I never saw a regulation I like” Cox was named head of the SEC by the Previous Administration.

**While we’re at it, can we pretend that Amber Benson will be my next wife, which is probably very little less likely than those other possibilities (especially since I’m already married to an sf-writing actress/director)? (Amazingly, even without those conditions, we would be using a BotE number of 50: though there is a legitimate argument that 60 would be easier to work with, I’m assuming no one is that stupid.)

***This is why 60 would have been easier; 15% of 60 is 9, so I wouldn’t have to pay attention to decimal places. 40 would also have been easier—and both certainly more realistic than 60 and arguably more realistic than 50, but I want to maintain the pretense of the U.S. Treasury that this is a liquidity, not a solvency, crisis. (They’re wrong, but it’s their game.)

****The reason we can tell the difference on the losses is the possibility that the hedge fund treats the position as if it were an in-the-money Call option for which the Fed paid the in-the-money portion; the real returns to the hedge fund of the position in a TARP security are the same in both cases; there would be differences in the way the rest of the portfolio was managed, though, which are left as an exercise to the reader.