Recalculating the Geithner put

A certain Nemo has put together a nice illustration of how exactly the structure of the Legacy Loans Program that Treasury announced yesterday amounts to a big subsidy to private investors, and Felix Salmon and Paul Krugman have given it wider currency. It’s a great post, and a clear illustration both of how option-pricing works and how non-recourse loans do in fact add up to a subsidy. But the values that Nemo plugged into his calculations struck me as problematic.

Nemo imagines 100 loan pools at \$100 face value for which an investor, with 93% financing from Treasury and the FDIC, pays \$84 each. If half the loan pools turn out to be worth nothing and half turn out to be worth \$100—an average value of \$50—this would be the result:

The bank unloaded assets worth \$5000 for \$8400.  So the private investor gained \$100, the Treasury gained \$100, and the bank gained \$3400.  Somebody must therefore have lost \$3600…

…and that would be the FDIC, who was so foolish as to offer 6:1 leverage to purchase assets with a 50% chance of being worthless.

My problem with this example is that real estate loans are never going to be worth \$0.00 (some securities based on real estate loans might have no value, but I’ll get to that later). So what if, I wondered, you went with the same \$50 average value of the 100 mortgage pools but assumed that half were worth \$25 and half were worth \$75. Here’s what I came up with after doing some quick calculations using the same investment terms as Nemo did:

The investor bids \$84 for each of the pools, \$6 of which he has to put up himself (the rest is equity financing from Treasury and loans from the FDIC).

Half the pools are worth \$25, a \$2950 loss, of which \$300 is borne by the investor and \$300 by Treasury, leaving \$2,350 cost to the FDIC (minus interest payments by the investor, but let’s ignore those for simplicity’s sake).

Half the pools are worth \$75, a \$450 loss, which is shared equally between the investor and Treasury.

Total: investor loses \$525 of initial \$600 investment, the Treasury loses \$525, and the FDIC is out \$2,300

Still a pretty bad deal for the FDIC and for Treasury, but at least investors aren’t making money at the expense of the government. The interests are aligned.

What happens, then, if half the pools are worth \$50 and half are worth \$100?

There’s a \$1,700 loss on the \$50 pools, of which \$300 is born by the investor, \$300 by Treasury and \$1,100 by the FDIC.

There’s a \$480 gain on the \$100 pools, which is split evenly between the investor and Treasury.

The total: The investor makes \$180 on a \$600 investment, Treasury makes \$180, and the FDIC is out \$1,100.

And of course if all the pools are worth more than \$84, everybody makes money.

The lesson here is that the interests of investors and government are aligned if all the mortgage pools are money losers (or winners), but that things get a little weird if there’s a mix of winners and losers. In terms of incentives for the private investors, I can’t quite figure out what that means.

When it comes to mortgage-backed securities, the subject of Treasury’s Legacy Securities Program (official slogan, “It’s not toxic, it’s a Legacy“), it may be possible for some to go to zero as in Nemo’s example. And in general, I imagine there will be a lot more uncertainty in pricing these than in pricing pools of loans. The government is offering less in the way of direct leverage for this program, and is also planning to concentrate it among just five asset managers, who would each presumably have to consolidate all their investments in a single portfolio. But by offering non-recourse loans, it is still offering a subsidy. Which is of course the idea.

Update: A re-reading of the Legacy Loans Program FAQ reveals that Treasury will also be getting warrants to buy shares in the banks that sell their loans. Meaning that if the private investors overpay, there might at least be some upside on the warrants because banks will have succeeded in offloading assets at inflated prices. Of course, if it turns out the loans are worth a lot less than they sell for, as Brad DeLong puts it, “we are then in a world in which the only things that have value are bottled water, sewing needles, and ammunition.” Warrants to buy bank shares are not on that list.

Update 2: Make sure to look at Nemo’s comment below. It’s important (and a bit embarrassing for me). Basically, the \$0-\$25 distinction is totally irrelevant. All that matters is that the investor thinks some pools will be winners and some will be losers—but it doesn’t know which are which.