Friday, April 17, 2009

Game Theory on the Toxic Asset Purchase Plan

A few weeks ago, the government suggested a plan that would allow financial companies to bid on "toxic assets" and use government money to help lever up the transaction.

I won't get into the exact details, but roughly speaking select financial firms can bid to buy assets that other financial firms want to sell---If the market price is $100 million, the buyer can put up some equity ($10 million) the government would match the equity ($10 million) and provide some cheap FDIC financing for the remainder ($80 million). And according to the treasury the loans will be non-recourse ("Through this new program, non-recourse loans will be made available to investors to fund purchases of legacy securitization assets.").
If everyone were to bid honestly what they think the assets are worth, the plan could work---But I wanted to investigate if firms would have an incentive to overbid---or to somehow screw the taxpayer for the firms benefit.

The following example is very extreme, and more of a mental exercise---Suppose that there are two Companies (A & B)---And they are identical, and each owns a worthless asset on their books that is currently being held on their books at $100 million.

There are 4 Different Scenarios that could happen (See the Game Theory diagram above for Nash Equilibrium).

1) Neither firm sells nor buys toxic assets---In a few quarters they each must recognize a 100% loss (or a $100 million loss) and the government loses nothing.

2) Both firms decide to sell and buy $100 million (The Carrying value) of toxic assets---essentially they swap assets, paying $10 million in equity to buy the others' toxic asset. In a few quarters' time the toxic assets go to zero---Each firm loses their $10 million in equity by buying the other's assets---But at the time of the transacation they were paid $100 million in cash ($10 million from their competitor and $90 million from the government). So even though the 'buying firm' loses $10 million of it's equity investment (which is recognized as a loss), as long as another firm purchases assets at an inflated value, it gains. However, the government loses $90 million from each loan it made--or a $180 million loss.
3) & 4) Are the same---One firm decides to not to sell it's asset AND buys a toxic asset---In a few quarters, the firm that bought bad assets for $10 million equity investment and did not sell their assets---loses $110 million dollars. The firm that sold and did not buy does not have write anything off and loses nothing, while the government loses $90 million.
With no collusion, the Nash Equilibrium is for neither bank to buy toxic assets at inlated prices. (However, they may still choose to buy them at appropriate market prices). However, there are huge gains to be had by colluding---with only the threat of jail time and congressional hearings being the factors to sway decision makers away from such devious tactics.
It's anybody's guess to see if the purchase of illiquid mortgage backed securities and other investments will help the financial system (or hurt the tax payer)---but in 1 year's time we will have a pretty good idea.

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