In this post, I'm going to work out an example of how the Geithner plan might work. I got the inspiration from Jeffrey Sachs' excellent article in today's Financial Times, "Obama's Bank Plan Could Rob the Taxpayer." Nevertheless, I'm going to talk myself through his example to make sure I understand it, so that you can understand it as well. Hopefully, we might understand it well enough to be bidding on some of those so-called toxic assets.

Okay, let's begin with the government's motivation. Geithner wants to incent investors to buy toxic assets off the banks, so that a bank will have a clean balance sheet once all its toxic assets are sold off. Geithner indicated that the terms of the plan - the lending rates, loan sizes, and durations - are yet to be determined. The PPIP fact sheet says that for each dollar of private capital, the US Treasury will put up one dollar of equity capital, and in addition, the FDIC will provide up to 6-to-1 debt-to-equity financing (or 6 dollars of debt capital for each dollar of equity capital) via the expanded TALF or Term Asset-Backed Security Loan Facility. This means for each dollar of private capital, the government through the Treasury and FDIC will put up one equity dollar plus twelve (6 x 2 equity dollars) debt dollars, for a total of 13 dollars in financing. This amounts to roughly 93% financing. Thus, the government will provide up to 93% uncollateralized financing towards the purchase of toxic assets, implying that investors will have to put up 7% financing themselves. How will this work? Let's imagine ourselves as the investors.

Uncollateralized financing implies that an investor interested in buying a toxic asset will get a loan from the US government towards the purchase of the asset, without having to put up any collateral. If the investor defaults on this loan, the government gets nothing back. In Treasury-speak, this is called a non-recourse loan, i.e., there is no recourse for the lender, i.e., the Treasury, if the borrower defaults. Assume the government loan carries no interest. This assumption would favor the government's chances of success by making its plan even more attractive to potential investors.

How Investors Will Fare

Now, let's imagine a toxic asset called Bad Investment Fund, ticker symbol BIF. BIF has a face value of 1 million dollars, but what price should we reasonably pay for it? This is what we need to work out as investors. Let's say we analyze the pool of bad loans underlying BIF, and conclude that based on the characteristics of individual borrowers in the pool, we have a 20% chance (technically, probability) of being paid off fully, i.e., getting a million dollars. However, because the borrowers in this pool are so terribly in over their heads, there is an 80% chance that if we owned BIF, we would get paid only 200,000 dollars. A reasonable (technically, risk-neutral) investor would pay the probability-weighted average payoff for this asset. That is, s/he would compute a reasonable price to pay as:

Risk-Neutral Price (BIF)

= (20%)($1,000,000) + (80%)($200,000)

= $200,000 + $160,000

= $360,000

Fair enough? Well, okay why did we multiply the payoffs by their probabilities? If the payoffs were equally likely, we could just have used a simple average. But because they are not, we need to take a weighted average, by weighting the payoffs by their probabilities. This is like saying: "After taking all possible scenarios that may unfold in the future into account, we will pay a price that averages all those future scenarios." This gives you an idea of why we might use the term "risk-neutral" or "risk-adjusted" to describe this price. We have priced the asset to account for the risk inherent in any future scenario unfolding, i.e., we are indifferent or neutral to the risk inherent in a particular scenario.

Okay, but wait. Under the PPIP, we won't be paying for the asset entirely ourselves. The government will provide us an unsecured loan to the tune of 93% of the asset's value. Let's look at how we would compute the risk-adjusted price in this situation.

Let x be 1% of the price we, as investors, pay for this asset. We contribute 7x or 7% of the price paid. The government gives us a loan for 93x or 93% of the price paid. The price is 100x. Now, let's value the asset under the two scenarios in question.

Scenario 1: With 20% probability, the asset pays off in full. We would receive $1,000,000, of which we have to pay back our loan, 93x, to the government. We would therefore compute the payoff to investors as ($1,000,000 - 93x).

Scenario 2: We would only receive $200,000 and owe the government the 93x we borrowed. Given that $200,000 is less than the fair value of $360,000, it would be fair to assume that $200,000 is less than the 93x loaned to us by the government. Thus, the government would recover $200,000 out of the 93x that it loaned to us as investors, and the payoff to us would be zero.

As investors, our risk-neutral price would be the probability-weighted average payoff under these two scenarios as usual.

Risk-Neutral Price Under PPIP (BIF)

= (20%)($1,000,000 - 93x) + (80%)($0)

= (20%)($1,000,000 - 93x)

Making a Profit

Knowing what we know thus far, how do we turn a profit by investing in a toxic asset? The way this plan is intended to work is that investors put up 7x and the government puts up 93x. This sets a practical limit on the value of x. Since 100x = $1,000,000, x could never be more than $10,000. That is, our own contribution would never exceed $70,000.

Since we know the risk-neutral payoff, and we put up 7x, we can compute our profit as:

Profit Under PPIP (BIF) = (20%)($1,000,000 - 93x) - 7x

Therefore, our percentage return would be:

Percentage Return Under PPIP (BIF) = Profit (BIF) x 100 / 7x

So, let's imagine that we put up any amount less than $70,000. Let's decide to pay 7x = $28,000 ourselves (so that x is $4,000). We can get a government loan for 93x, which works out to $372,000. The total price naturally would be $400,000 = 100x. So we submit a bid of $400,000, and it is accepted by the government.

Thus, under the terms of government financing, it would be reasonable to bid $400,000 for an asset whose risk-neutral price is actually $360,000! If our analysis is indeed correct, and there is truly a 20% chance of being fully paid and an 80% chance of recovering $200,000 only, our risk-neutral price would be the weighted average payoff over the two scenarios, as we computed before:

Risk-Neutral Price Under PPIP (BIF)

= (20%)($1,000,000 - $372,000) + (80%)($0)

= (20%)($628,000)

= $125,600

That is, we would have invested $28,000 and made a profit of $97,600 = $125,600 - $28,000. This would amount to a tidy government-subsidized expected return of ($97,600 x 100.0 / $24,000) = 349%.

Okay, so as investors, we would make out like bandits assuming we could analyze the underlying pools correctly to determine all of the modalities of failure and the recovery amounts and their associated probabilities.

But this is quite a big assumption to make. If, instead, our analysis had informed us instead that there is a 40% chance of being fully paid and a 60% chance of recovering $300,000, and it turned out that the real probabilities were 20% for being fully paid, and 80% of recovering only $200,000 instead of $300,000, would we end up losing money?

Firstly, the new assumptions would imply a new risk-neutral price:

Risk-Neutral Price (BIF)

= (40%)($1,000,000) + (60%)($300,000)

= $400,000 + $180,000

= $580,000

Now to what we, as investors, should pay under the new scenario.

Risk-Neutral Price Under PPIP (BIF)

= (40%)($1,000,000 - 93x) + (60%)($0)

= (40%)($1,000,000 - 93x)

However, given the higher risk-neutral price, we may bid higher than before. Let's assume we pay 7x = $49,000, so that x = $7,000, and the government puts up 93x = $651,000, so that the total bid amounts to $700,000. Once again, we're overbidding the risk-neutral price of the asset. Our expected payoff assuming a 20% probability of full recovery and 80% probability of recovering $300,000 would be:

Risk-Neutral Price Under PPIP (BIF)

= (20%)($1,000,000 - $651,000) + (80%)($0)

= (20%)($349,000)

= $69,800

Thus, we would have invested $49,000 and made a profit of $20,800 = $69,800 - $49,000. In terms of return, we would have had a return of ($20,800 x 100 / $49,000) = 42%, even after being wildly off the mark in our analysis. Because the government is bearing most of the risk, it is tilting the game in favor of investors.

How the Government Will Fare

Let's now take a look at how the government will fare in this grand bargain, assuming the first set of failure scenarios, i.e., 20% full recovery, 80% recovery of $200,000. From the government's perspective, their expected payoff would be calculated as:

Government's Expected Payoff Under PPIP

= (20%)($372,000 - $372,000) + (80%)($200,000 - $372,000)

= (20%)($0) + (80%)(-$172,000)

= -$137,600

That's an expected loss of 37%, not a profit. In this particular situation, the best case for the government is that it recovers its loan fully. Any chance of having a failure scenario unfold tilts the equation towards a loss for the government.

Will the PPIP Lead to Price Discovery?

Since investors are not actually buying the toxic assets entirely with their own capital, the PPIP will not lead to price discovery. Investors' bids will have no relationship to the price paid for the asset eventually. The government would accept the bid that has the highest amount of private capital, and then determine how much additional dollars it would add in to pay "fair" value for the asset. To do this, the government would need to model the asset value itself. If it paid "fair" value, the banks would be no better off than before. That is, they would remain undercapitalized and that would trigger an FDIC review of their Tier I Capital requirements.

Who Benefits from the PPIP and Who Pays

Assuming things work as explained above, who benefits from this plan? The money from the winning bid amongst all of the bids put in by various investors will go to the bank selling the toxic asset, thereby benefiting the banks' equity holders. Since the government is losing money in any failure scenario, this is not essentially different than an ordinary bailout. Money is flowing from the government to the banks.

Investors also benefit handsomely provided they properly assess all the failure scenarios and their probabilities of occurrence. This would require a lot of analysis - there will be far more than just the two scenarios in our simple example. Only sophisticated investors will be able to take advantage of this offering. We hope your particular pension fund or mutual fund does so. Even if it does, it will skim a significant chunk of the profits and give you the remainder.

Who pays? Oh well, that doesn't take much explanation. We, the tax payers, of course. Will this plan succeed? It depends on several factors. Firstly, investors should be willing to put up a sufficient quantity of money for these assets. Otherwise, the government will have to finance most of their purchases. Secondly, the total amount obtained from the investors and the government for these assets should be enough to recapitalize the banks. It's not clear that the currently appropriated monies are enough to recapitalize the banks. That leaves the taxpayers open to being raided once again.