Joseph Stiglitz, Paul Krugman, and Jeffrey Sachs have all now published articles debunking the logic behind Tim Geithner’s bank rescue plan. The Stiglitz article does the best job, showing how the plan perfectly mirrors all the bad practices that got us into the financial crisis in the first place. All three articles attempted to give a numerical example of how the bailout would work in order to illustrate the perverse incentives involved. All three also skipped over the crucial leap in logic that shows why the plan would lead participants to overpay for subprime mortgage assets. Call me crazy (or dumb) but I don’t think most of the public is that familiar with probability theory, much less risk-neutral valuation techniques, so I thought I’d break it down here.
Here’s the Krugman version of the example: imagine an asset that pays $150 with a 50% probability and $50 with a 50% probability. How much would a normal investor pay for it?: $100. Now, imagine the government were loaning the investor 85% of the total through a non-recourse loan. A non-recourse loan in this case would mean a loan you pay back if the asset pays off $150, but if the asset pays off $50, you give the government the asset and have to pay back nothing (i.e. the asset is the only collateral). How much would a normal investor pay under these conditions?: a little over $130.
All the examples left it at that. Maybe everyone’s a math whiz except me (a real possibility) and could follow that no-problem, but this took me a second. Here’s the breakdown:
The “normal investor” in the example above is a risk neutral investor. As this nice article explains, a risk-neutral investor is someone who doesn’t need to be compensated to hold risk. This type of investor will value the asset in the example at $100 because this is the expected payoff:
Expected payoff = .5 * high-return + .5 * low-return = risk-neutral value
where high-return = $150 and low-return = $50
i.e.
.5 * $150 + .5 * $50 = $100
If the investor were risk-averse, he would want to pay lower than $100 so that he would get some compensation for the risk of holding the asset. If the investor were risk-loving, he would pay more than $100 for the possibility of getting $150. In other words, assuming no interest, the risk-neutral investor would pay a price that would make his expected profit equal to zero–he pays the expected return (in a world with interest, he would pay the expected return discounted (reduced) by the risk-free interest rate, since he’s risk-neutral and could just as well invest an equal amount in the risk-free asset).
So what happens when the risk-neutral investor gets a 85% non-recourse loan? Using the assumption that the investor is risk-neutral, we start with his expected profit equal to zero, i.e. he/she pays $x for the asset, where $x equals the expected return.
So, without the loan, we have:
expected return = price paid
i.e.
.5 * ( $150 ) + .5 * ( $50 ) = $x
or,
.5 ( $150 – $x ) + .5 * ( $50 – $x ) = 0
so $x = 100
Examining the last equation, ($150 – $x) is what you get if the asset pays off; let’s call it the good state. ($50 – $x) is what you get if it doesn’t pay off; we’ll call it the bad state.
good state = ($150 – $x)
bad state = ($50 – $x)
With the government loan, the good state stays the same. The government loans you 85%; you put up 15% (in the real plan, you’d put up 7.5%, but no matter); when the asset pays off, you get $150 and pay the government back. So your good state under the loan is:
good-state* = ( $150 – .85*$x – .15*$x ) = ( $150 – $x)
Same as before. Your bad state changes, however, since, under the loan, if you get the bad-state payoff, the government loses what it gave you and gets the asset in return, and you lose what you put up, i.e. 15% of the purchase price. In other words, the bad-state payoff for you is:
bad-state* = ( -.15*$x )
Putting it all together, under the loan:
.5 ( $150 – $x ) + .5 (-.15*x) = 0
Solving for $x, we get:
$x = $130.43
This gets us to the point all the articles made: without the loan, the risk-neutral investor would pay $100; with the loan, $130.43. In other words, the government is providing a 30.43% subsidy to the banking sector for this asset purchase. Considering that, under the real plan, the amount loaned (what’s called a “haircut”) is actually closer to 92%, and that the the government puts up half the equity, and you can see the anatomy of a historic act of theft taking shape (in the above example, you would put down $19.56, or .15 * $x, so under the real plan you’d put down half that). As is plain from this breakdown, the primary idea behind the plan is to get investors to overpay for the toxic mortgage assets, and thus to transfer wealth from taxpayers to bankers. As with previous bailouts, this plan does nothing to ensure lending will resume; it simply rewards those who invested in the bad assets in the first place, in the hope that they learned their lesson and will do better in the future. Obama’s corrupt coddling of his campaign contributors continues.
