Krugman's "analysis" of the Treasury bail-out proposal, "No Deal", is so weak it is embarrassing:
I hate to say this, but looking at the plan as leaked, I have to say no deal. Not unless Treasury explains, very clearly, why this is supposed to work, other than through having taxpayers pay premium prices for lousy assets.
The Treasury plan, by contrast, looks like an attempt to restore confidence in the financial system — that is, convince creditors of troubled institutions that everything’s OK — simply by buying assets off these institutions. This will only work if the prices Treasury pays are much higher than current market prices; that, in turn, can only be true either if this is mainly a liquidity problem — which seems doubtful — or if Treasury is going to be paying a huge premium, in effect throwing taxpayers’ money at the financial world.
No. If the problem is liquidity rather than solvency (a big if, and Krugman guesses it is solvency) then removing the troubled assets at fair value will reduce the variance of the firms balance sheet without changing its expected value. This reduction in value may be enough to reassure lenders thatt the firm in question is safe.
Developing... I have more in the UPDATE here but I am still working on my scintillating killer example of the impact of mean and variance on lenders (but not equity holders).
KILLER EXAMPLE: *IF* this is a liquidity problem (and Krugman acknowledges it might be) then it will not be necessary to pay a premium for troubled assets. Paying a "fair" price (whatever that is in this uncertain world) will preserve the current expected net worth of the firm but greatly reduce the variance of future net worth. That will be very appealing to prospective lenders.
For example - suppose a firm holds a large pot of troubled assets that will, over the next ten years, produce uncertain cash flows. The assets are currently valued at 50 cents on the dollar. After careful analysis, prophets and seers conclude the following:
There is a 20% chance the assets will return 25 cents on the dollar; resulting losses will bankrupt the firm.
There is a 60% chance the assets will return 50 cents on the dollar, allowing the firm to survive.
There is a 20% chance the assets will return 75 cents on the dollar, allowing the firm to live long and prosper.
The "fair" price for these assets is 50 cents / dollar. However, if the firm continues to hold them there is a 20% chance of bankruptcy. This grim prospect will scare away all but the hardiest of junk lenders, thereby creating a liquidity crisis for the firm.
If the firm can sell the assets at a fair price of 50 cents the expected value of its net worth is unchanged but the probability of bankruptcy drops to some very low and acceptable level. Liquidity crisis solved, even though the assets were not sold at a premium.
Obviously this doesn't work if the firm has a solvency problem, i.e., at fair value the net worth of the firm is negative.
However, Krugman's general statement that absent premium prices this plan cannot succeed is false.