Calculated Risk links to video of Austan Goolsbee of the White House Council of Economic advisers, discussing how the Geithner plan aligns the incentives of the public and private sector participants. I had dubbed this idea a fib but Goolsbee makes it sound plausible: “if the private guy makes money, the government makes money. If the private guy loses money, the government loses money.” CR links to an example that explains how this plan could still see the private guys make money and the government lose money but it doesn’t explain how the price gets set, which is sort of the crucial issue. So, here’s a simple numerical example that shows how the price gets set. The point is probably pretty obvious, but I found it self-instructive to work through the figures.
The two keys to understanding why public and private incentives are not aligned are (i) Assets with uncertain payoffs will be auctioned off in small lots, so private investors can (and will) purchase many different lots (ii) The asymmetric incentives such that private investors get a higher rate of return on the investment in the cases when the assets deliver a positive return.
As described here, the conditions of the Geithner plan are a bit different than described in my earlier post. The government will put up 93 percent of the funds, six-sevenths in the form of debt with the remaining one-seventh equity component equally split between the government and private investors.
Now consider the case of a bunch of ex-ante identical assets, each of which pays off either zero or 100 with equal probability. A large number of these assets come up for sale, so by the law of large numbers the average payoff will be 50. How much would the assets sell for under Geithner plan conditions? Suppose private investors purchase each asset for X. In this case, half the time, their profit will be -X/14, while the other half of the time their profit will be 0.5(100-X).
This implies an average profit of 25 – (2/7)X. Comparing this with the initial investment of X/14, we can calculate the rate of return on this strategy as a negative function of X. Suppose that the rate of return needed to be 10% for participating private investors. In other words that (25-(2/7)X )/ (X/14) = 0.1. In this case, we can solve to get that the purchase price will be X=85.4.
So, here’s how the spoils get divided out. The public-private consortium buys the assets for 85.4, with 79.3 coming from the taxpayer and 6.1 coming from the private investors. The private investors get back an average of 6.7 to give them their 10% return. But since the pool of assets only pays out an average of 50, the average return for the taxpayer is 50 – 6.7 = 42.3, implying an average return for the government of -47%.
One can re-do the calculations using other probability distributions and private sector rates of return but these figures suggest that the Geithner plan conditions could work to boost prices for these assets by about 70%.
The one caveat here will be a familiar one from the early days of the meltdown: Correlated risk across the pools of securities. If these securities are all correlated, then perhaps there are scenarios under which all of them produce very poor payouts. This may require higher risk-adjusted rates of return than the 10% used here, and this may limit how much private investors will bid.
Update: It may be useful to clarify that the 10% return for private investors in this example is not supposed to represent some supra-normal return earned by these investors. Instead, this is just assumed to be the required rate of return for taking on a risky investment of this sort. I see now that some can intepret this story as “public gives subsidy to hedge funds, hedge funds then make out like bandits”. The problem here is the classic public finance issue of the incidence of a tax or subsidy. Just because a particular industry is taxed or given a subsidy, that doesn’t mean that they bear all the cost or obtain all the benefit. In this case, the assumption that there is a 10% rate of return, which gets enforced in a competitive auction in which the funds bid against each other, means that the subsidy gets transferred in full to the banks selling the bad assets. It’s the banks that make out like bandits from this deal, not the hedge funds.