Recently, as part of our work  with Pew on Subsidyscope.com, we’ve been taking a close look at the performance of investments made through the Treasury’s Troubled Asset Relief Program (TARP). My colleague Ryan Sibley and I investigated an inconsistency between the language Treasury initially used to describe the TARP Capital Purchase Program (CPP) and the language found in a footnote on the final contracts. In many cases the change may have diminished the value of Treasury’s investments; at a minimum, it’s resulted in confusion over the program’s actual terms.

Under CPP, Treasury purchases a stake in ailing banks in the form of preferred shares and warrants – the intention being that these assets will be sold, once the banks recover, allowing the government to recoup its original investment. The pricing of these assets is critical to ensure that Treasury, and in turn taxpayers, receive a fair deal. If the price is too high Treasury receives a smaller stake in the bank and will not get as good a return once the assets are sold, potentially resulting in a subsidy to the bank.

Most of the assets Treasury received under CPP were in the form of preferred shares, a special kind of stock with a guaranteed dividend payment. However, Treasury also received a smaller number of warrants to buy common stock equal to 15% of its investment. The warrants set a “strike price” for the stock based on the current market price, allowing Treasury to buy stocks at that price on a future date – up to 10 years from the date the warrants are issued. If the strike price was set at $20 and the market price for the stock returns to or exceeds the strike price Treasury would be able to buy the stock for $20, pocketing any difference. However, if the price never returns to $20 the warrants would be worthless.

The inconsistency we discovered involves how strike prices are set. The term sheet Treasury posted on its Web site when CPP was announced last October describes a method for calculating the strike price based on the average market price over the 20 days before a transaction closes. However, in the final contracts with CPP recipients Treasury chose to calculate the 20-day average based on the date the banks initially applied for CPP funds; in many cases these dates differ by weeks. In the intervening period the stock prices for many banks declined, resulting in a difference in the final strike price of as much as 30% when comparing the two methods of calculation.

We examined 228 CPP transactions and found that 185 (82%) received less favorable pricing as a result of the language change. On average the new language raised the strike price of the warrants by 8% (to Treasury’s detriment); the difference was worse for many of the larger transactions. For example, with Bank of America, which received $25 billion under CPP, the strike price found in the final contract was $30.79. It would have been $25.94 based on the language found in the term sheet, a 16% difference to Treasury’s detriment. (See this Google spreadsheet for a full list of transactions and our calculation of strike prices.)

It’s important to point out that the strike price should not be confused with the “value” of the warrant. While the strike price is one factor, the final determination of value depends on future performance of the stock. As a result, “options pricing” as it is called, requires simulating the possible outcomes to judge the likelihood that the market price will return to the strike price. This is both complex – the most common method for doing this, the Black-Scholes equation, garnered a Nobel Prize in 1997 – and is far from an exact science. (See this recent New York Times article on the challenges of quantitative finance, including a discussion on Black-Scholes.) That said, the less favorable the strike price, the less likely it is that Treasury will be able to use the warrant to help recoup its investment.

Also, it’s worth noting that Treasury was fully within its rights to change the program language. In fact, Treasury may have been attempting to ensure a better deal for taxpayers on the assumption, although incorrect, that prices would rise after banks initially joined CPP, in turn inflating the final strike price.

The fundamental problem is one of transparency and clarity in communicating the program’s terms. Today the Treasury’s website still presents key documents that incorrectly describe the strike price calculation – only by reading the footnote on the last page of the contract would a visitor to the site realize that the actual terms differ from the terms described in many more prominent locations. Perhaps then it’s unsurprising that even some of the participating institutions have incorrectly communicated the strike price calculation in SEC statements and press releases. And even as recently as January, Bloomberg ran an article incorrectly describing the terms.

Given the magnitude and complexity of programs like CPP we should ask for all the clarity we can get.