Fair Value Pricing, Government Market Making and PPIP

How to Value Illiquid Assets (Including a Wolfram Demonstration Project Interactive Visualization with Source Code)



This article was originally designed in February 2009 to provide a method for the government to dispose of Banks illiquid assets. While the timeliness of that issue may have lapsed, the article remains methodologically important as a tool to help value any type of assets that is illiquid and for which a consensus price is difficult to guess.
This article argues that the administration would get a fairer deal in buying troubled assets by becoming a market maker on those assets bought at a most refined level of granularity using a proposed relatively straightforward market-making method. This approach further has the benefit of being minimally surgically invasive while most speedily addressing the problem.

The approach described here indeed generalizes to all situations where the value of a large block of a priori illiquid assets must be found, in a manner that can be traded as such in a mark to market perspective

Men, it has been well said, think in herds;
it will be seen that they go mad in herds,
 while they only recover their senses slowly,
and one by one.

Charles Mackay

Editorial Note (March 29, 2009)

As of March 23, 09, a “Public-Private Investment Fund” (PPIF) was announced that establishes 50/50 equity owned public-private funds coupled with low interest government loans for 85%[1] of each fund’s balance sheet. These funds would then be mandated to buy troubled assets. I view this as being essentially a further thought out proposal that nonetheless keeps the structure of the original Paulson TARP plan of September 2008 .
The 50/50 public private match is somewhat in the spirit of the Warren Buffet idea discussed below. As a result the article in its original form as written in mid February 2009 remains quite relevant to the debate as of the end of March 2009 and shows how the plan announced is a minor variation on what was anticipated then. The graphic description of the PPIF is also provided here.

An interesting insider account on TARP from a treasury official is here at the WSJ on Aril 2, 2009

Note also that TARP and PPIP are used herein interchangeably for legacy historical reasons as what was earlier named TARP became re-branded post March 23, 2009 as PPIP.

With Permission from Dave Granlund gratefully acknowledged


In February 2009, the administration was seriously considering a proposal to set up a so-called “Bad Bank that would buy troubled assets of banks in order to help them clean up their balance sheets and re-pump liquidity in capital markets. According to news reports, such assets would be bought at fair value. This was a revival of the original intent of the Paulson TARP program proposed in September 2008. The instinct is right, but as Paul Krugman pointed out in his Jan 19, 2009 column in the NY Times among others, the real question was what does “fair value” mean?

This is not a trivial question and there are many well intended ways to be wrong about it. Ms. Blair, the FDIC chairwoman says “We don’t have really any rational pricing right now for some of these asset categories”. This is probably what caused the original TARP plan to be abandoned. On October 1, 2008, as the debate on the first installment of the TARP program was raging, in an interview with Charlie Rose, Warren Buffet proposed, in order to ascertain fair value, that banks first go out and sell at least a portion of those assets in the markets. The Government/Bad Bank would then come in and buy the rest of those assets at the price obtained in the market.  [Note that the government announced PPIF with its government matching fund implement the spirit of this idea with within many separate entities competing against one another and further driving  prices up rather than down]

What Not To Do 

Mr. Buffet’s proposal sounds fair enough at first, and his initial pricing instinct is in the right direction. Yet acting on his proposal exactly as formulated would be seriously ineffective and could represent a substantial and unjustified amount of corporate welfare on a large scale. His pricing approach is structurally flawed in a potentially severely consequential way.

We single out this example and the “Oracle of Omaha” to illustrate a more general cognitive bias that contributed to this crisis.  His intentions are unquestionably noble, his record of financial acumen impeccable. His influence with this administration and the general public at large is considerable. His moral authority on financial issues is such that, most if not all decision makers will be disinclined to directly question his analysis. Yet, it would be very costly to Mr. Buffet’s reputation and taxpayers if we find out too late the flaws in his analysis; I am sure Mr. Buffet would not want his reputation to be tarnished the way Mr. Greenspan’s or Rubin’s have been lately. Moreover, I am not aware of many alternative arguments made in the public debate as to at which prices those assets ought to be bought. The safest proposals tend towards recommending partial or total nationalizations in the form of equity investments in troubled institutions, and that is what the Paulson team ended up doing on a somewhat limited scale.  

Wemust also state that we do not single out Mr. Buffet because he said at that same interview “Beware of Geeks bearing formulas” and that in some respects we could be considered a Geek bearing formulas. We are a fervent admirer of Mr. Buffet, and his being steadfast in arguing that mark-to-market accounting is not and was not at the root of the present crisis has been refreshing in its good sense. His analysis on this precise matter however, can clearly be shown to be flawed in a way that neither looks geeky and without involving any formula[2]. Here’s why and what to do instead.

A Market Making Approach

Once the government decides to buy these distressed assets to provide liquidity, it ipso facto becomes a market maker and must quote prices like any rational market maker would. This price obviously depends on  the price at which the asset last traded. This is used as an anchor starting price from which to start bargaining. So requesting that banks first go out and sell at least a portion of those assets in the markets is a good way to establish that anchor price as Mr. Buffet hinted. But this is not absolutely necessary; any other last traded price in the markets would be acceptable as well. In Mathematics, this is called seeding the algorithm.There are two key factors that would well help effectively reach the fair price :

Factor 1. The inventory of those assets held by the market maker. The general rule is the higher the inventory held, the lower the market maker bid prices. Conversely, the lower the inventory held, the higher the market maker asks. This is the driver of market asset prices fluctuations in response to supply and demand forces that a true fair value pricing method or algorithm should reflect. Their are many ways to do this and in BICs 4 Derivatives Volume I : Theory , Chapter VII, I expand on many of those. A simple model reflecting this reality would be to apply a discount factor on each next unit of asset bought from the price of the previous one. Conversely an appreciation factor may be applied on each next unit of asset bought from the price of the previous one. 

Factor 2. This oft under appreciated factor in speeding up convergence towards fair market value of the security is the level of granularity or refinement of the unit security. The more granular the unit security, the faster the convergence towards fair price will be. That’s why stock markets, through unit stock granularity, work so well in revealing companies fair value.

If the discount factor reflecting factor 1 is too steep, it reflects a highly illiquid market. By contrast a high level of granularity reflective of Factor 2 helps the total price converge to where the market value actually should be while maintaining relatively narrow spreads on unit price quotes.

Furthermore, in the  simplified version of this model, the sensitivity on factor 1 (rd ) is structurally of a different order compared to the sensitivity on factor 2 (rf) : In this simplified model, the sensitivity on rd is polynomial while the sensitivity on rf is exponential.

An Example

Let’s look closely at how this matters in a simple example. Suppose Bank B wants to sell 100 units of toxic assets TB. It sells the first unit in the market at $1 and then liquidity dries up. According to Mr. Buffet’s prescription, the fair value of the remaining 99 units would be $99.

If we have a market maker whose price incorporates factor 1, a very generous pricing method for the seller could be for example requesting that every next unit bought would be at a 1% discount on the price of the preceding unit. By iterating the process on the 99 units, the fair-value of the remaining 99 units ends up falling to $63.03[3]

The starting unit price and the depreciation rate are of secondary importance as long as they are positive and non zero.  In our example above, if every toxic asset TB is further subdivided into 10 units of toxic assets, the fair value of the remaining 99.9 units would fall even down to $9.91[4].

Does that mean that the value of the remaining assets is $63.03? Or is it then $9.91? Not necessarily and probably none of those. As the unit price falls, bargain hunters will step in and bid higher. This will reset the Government bid price higher or allow it to progressively unload its own inventory at a potential profit, using a similar ask pricing formula. If no bargain hunter feels confident enough to step in, even greater unit asset granularity will ensure that the average unit price paid by the government is close to zero, reflecting true market sentiment. Some estimate that the total value of troubled asset held by financial institutions may be upwards of $10 trillion. The administration as of 02/26/2009 estimated a supplemental cost of  $750 billions on top of the original $700 billion TARP funds. A pricing error on such a scale would represent a serious fleecing of taxpayers.

As more bargain hunters step in, the markets will become liquid faster; the proportion of total assets held by the government Bad Bank will be smaller; government intervention in the markets will be minimized as it should be and Adam Smith’s invisible hand will work its magic yet again.  The example above shows that setting up, managing and winding down such a fair value system can be fairly straightforward and at minimal cost.



The present article has presented a general approach for pricing illiquid assets using a market making approach. It has the advantage of potentially minimizing the scope of government intervention while being effective at speedily restoring liquidity or clearing the market of its most troubled assets. The assets discussed here may be the underlying PPIP assets themselves or synthetic forms of those.

The more detailed follow up to this article is the knol titled: “Estimating Asset Costs for PPIP in a Market Making Framework & BICs

My article in the 2009 summer edition of The Investment Professional uses BICs to analyze the flaws in the Treasury’s PPIP for Banks’ troubled assets.Check it out http://www.theinvestmentprofessional.com/vol_2_no_3/abstract-bics.html

August 15, 2009 editorial comment:“With signs of impending economic peril dissipating, the PPIP looks to become one of the greatest government programs that never were.Yet the structural tools used in the analysis here and the core criticisms they lead to makes it a Gedankenexperiment whose lessons are still very worth learning.”

Oct 22, 2010Early returns on PPIP funds and possible reasons: http://www.bloomberg.com/news/2010-10-22/ppip-funds-surge-36-on-average-in-first-year-treasury-says.html

Wolfram Demonstration Project

This piece has been peer-reviewed as part of a submission to the Wolfram Demonstration Project that is now published. During the review process which in this case lasted over a month and included at least 9 requests for edits, the demonstration’s content was rigorously reviewed by experts in relevant fields, and automated software-quality-assurance methods were used to check its operation. As stated in the FAQ page, the demonstrations are academic publications as every demonstration undergoes a rigorous review process that checks for quality, clarity, and accuracy. I have chosen the creative combination of a knol and a Wolfram Demonstration Project because such a format provides both speed, intense third party review and an interactive output with source code that any reader can check for themselves.


"TARP Toxic (Illiquid) Assets Pricing Model" from the Wolfram Demonstrations Project

This knol tiny url: http://tinyurl.com/cx44cy