ABSTRACT

Smoke and Mirrors

BICS, THE PPIP, AND THE FALLACIES OF EXPECTATIONS-BASED RISK MANAGEMENT

Leading economists such as Paul Krugman have criticized Treasury Secretary Timothy Geithner’s plan for US banks’ toxic assets. True, the plan is structurally flawed; but the arguments of Krugman and his cohorts are based on the same risk management fallacies that were responsible for the meltdown in the first place. Their erroneous approach to risk and uncertainty and the questionable picture they draw of future events erect a dangerous analytical framework for investors evaluating Geithner’s plan in particular and involved with risk management and hedging strategies in general.

However, effective tools do exist to address the risk management fallacies these economists perpetuate. Both conceptually and practically, BICs (basis instrument contracts), a set of hedging contracts that I developed in 2001, help investors ascertain the viability and profitability of participating in the Treasury’s plan and offer an effective means for the government to reevaluate the specifics of its approach. Their applications are not confined to the Geithner plan; from a broad investing perspective, BICs facilitate increased accuracy in estimating actionable pricing probabilities with hedging value.

Let’s say we are in a multiperiod trading environment at the end of which is a payout that’s a function of the realized values of underlyings observed in the timeframe. A BIC is a unit representative of a class of contracts that together as a set compose or replicate the payout—no matter how unusual, complex, or illiquid—in a static manner. (For a more extensive definition, see Kongtcheu, June 2, 2009.)

THE KRUGMAN ILLUSION


As Treasury Secretary Timothy Geithner prepared to announce his plan for the banks’ toxic assets on March 23, 2009, those economists who felt the plan would be an unjustified subsidy to the financial services industry strove to come up with simple analytic models to explain their objections to the subsidy’s structure and scope to the public. Geithner’s PPIP (public–private investment plan), also called the PPIF (public–private investment fund), established 50–50 equity-owned public–private funds, coupled with low-interest government loans, for 85% of each fund’s balance sheet. These funds were to be mandated to buy troubled assets. Essentially, the structure was an elaboration of former Treasury Secretary Henry Paulson’s TARP (Troubled Asset Relief Program) plan of September 2008.

A number of economists and financial analysts went head to head in blogs and op-ed columns to propose alternative plans or structures to the PPIP. The most prominent arguments were based on expectations analysis and coalesced around the “Geithner Put,” the imbalance between the risk–reward implications of the plan for taxpayers as opposed to the risk–reward implications for investors. Paul Krugman was one of the most relentless and prominent opponents of the plan, in large part via his New York Times column and blog. Here’s how he made his case (2009):

“Suppose that there’s an asset with an uncertain value: there’s an equal chance that it will be worth either 150 or 50. So the expected value is 100. But suppose that I can buy this asset with a nonrecourse loan equal to 85% of the purchase price. How much would I be willing to pay for the asset? The answer is, slightly over 130. Why? All I have to put up is 15% of the price—19.5, if the asset costs 130. That’s the most I can lose. On the other hand, if the asset turns out to be worth 150, I gain 20. So it’s a good deal for me. Notice that the government equity stake doesn’t matter—the calculation is the same whether private investors put up all or only part of the equity. It’s the loan that provides the subsidy. And in this example it’s a large subsidy—30%.”

Krugman seems to have structured a neat example. But he’s actually perpetuating two separate dimensions of a central fallacy that is at the core of the risk management failures leading up to the crisis. The work of Frank Knight (1921) classifies the first of these dimensions as pertaining to risk, and the second as pertaining to uncertainty.

FIRST FALLACY: RISK AND PROBABILITIES


To begin with, by basing his reasoning on expectations assessments, Krugman overlooks the crucial relationship between investors’ preferences and resource constraints. Many investors who have already suffered major losses do not, unlike the government, have limitless liquidity and a flexible time frame. They could quite reasonably demand more cushioning for the risks they’re facing.

To drive the point home, here’s an example. Suppose Krugman’s net worth is $100 million. He flips a coin, with an equal probability of heads or tails. If it’s heads, he receives $1 billion; if it’s tails, he must pay out his net worth of $100 million. Is he a gambling man? Even without knowing the structure of Krugman’s risk preferences it’s fair to say that many investors would not accept such a risk, even with an expected gain of $450 million. This scenario may seem like a bit of a stretch, but it’s not just a thought experiment—hedge fund manager Victor Niederhoffer, for instance, took such a bet in 1997, though perhaps without appreciating the full implications of his wager. He lost.
The uncertainty factor must cease to lurk in the industry’s collective blind spot if the PPIP is to be properly approached and if further global institutional failures are to be avoided.

Naturally, relative constraints on respective resources tend to lead investors to request excess incentives beyond fair-value expectations. It’s a logical continuum of duress pricing. Should a deal go south in a scenario like the one above, the investor’s credit could be impaired, raising the subsequent cost of capital. The high cost of provisioning for such contingencies may explain many requests for positive expected excess returns and certainly throws into sharp relief the reason that not too many investors are likely to rush off to start a PPIF. As Black Swan author Nassim Taleb would say, “Never cross a river because it is on average four feet deep.”

Many of the firms taken down by sundry financial crises have made the same expectations-based mistake as Krugman. They’ve executed investment decisions based on expectations profiles, without a full appraisal of the sustainability of downside scenarios that even higher-order metrics such as standard value at risk fail to capture. Macroeconomists, with their tendency to assume unlimited liquidity and life span, are most prone to this kind of oversight.

While expectations-based risk management is particularly troubling in terms of the PPIP, it also threatens the integrity of the broad field of derivatives pricing and hedging methodologies. A derivatives contract can be viewed as an uncertain future payoff that is a function of as-yet unobserved values of underlyings on a future timeline. These underlying future values may be spanned along multiple scenarios, after which standard pricing algorithms compute the derivatives contract price as a discounted average of the contract’s payoff for each scenario, weighted by the assumed likelihood of the scenario.

In numerous cases—including AIG and many of the recently failed insurance companies—risk management has relied on the implied law of large numbers to average out large-scale losses. But as John Keynes (1923) has it: “The long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is past the ocean is flat again.”

SECOND FALLACY: UNCERTAINTY AND PROBABILITIES

Beyond risk, there’s another major blunder in Krugman’s analytic framework. Why are the probabilities taken to be 50–50? Why are the possible states 50 and 150? Most pressing is the question of how his conclusions—namely, the premium of 30%, rather than, say, a mere 1%—can hold if his assumptions are false. By ignoring the critical role of uncertainty in setting probabilities, Krugman perpetuates a widespread philosophical failure of risk management. The uncertainty factor must cease to lurk in the industry’s collective blind spot if the PPIP is to be properly approached, and, more importantly, if further global institutional failures are to be avoided.

State-of-the-art hedging strategies on financial derivatives work by dynamically taking opposite positions in underlyings or their substitutes, in proportions that offset changes in the estimated values of the derivatives contract over time. Even when the incremental rehedging time scales are small, thereby constraining the scale of the bet and ensuring sufficient repetition for true probabilities to emerge, failure to compute probabilities properly can still lead to large-scale losses. In the lead-up to the credit crisis, many risk managers seriously underestimated the default probabilities of the mortgage pools that were the basis for pricing the more sophisticated mortgage-backed securities. That underestimation can be blamed for bringing down several trading houses that had set up sophisticated dynamic hedging strategies. They met their makers when the law of large numbers made estimation errors inexorably evident.

The Monty Hall problem is pertinent to a discussion of uncertainty. The solution to that probability puzzle demonstrates that someone faced with a choice of three mystery doors, who assumes a 50–50 chance of picking the correct door, and consistently sticks with the same door during the process of eliminating nonwinning doors, will predictably lose about 33% of his or her stake at each iteration. In the Monty Hall puzzle, as elsewhere, probability uncertainty may lead to overbidding losses.

FLICK MY BIC

Robust risk management strategies must be based on directly trading contracts that encapsulate and lock in expectations for future scenarios. Let’s relate this assertion to the scenario Krugman proposes in the Times.

Rather than working with expectations as Krugman does, an investor could buy a contract that will pay out either 7.5% of an asset’s purchase price or 50% of the difference between the asset’s purchase price and 50, whichever is smaller (assuming that the price of the asset could result in a loss in an adverse scenario in which the asset’s worth is only 50). Then the investor could finance the deal by selling a contract that will pay out 50% of the difference between 150 and the asset’s purchase price if the asset turns out to be worth 150. In this situation, if the toxic asset’s purchase price is 130 or less, the contract bought would be cheaper than the contract sold, resulting in a net and present risk-free profit without any future exposure.

Public–Private Investment Funds, 

Expected Break-Even Pricing

Expected break-even prices by the percentage of a PPIF held as equity when such equity is equally distributed between government and private investors. For example, if 15% of the PPIF is held as equity, the expected maximum purchase price will be $130.43. A percentage of PPIF held as equity of 50% or higher will lead to a purchase price of $100. The curve is obtained as the solution of the equation that solves for the value zero the expectation of the smallest of the equity ratio (er) multiplied by the asset price and the difference between the asset price and its ultimate disposal price ($50 or $150).

The hedging contract encapsulating risk in this example is usually called an ADS (Arrow–Debreu security), the most trivial form of a BIC. In this framework, the unhedged investor is actually selling one ADS and buying a second one, while deciding on a price at which to buy the related troubled assets immediately. The price at which ADSs trade helps set their maximal asset purchase price.

Constraints of time and resources impel risk managers to base probabilities and expectations on questionable statistical inferences. That can become very treacherous in the event of an unsustainable downside and in the absence of anyone willing to trade contracts based on the probabilities assumed. BICs encapsulate the rational expectations of investors and the limited resources of those who trade them. They emphatically stress the need to look for replicating alternatives to offset risks. When BICs or their substitutes exist, their quoted prices should be the basis for inferring actionable pricing probabilities with hedging value.

BICS: MANAGING RISK AND UNCERTAINTY


As the simplest kind of BIC, the ADS is a good pedagogical tool for working through relatively simple scenarios like Krugman’s. In real life, though, outcomes play out in multiple-period time frames that make natural extensions of ADSs computationally impractical. The general BIC structure overcomes the particular limitations of the ADS. BICs provide a viable alternative for real-world applications on a large, systematic scale, and incentivize responsible risk managers to advocate for the establishment of useful exchanges on such contracts (Kongtcheu, June 2, 2009). BICs replace the evasive and sometimes misleading concepts of probability and stochastic processes with the more tangible notion of a contract that locks in both risk and uncertainty, addressing, in practical and structural terms, long-standing deficiencies in the traditional probabilistic framework.

But hedging with BICs can’t eliminate all the risks and uncertainties, all the time, because BIC markets or exchanges may not be available for every type of randomly fluctuating event. Responsible risk management must mandate the hedging of risky contracts in order to reduce the worst possible scenarios in the residual exposure to a level that does not severely strain available institutional resources. FAS (Financial Accounting Standard) 133 and FAS 157 are written in this spirit of responsible risk taking, as is IAS (International Accounting Standard) 39, which sets a minimum required percentage for the hedged and unhedged portions of derivatives contracts. Still, the complexity and imprecision of these accounting rules often render them ineffective. In contrast, the rigorous mathematical framework of BICs enables an efficient approach to conscientious risk management.

KRUGMAN: RIGHT ANSWER, WRONG METHOD


Though no start date has been made public, the PPIP is expected to launch in early summer 2009. Investment managers with constrained resources who participate in PPIFs must be mindful of the multiple dimensions of the risk assumed and the prudential value of hedging exposure with trading instruments, like BICs, which offset uncertainty about the ultimate sell-off value of the troubled assets purchased as early as possible.

Many of those advocating against the Geithner Put’s generosity toward investors have borrowed Krugman’s approach, and have met with some argumentative success. Their efforts may have led to continued tightening of the terms of the PPIP, to the detriment of investors. In April 2009, Risk News reported that the subsidized government loan had been lowered from 85% to 50% of the funds’ balance sheets (Madigan 2009). Plugging those updated numbers into Krugman’s example changes 130.43 (“slightly over 130”) to 100, rendering the embedded put worthless.

If Krugman’s approach is fallacious, however, his instincts are true. The PPIP is indeed a major stumble for the administration, which could have restored market liquidity on troubled assets more quickly and efficiently had it become a market maker on those assets purchased or sold at the most refined level of granularity deemed practical, using relatively straightforward market-making methods. Such an approach would have been timelier, more surgical, and more durable, and could have been made part of the Federal Reserve Open Markets Operations’ standard arsenal.

The deeply unsettling problem with the arguments coming from Krugman and, subsequently, Joseph Stiglitz (2009) is their presumption of having definitively quantified the scope of the subsidy provided to potential PPIP investors, using the same flawed quantitative risk management tools that led to the crisis, and to the establishment of the plan, in the first place. But Krugman is right that the structural defects in the evolving PPIP may well be detrimental to the taxpayer (Kongtcheu, May 30, 2009a, and May 30, 2009b), and officials’ serious reservations regarding this may explain some of the several delays and adjustments to the launch of the plan. From the investor’s perspective, the PPIP’s path to profitability is far from straightforward, unless cost-effective replicating trading instruments in the spirit of alternative BICs can be found and calibrated in an efficient, effective hedging strategy.

REFERENCES


Keynes, John M. 1923. “Chapter 3.” A Tract on Monetary Reform. London, UK. Macmillan and Company. (Prometheus Books 1999.)
Kongtcheu, Phil. 2009. “TARP Toxic (Illiquid) Assets Pricing Model.” Wolfram Demonstrations Project.
———. May 30, 2009a. “Estimating Costs for PPIP Assets in a Market-Making Framework and BICs.” Knol.
———. May 30, 2009b. “Fair-Value Pricing, Government Market Making, and PPIP.” Knol.
———. June 2, 2009. “Introduction to Basis Instruments Contracts (BICs) for Mathematics, Finance, and Economics.” Knol.
Knight, Frank H. 1921. Risk, Uncertainty, and Profit. Boston, MA. Houghton Mifflin.
Krugman, Paul. March 23, 2009. “Geithner Plan Arithmetic” [post on “The Conscience of a Liberal” blog]. New York Times.
Madigan, Peter. April 20, 2009. “More Than 100 Firms Apply to Buy Toxic Assets under PPIP.” Risk News.
Stiglitz, Joseph E. April 1, 2009. “Obama’s Ersatz Capitalism.” New York Times.

Phil Kongtcheu is the CEO of PFK Technologies, a financial risk management consulting firm, and the author of BICs 4 Derivatives, Volume I: Theory (as Obi-Wan Yoda).