black swan event in economics

The concept of fair market value is central to litigation and bankruptcy asset valuations. As such, bankruptcy asset valuation methods affect every part of the reorganization or liquidation process.


As per the authoritative bankruptcy valuation paper, “Valuation Methodologies: a Judge’s View by US Bankruptcy Judge Christopher S. Sontchi (Chief Judge, D.Delaware), a company and/or its assets can be valued in one of four ways (as paraphrased in this section, below):
1. Estimation of current asset values, typically using liquidation value or replacement value;
2. Discount of expected cash flows (DCF);
3. Relative value analysis of comparable companies / assets; and
4. Contingent event assessment.

According to Chief Judge Sontchi, other than option pricing method, all of the above bankruptcy asset valuation methods, either individually or in various combinations, are routinely presented to bankruptcy courts in valuation hearings. No matter which methodology is used, however, the goal remains the same: to determine as accurately as possible what the sale price would be; i.e, “price discovery.” Let us review these valuation methods in the order addressed by Judge Sontchi:

LIQUIDATION VALUE VALUATION METHOD. Liquidation value, at first blush, seems less useful than, say, discounted cash flow analysis or comparable sale analysis. However in a Chapter 11 setting, this value takes on significance because a standard Chapter 11 debtor must show, for Plan confirmation, that each claim-holder has either voted for plan confirmation or would otherwise receive no less than liquidation value under a Chapter 7 proceeding.

DISCOUNTED CASH FLOW VALUATION METHOD. The discounted cash flow method assumes that the value of an asset is the present value of expected future cash flows from it, reduced by a discount rate that contemplates risk and the cost of capital. The cash flow projections used for valuation typically come from management’s estimates of future performance. As such, cash flow estimates are necessarily subject to uncertainty relating to matters specific to the firm as well as to broader issues such as the general state of the economy.

COMPARABLE ASSET VALUATION METHOD. In comparable valuation, the value of an asset is derived from the pricing of comparable assets, standardized using a common variable, such as, e.g., EBITDA. Unlike discounted cash flow valuation, which is a search for intrinsic value, relative valuation is a search for market value. In this analysis, one assumes that the market is correct in the way it prices assets and firms on average.

The two most common comparable valuation methodologies used in chapter 11 cases are the comparable companies analysis and the comparable transactions analysis. Under both methods, one determines a metric by which to value the company such as EBITDA. One then looks to either comparable publicly-traded companies or control transactions involving comparable companies to determine the appropriate multiple to apply to the selected metric to reach a conclusion of the target asset value.

CONTINGENT EVENT VALUATION METHOD. The premise underlying the use of option pricing models in valuation is that discounted cash flow models tend to understate the value of assets that provide payoffs that are contingent on the occurrence of an event. As per Chief Judge Sontchi: “[f]or example, consider undeveloped oil reserves. One could value this oil reserve based on expectations of oil prices in the future but this estimate would miss the fact that the oil company will develop the reserve only if oil prices go up and will not if oil prices decline. An option pricing model would yield a value that incorporates this right.”

As a practical matter, bankruptcy judges have become familiar and comfortable with the discounted cash flow, comparable companies and comparable transactions methodologies described above. These methods are often referred to as the “standard” bankruptcy asset valuation methods. Chief Judge Sontchi explains:

Of course, there are other valuation methodologies such as contingent claim valuation. While use of an alternative valuation may be appropriate, one should be reluctant to depart from the familiar. The judge will be inherently suspicious of the use of such an alternative valuation. The valuation professional should be prepared to provide a clear reason for not using the DCF, comparable companies and/or comparable transactions methodologies.

Valuation Methodologies, a Judge’s View, ABI Law Review, Vol. 20:1

These are the standard bankruptcy asset valuation methods in wide use today.


Standard valuation models are concerned with assessing value of a particular asset–be it a physical or intangible asset, or an entire company. Factors that influence valuation are book value (price paid), comparable asset prices in the industry and general economic factors such as interest rates and stock prices.

The main thesis of this series of articles is that insufficient attention is paid to general economic factors. In pricing an individual asset, it is no longer sufficient to focus on price movements of interest or stocks in the general economy. Rather, we need to look deeper into the credit and derivative markets to understand the true risk that general economic factors create for specific assets. We also need to recognize the inherent limitations of valuation models, such as the Black Scholes Equation, based on Gaussian mathematics, since any normal distribution of value might be instantly distorted by an unpredicted “long-tail” event; thus rendering a valuation meaningless.


In a world in which the value of numerous asset classes is artificially manipulated, it becomes necessary to carefully deconstruct the assumptions that underlie the value methods described above. With exception of simple metrics such as book value and some instances of replacement value, the most important assumption underlying each of these primary valuation metrics is the “normalcy bias,” both the assumption of normalcy in human psychology, and the assumption of the normal distribution in statistics and financial analysis. The assumptions underlying these normalcy biases are present in virtually every assessment of fair market value made by a court. These biases include the following assumptions:

–prices will be stable over the relevant period of valuation: typically 3 to 5 years.
–back-testing historic asset prices is a reasonable approach to predicting future asset prices.
–future cash flows will be reasonably stable over the expected discount period.
–any fluctuation in prices and values will revert to a historic mean during the relevant period of valuation.
–what happened yesterday will be a good guide to what is likely to happen tomorrow.


Chief Judge Sontchi underscores the normalcy bias in the thought process of judges, when he cautions that in choosing a valuation method, lawyers “should be reluctant to depart from the familiar. The judge will be inherently suspicious of the use of such an alternative valuation.”

This comment is a classic case of the normalcy bias in human psychology–but, in truth, it is required for stable functioning of our legal system. Our system expects stability; clients expect predictability. The very notion of stare decisis is an expression of the high premium placed on stability. Stability and predictability in the legal system give our society the comfort and trust in the judiciary, and allow litigants and parties to expect a fair outcome in the handling of their cases.

So, in this valuation discussion series we wholeheartedly endorse the importance of normalcy bias in judges’ handling of bankruptcy matters and other cases.

But what happens when the natural and necessary normalcy bias of a judge bumps up against flawed and misleading normalcy bias built into current valuation models during times of economic uncertainty? In that event, stability of the legal system can be undermined if litigants and parties receive unfair results based on flawed bankruptcy asset valuations and, ultimately, may lose faith in the entire process. Obviously we should all strive to avoid that result. Rather, judges, attorneys and valuation experts owe it to everyone involved to diligently pursue the most logical and correct valuation methods available.

Unfortunately, in today’s chaotic environment, bankruptcy asset valuation methods based on the normalcy biases built into statistical and financial analysis are likely to disappoint and disrupt fair litigation outcomes. To put it bluntly: during times of economic distress, the financial models typically relied on for valuation assessments don’t work. And that’s a problem.


Financial valuation methods widely used today assume the validity of Newton’s law of averages; or, put another way, that calculus computations can accurately predict changes to a dynamic system. This theory assumes that an economic system can be accurately modeled by building from a small amount (low dimensionality) of observed time-series data, then building out a complete model based on limited observations using assumptions of standard deviations analysis and other tools of probability theory. Importantly, the model assumes a normal distribution of all data in the model, based on the limited observations of collected data.

One fundamental problem with this approach is that it ignores the reality that complex dynamical systems (such as a global economic society) cannot be represented by a small sampling of data because each actor in an economy is a self-driven decision-maker. In reality, there is no such thing as a normal distribution of economic actors.

Another fatal flaw of using calculus to model complex financial/economic dynamics is that the normal distribution theory assumes standard deviations form a normal and natural “mean” (average) calculation. This means that “long-tail” events that only happen in remote instances, are ignored, because their likelihood of occurrence deviates too far from the standard deviations built into the calculus model.

This is why “once-in-a-century” events are ignored in calculus-based financial models, because the standard deviation for such events is so far from the mean that the concept of “standard deviation” becomes meaningless. If any possibility can happen, then how can one develop a theory that predicts anything at all? One cannot.

So if the beginning point is to use calculus to describe dynamical systems, the assumptions must fit the capacity of the model, which in the case of calculus is the normal distribution. Therefore outlying events too remote from the standard deviation must be ignored or the model will be broken. So in today’s world, limitations of the model drive bad results in predicting complex dynamical systems, such as the global economy.

For a glaring example of the truth of this statement, one need look no further than the widely-used Black Scholes valuation equation. Once the holy grail of investing, blind reliance on the Black Scholes equation was singularly responsible for the failure of Long Term Capital Management (LTCM) and the financial crisis of 1998 that nearly bankrupted several Latin American countries.

LTCM placed absolute faith in the normalcy-bias analytics underlying the Black Scholes formula and refused to adjust investment positions based on data that contradicted the model–LTCM refused to account for outlier events that were staring them right in the face. The proverbial black swan events. The result was failure in 1998 of LTCM, the $126 billion hedge fund, and the resulting bailout by Wall Street banks, engineered by the New York branch of the Federal Reserve.

Incredibly, notwithstanding the abject failure of the Black Scholes formula on the world’s largest stage, it is still widely used today for asset valuations by hedge funds and investment banks. Almost certainly, bankruptcy and civil court judges have been introduced to this valuation equation.

Again, admittedly, this equation and other bankruptcy asset valuation methods based on Newton’s law of averages can work reasonably well during times of economic stability. But the problem with these valuation models is the normalcy bias–the assumption that financial systems will naturally revert to a stable mean or median. This is simply not true during times of economic instability.

Valuation models based on a normalcy bias abjectly fail to account for outlying crisis conditions; and rather assume only that crisis events happen once in a very great while, so there is no need to account for the possibility of a crisis–the proverbial black swan event popularized by financial author Nassim Taleb.

But what happens in an economy when black swan events are no longer “once-in-a-century” occurrences; but rather, happen with high regularity in every business cycle? When that happens, bankruptcy asset valuation methods that don’t account for supposed “once-in-a-century” crisis events are no longer reliable.

And that is where we are today, from at least 1998 to 2008 to 2020. We are in a cycle of crisis events that are supposedly so rare that financial valuation models need not account for them–and yet they are occurring every few years, with an enormous destructive consequence for our economy and peoples lives.


It is time to re-evaluate our bankruptcy asset valuation methods.  But how?

Judges rightly resist the idea of a “wait-and-see” approach to valuation, but it is also not realistic to confirm a plan based on bankruptcy asset valuations that may drastically change during the 3 to 5 year (or more) life of the proposed plan. Nor is it realistic to ask for a valuation change during the middle of a plan based on a material change in economic circumstances or asset value.

The plan’s initial asset valuation establishes security and collateral rights, determines rights for adequate protection, determines claim amounts and allows the plan to be confirmed. A very chaotic situation would result if creditors and debtors needed to entirely revisit the bankruptcy process with each material change in economic conditions. For this reason, courts and lawyers must do our best to arrive at workable bankruptcy asset valuations that can reasonably sustain economic changes during the proposed life of a plan, and beyond.

The primary thesis of this blog series is that bankruptcy asset valuation methods in 2020 must now account more completely for global economic conditions than ever before, due to Federal Reserve policy and the unavoidable influence of global derivatives trading markets. In theory, the standard valuation models used in bankruptcy courts and other civil courts will continue to work, even in times of asset value distortions, as long as a correct attention is placed on global economic conditions. This requires courts and valuation experts to account for the impact speculative derivatives may have on the value of an asset and asset class.

We suggest that a valuation approach incorporating a modern scientific method called “complexity theory” can help adjust our standard bankruptcy asset valuation models to more accurately anticipate the value distortions created by market interventions and derivatives trade. This concept is discussed next in Part 4: Modifying the Standard Valuation Models.

bankruptcy asset valuation methods