Questioning the Obvious
Bender challenges default assumptions about how future prices are distributed. Options are sensitive to the shape of possible outcomes, not simply whether a share is expected to rise or fall. If an investor has a different probability assessment from the one reflected in prices, the relevant question is whether that assessment is better grounded—not whether it is more imaginative.
Our interpretation is to compare whole payoff tables. Two views can share a mean while assigning very different chances to extreme moves. An option can look cheap under one distribution and expensive under another. The book’s discussion is conceptual; modern pricing is not reducible to the claim that every option uses one naive bell curve. A probability model must confront observable prices, costs and model error.
Why a physics student turns to options
Bender’s background combines mathematics, exchange-floor experience and serious games such as Go and backgammon. He distinguishes professional use of an edge from casual gambling. The point is not that a favourable bet wins every time; it is that one must keep making sound decisions after losses without risking a stake so large that an ordinary adverse run ends participation. This bankroll question comes before the discussion of option valuation and remains necessary even if the trader’s probability estimate is good.
The real unknown in an option model
His central argument is that, given the full distribution of prices at expiry, calculating expected option payoffs is straightforward compared with estimating that distribution. He objects to treating one convenient shape as an adequate description of every stock and period. Support beliefs, fund inflows, limited floats and feedback from past performance can affect price behaviour. He is not offering a replacement formula that fits all markets; he calls for market-specific reasoning about outcomes and probabilities. Those probabilities remain estimates, not knowledge of the future.
The book’s examples: fund flows and bankroll
One mechanism he describes is a sector feedback loop: strong performance attracts fund subscriptions, sector funds buy more of the same kind of stocks, and prices may strengthen further. This explains why he questions an overly simple picture of independent random moves. Separately, he asks whether a person should risk all their wealth on a very favourable coin-toss payoff. The numerical edge alone cannot answer because the personal cost of losing everything differs from the benefit of extra wealth. The example exposes the gap between maximising expected money and preserving the ability to continue.
Schwager’s explanation and a technical distinction
Schwager pauses to explain probability distributions and the relationship between price ranges and probability mass. His concluding lesson is to make the assumed distribution explicit before choosing an option structure. An editorial clarification is useful: the standard Black–Scholes framework models prices as lognormal under its assumptions, rather than saying raw prices follow a symmetric normal curve. The chapter’s broader challenge remains about the adequacy of assumptions. The study exercise should test that challenge without pretending that every option market participant uses the same simplistic model.
Worked example
Model A ends at 100 with certainty. Model B ends at 50 or 150 with equal chance. Both average 100, but a call with strike 100 pays 0 in A and averages 25 in B, before premium.
Limits
A more elaborate distribution is not necessarily more accurate. Options add expiry, volatility and execution dimensions.
Case connection
Bender questions assumed distributions. Ask whether ordinary historical price data capture a sudden change in the supply needed to close shorts.
Volkswagen: when the exit becomes scarce
A view about a company’s value is different from the ability to buy shares back when required.
A disclosure changes the setting
On 26 October 2008, Porsche disclosed 42.6% ownership of Volkswagen ordinary shares plus cash-settled options relating to 31.5%. These were different forms of exposure, not 74.1% direct share ownership. In a release dated 29 October, Porsche described extreme price movements and proposed settling hedges relating to up to 5% of the shares, depending on conditions. That was an announced intention, not proof that every proposed transaction occurred. [1, 2]
Interpretation: covering needs a seller
A short seller eventually needs to close or otherwise settle the obligation. A view that a business is overvalued cannot produce shares on demand. If urgent buyers compete for a limited supply, the price needed to complete a transaction can separate sharply from a long-term valuation. The mechanism is about timing and availability. It does not require every buyer to believe the business has suddenly become more productive, nor every short seller to share the same thesis.
Do not confuse a contract with a share
Cash settlement pays a contractual amount rather than automatically delivering the underlying shares. A counterparty may hedge its exposure, but the headline option percentage alone does not disclose every hedge or every available share. Subtracting a few published percentages and calling the answer the exact tradable supply would be too confident. Separate legal ownership, economic exposure, potential hedging demand and actual market liquidity before drawing a conclusion. This distinction connects directly with the book’s options appendix.
Hypothetical: right eventually, unable to wait
Suppose a fictional trader shorts 100 shares at 100. At a price of 200 the mark-to-market loss is 10,000 before fees, and funding requirements may force a decision. A later fall to 60 would not rescue a position already closed at 200. These are invented prices, not a Volkswagen trade reconstruction. The example separates the terminal forecast from the path required to reach it. A plan needs a financing and exit assumption as well as a valuation opinion.
Different questions for different chapters
Galante’s chapter asks whether a bearish business case includes the special risks of being short. Minervini’s asks what happens when an intended exit level cannot be obtained. Masters’s asks how a dated disclosure changes the catalyst. Bender’s asks whether a probability distribution built from ordinary conditions misses a change in available supply. These are teaching comparisons, not claims that any of these traders participated in this episode or used a particular strategy on Volkswagen.
Source limits matter
The cited releases are Porsche’s own contemporary statements. They establish what Porsche disclosed and proposed; its explanation of responsibility is an interested party’s account, not an independent finding about every cause or motive. This case therefore avoids treating the company’s blame of short sellers as a settled verdict. Nor can public percentages reveal each participant’s borrowing terms. A defensible explanation can describe a plausible scarcity mechanism while remaining explicit about information it does not possess.
The habit to keep
Before evaluating a short thesis, write a second thesis about how it can be financed and closed. Ask what changes if the available supply contracts. An attractive destination does not guarantee a survivable journey, and a contractual exposure does not tell you everything about the underlying shares.
Consider
What would a share-availability check add to a valuation argument?
Analysis guide
Distinguish borrow availability, financing capacity and executable liquidity. Explain why a cash-settled option percentage is not direct ownership.
Porsche · Holdings disclosure, 26 October 2008 · Porsche · Statement dated 29 October 2008
Reflection
Which tail assumption has the greatest effect on your example’s payoff?