Madoff: A Riot of Red Flags: formula sheet

Key formulas

Collar (split-strike conversion) payoff at expiry

P&L per share = max(K_put, min(S_T, K_call)) − S_0 + net premium (net premium = call premium received − put premium paid)

Value is floored at the put strike and capped at the call strike. Net premium is premium received on calls minus premium paid on puts.

Maximum gain of a collar

Max gain = K_call − S_0 + net premium

Net premium = call premium received − put premium paid. It can be positive or negative.

Maximum loss of a collar

Max loss = S_0 − K_put − net premium

Occurs when S_T ≤ K_put. Max loss is stated as a positive number for a loss. If the computed value is negative, the collar locks in a minimum gain (a guaranteed profit floor).

Ponzi solvency condition

New inflows + real income ≥ redemptions + promised payments

When this fails, the scheme collapses. Real income is near zero in a pure Ponzi scheme.

Sharpe ratio

Sharpe = (Rp − Rf) ÷ σp

Use annualised return and annualised volatility. An unusually high value for a strategy of this type is a warning sign.

Annualising monthly volatility

σ(annual) = σ(monthly) × √12

Assumes returns are independent month to month. Convert before comparing with annual figures.

Beta to the market

β = Cov(Rp, Rm) ÷ Var(Rm) = ρ × σp ÷ σm

A collar on large-cap equities should show clearly positive beta. Near-zero beta is a red flag that calls for checking, not proof on its own.

Capacity test

Required option contracts ÷ market option volume or open interest

If one fund would need a large share of total market volume, the claimed strategy is not feasible at that size.

Collar payoff bounds

Stock loss is limited below the put strike; gain is capped at the call strike (net of premiums)

Returns should be bounded but not smooth. Gains and losses should follow the market inside the bounds.

Independence test

Manager ≠ custodian ≠ administrator ≠ clearing broker ≠ auditor

A rule of thumb, not a formula. Each role should sit with a separate, credible party. Any overlap removes a check.

Auditor adequacy check

Auditor size and expertise ≥ complexity and size of assets audited

A tiny auditor for a very large, complex fund is a red flag. It is a judgment test, not a numeric rule.

Red flag classification

Operational flag = missing independent control; Performance flag = results or strategy that do not add up

Exam questions often ask you to sort a given warning sign into one of these two groups.

Ponzi test

Cash paid out to investors > Cash earned from real investments → scheme depends on new inflows

A scheme survives only while new deposits exceed redemptions. A wave of redemptions, as in late 2008, exposes it.

Independent verification rule

Claim = Trusted only if confirmed by an independent third party

Confirm assets with the custodian, trades with the clearing house or counterparty, and returns with the administrator. Never rely only on manager-provided records.

Operational due diligence checklist

Custodian + Administrator + Auditor + Governance + Valuation + Service-provider independence

Each item should be independent of the manager. In Madoff's case the broker-dealer, adviser and custodian functions were all under one roof.

Plausibility check on returns

Sharpe ratio = (Rp − Rf) ÷ σp

An unusually high Sharpe ratio with very few down months is a warning sign, not proof of skill.

Quick revision

• A Ponzi scheme pays earlier investors from money raised from new investors, not from real investment profits.
• It fails when redemptions exceed new inflows.
• Madoff claimed a split-strike conversion strategy, but the reported results did not match how that strategy would behave.
• Returns that were consistently smooth and steady, with very few down months, were a performance red flag.
• A strategy that cannot be explained or replicated by others is a red flag.
• Madoff's firm acted as its own broker-dealer and custodian, so there was no independent check on trades or assets.
• The auditor was a very small firm, which was unsuitable for the scale of assets managed.
• Secrecy and unwillingness to give transparency to investors are governance red flags.
• Feeder funds collected fees while relying on Madoff and often did not carry out full independent due diligence.
• Due diligence should verify trades, custody, service providers and the plausibility of returns independently.
• Regulators received warnings and failed to investigate them effectively.
• Key lesson: independent verification and segregation of duties matter more than reputation.

Common mistakes

• Saying Madoff's problem was that split-strike conversion is a bad strategy in itself. Fix: The strategy is a legitimate collar. The issue is that it could not produce the reported returns, and the trades were not real.
• Describing the strategy as long calls and short puts. Fix: Remember: short out-of-the-money calls (caps gains), long out-of-the-money puts (protects losses), on top of a long stock basket.
• Treating smooth returns as proof of fraud. Fix: Say that smooth returns are a red flag that calls for verification. Some low-volatility strategies exist, but they must match the strategy's logic.
• Saying a collar strategy should have no losing months. Fix: A collar limits losses but does not remove them. The stock can fall to the put strike, and premiums cost money.
• Treating consistent returns as an operational red flag. Fix: Smooth returns are a performance and strategy flag. Operational flags are about who holds assets, audits, clears and reports.
• Saying the auditor was a red flag only because it was unknown. Fix: The issue is capacity and independence: a tiny firm could not credibly audit a very large, complex operation.
• Treating the fraud as undetectable. Fix: Remember that many red flags were visible and checkable. The failure was in acting on them, not in access to information.
• Focusing only on investment red flags such as smooth returns. Fix: Give equal weight to operational flags: the manager as custodian, the tiny auditor, and no independent verification of trades.
• Saying the SEC lacked information about Madoff. Fix: Say the SEC had the information but failed to verify, escalate and act on it, partly through weak expertise and process.
• Treating the fraud as an investment risk problem. Fix: Frame it as an operational and governance failure: custody, administration, audit and independence.

Exam tips

• Know the three legs of the collar and the payoff shape. Expect questions that ask what the strategy should have produced.
• Link every red flag to a control: returns to performance review, structure to independent custody, secrecy to operational due diligence.
• Watch for answer options that call the fraud 'unlucky' or 'a model error'. Those are wrong.
• Do not rely on memorised dollar totals. Focus on mechanics and reasoning.
• If asked what a due diligence team should do, choose independent verification of trades, custodian and auditor.
• Expect case-style questions that give a few numbers and ask which feature is the red flag. Eliminate answers that call the results normal for the strategy.
• Know the strategy by name: split-strike conversion, a collar on a basket of large-cap equities.
• Watch the units. Convert monthly figures to annual before comparing.