σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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Market Structure skill›Module 4 · Rules, costs and data›Topic 4.3·~40 minIntermediate

Corporate actions and calendars

Skill positionModule 4 of 4 · Topic 3 of 4
4.3 Corporate actions and calendars
—Lab score— / 100Total XP—Streak—

When the price series lies

A corporate action is an event that changes a company's securities without any trading profit or loss: cash dividends, stock splits and reverse splits, spin-offs, mergers, ticker changes and delistings. They matter to data because the raw price series jumps even though no investor gained or lost anything.

A cash dividend has four dates: the declaration, the ex-dividend date, the record date and the payment date. You receive the dividend only if you buy before the ex-dividend date. Since US stocks moved to T+1 settlement in May 2024, the ex-dividend date and the record date fall on the same day, and on that day the price typically opens lower by about the dividend.

A stock split changes the number of shares and the price in opposite directions: in a 4-for-1 split each share becomes four and the price is divided by four, leaving the company's value unchanged. A reverse split does the opposite. To make a price history comparable, data providers adjust old prices (and volumes) for splits and dividends. The QuantCraft price files are adjusted this way: there is no raw close, and the data holds only stocks that still exist, so companies that were delisted are missing.

  • Ex-dividend date: buy on or after it and you do not get the dividend.
  • Split: shares and price change in opposite directions, value unchanged.
  • Adjusted price: history rescaled so splits and dividends do not look like returns.
  • Survivorship: delisted companies are missing, so past results look better than reality.
A split in the raw dataA stock closes at 400.00, then splits 4-for-1 and closes at 100.50 the next day. The raw return is 100.50 / 400.00 − 1 = −74.9%, which is not a loss. Dividing the old price by 4 gives 100.00, and the adjusted return is 100.50 / 100.00 − 1 = +0.5%. For a dividend, if a stock closes at 100.00 and pays 1.00 on the ex-date, earlier prices are multiplied by (100 − 1) / 100 = 0.99.
The calendar is part of the dataUS exchanges close on about ten holidays a year and close early at 13:00 ET on a few days such as the day after Thanksgiving and Christmas Eve. Monthly options expire on the third Friday, which brings volume spikes. A missing bar on a holiday is not a data error, and a session with fewer than 390 minutes is normal.

Lab · what's graded

  • Actions and effects20 pts
  • Dividend timeline15 pts
  • Adjusting for a split15 pts
  • Adjusting for a dividend15 pts
  • A −75% day10 pts
  • Calendar facts10 pts
  • Adjusted prices and survivorship15 pts
0/ 7 answered
Tasks
1Match20 ptsNot answered

Match each corporate action to its effect.

Pick the partner of each item on the left.

4-for-1 split
1-for-10 reverse split
Cash dividend
Delisting
2Order the steps15 ptsNot answered

Put these events of a cash dividend in chronological order.

Drag to reorder, or focus an item, press Space to lift it, the arrow keys to move it and Space to drop it.

  1. 1Payment date: the cash arrives
  2. 2Declaration: the company announces the dividend
  3. 3Ex-dividend date: buyers no longer get the dividend
3Numeric answer15 ptsNot answered

A stock closed at 400.00 before a 4-for-1 split. What is that close on the split-adjusted basis?

adjusted close=\text{adjusted close} =adjusted close=accepted: ± 0.01
4Numeric answer15 ptsNot answered

A stock closes at 100.00 on the day before the ex-dividend date and pays a dividend of 1.00. What factor multiplies all earlier prices in the dividend-adjusted series?

factor=\text{factor} =factor=accepted: ± 0.0001
5Choice10 ptsNot answered

The raw close drops from 400.00 to 100.50 overnight, a return of about −75%. What is the most likely explanation?

6Choice10 ptsNot answered

Select every true statement about the US trading calendar.

7Explain in words15 ptsNot answered

In two or three sentences, explain why a backtest should use adjusted prices and what is wrong with a dataset that only contains surviving stocks.

Math modeKeyboard or LaTeX inputTask 1 of 7 · Ctrl ⏎ to check

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