Stock Splits, Dividends & Option Impact

TAKEAWAYS:

• Stock splits halve share prices but double option contracts (e.g., 100 shares → 200 shares at half price).
• Dividends reduce option value by the present value of the dividend; call options lose more than puts.
• American options can be exercised early to capture dividends, unlike European options.
• Stock splits and dividends adjust option strike prices but not their intrinsic value formula.
• Equity swaps use dividends to swap fixed/floating returns without direct stock ownership.
• Hedging with options requires recalculating Greeks (Δ, Θ, Vega) post-split/dividend.

1. Stock Splits: Mechanics and Option Adjustments

Definition and Impact

A stock split increases the number of shares outstanding while proportionally reducing the share price. For example:

• A 2-for-1 split: 1 share → 2 shares; price halves (e.g., Rs 100 → Rs 50).
• Option contracts adjust: Each new share gets its own option (e.g., 1 call for 100 shares → 2 calls for 200 shares).

Key Adjustments:

Why?

• Intrinsic value remains the same (e.g., Rs 20 call on Rs 100 stock → Rs 10 call on Rs 50 stock).
• Extrinsic value (time value) may change due to market reaction.

Worked Example: RK Company Split

Scenario:

• RK Company announces a 2-for-1 split. Current:
  • Stock price = Rs 230
  • Call option (exercise price Rs 200) = Rs 45
  • Put option (exercise price Rs 200) = Rs 15

Adjustments:

1. New share price: Rs 230 / 2 = Rs 115
2. New strike price: Rs 200 / 2 = Rs 100
3. Option contracts: 1 call → 2 calls (for 200 shares).

Intrinsic Value Check:

• Before split: Call intrinsic = Rs 230 – Rs 200 = Rs 30
• After split: Call intrinsic = Rs 115 – Rs 100 = Rs 15 (per contract, but total intrinsic doubles).

Mermaid Diagram: Stock Split Impact on Options

graph TD
  A["Original: 1 Share, Price = Rs 230"] -->|"2-for-1 Split"| B["2 Shares, Price = Rs 115"]
  A -->|"Call Option: 100 shares, Strike = Rs 200"| C["Intrinsic Value = Rs 30 (per 100 shares)"]
  B -->|"Call Option: 200 shares, Strike = Rs 100"| D["Intrinsic Value = Rs 30 (per 200 shares)"]
  C -->|"After Split"| E["Rs 15 (per 100 shares, but total intrinsic unchanged)"]
  D -->|"Before Split"| F["Rs 30 (per 100 shares)"]

Dividends: Cash Payments and Option Value

Dividends reduce option value because they lower the stock price post-payment. The present value of the dividend is subtracted from the option’s fair value.

Formula for Dividend-Adjusted Option Price: For a call option: $$C_{adj}=C_{original}-e^{-rT}\times D$$ For a put option: $$P_{adj}=P_{original}-e^{-rT}\times D$$ Where:

• $D$ = Dividend amount
• $r$ = Risk-free rate
• $T$ = Time to dividend payment (in years)

Example: ABC Company Dividend Scenario:

• Stock price = Rs 170
• Dividend = Rs 10 (paid in 2 months)
• Risk-free rate = 8% (continuous compounding)
• Call option (exercise price Rs 170, 3 months to expiry) = Rs 12

Calculation:

1. Present value of dividend: $$D_{PV}=10\times e^{-0.08\times (2/12)}=10\times e^{-0.0133}\approx 9.87$$
2. Adjusted call price: $$C_{adj}=12-9.87=\text{Rs }2.13$$

Why Puts Are Less Affected:

• Calls: Dividends reduce stock price → lower intrinsic value.
• Puts: Dividends increase stock price → higher intrinsic value (but extrinsic value drops).

2. Stock Splits vs. Dividends: Key Differences

3. Real-World Applications

## In the real world

1. Nepal Stock Exchange (NEPSE) and Equity Swaps

   • Company: NEPSE trades stocks like Ncell and NTC. Investors use equity swaps to hedge against dividend risks.
   • How? A pension fund swaps fixed returns for Ncell’s dividend yield (e.g., 5% annual dividend) without owning shares.
   • Why? Avoids volatility while capturing income.

2. Daraz and Supplier Payments

   • Scenario: Daraz suppliers receive dividend-like cashbacks (e.g., Rs 500 per order). If Daraz issues call options on its stock, suppliers’ cashbacks act like dividend equivalents, reducing call option value by Rs 500 × $e^{-rT}$.

3. Pathao and Driver Incentives

   • Analogy: Pathao’s promotions (e.g., Rs 100 bonus per ride) resemble dividends. If Pathao’s stock had options, drivers’ bonuses would decrease call option premiums by their present value.

Worked Example: Equity Swap with Dividends

Scenario: An asset manager wants to swap fixed returns (6%) for Ncell’s dividend yield (4%) using an equity swap.

Given:

• Notional principal = Rs 60 million
• Dividend payment dates: 90 and 180 days
• Risk-free rate = 5%

Steps:

1. Calculate dividend present values:
   • Day 90: $D_1=4\%\times 60M\times e^{-0.05\times 0.25}=2.4M\times 0.9877\approx 2.37M$
   • Day 180: $D_2=4\%\times 60M\times e^{-0.05\times 0.5}=2.4M\times 0.9753\approx 2.34M$
2. Total dividend PV: Rs 4.71 million
3. Fixed payment: Rs 60M × 6% × 0.5 = Rs 1.8M (for 90 days)
   • Net cash flow: Rs 1.8M (paid) – Rs 2.37M (received) = Rs –0.57M at 90 days.

Mermaid Diagram: Equity Swap Cash Flows

4. Hedging Strategies with Splits/Dividends

Option Greeks Adjustment

When a stock splits or pays dividends, Greeks (Δ, Θ, Vega) must be recalculated:

• Δ (Delta): Changes due to new strike price.
• Θ (Theta): Time decay accelerates post-split.
• Vega: Sensitivity to volatility remains but is scaled by split ratio.

Example: American Put Exercise

• Scenario: A Rs 100 strike put on Rs 110 stock (2-for-1 split → new strike Rs 50, stock Rs 55).
• Action: Holder may exercise early to capture dividends (if American option).

5. Common Exam Pitfalls

1. Misapplying Split Adjustments:

   • ❌ Wrong: "Strike price doubles after a 2-for-1 split."
   • ✅ Correct: "Strike price halves."

2. Dividend Timing:

   • ❌ Wrong: "Dividends increase call option value."
   • ✅ Correct: "Dividends decrease call option value by their present value."

3. American vs. European Options:

   • ❌ Wrong: "European options can be exercised early for dividends."
   • ✅ Correct: "Only American options can be exercised early."

## Exam Tip

Focus Areas:

1. Stock Split Adjustments:

   • Memorize the split ratio formula for strike prices and contracts.
   • Know that intrinsic value per share stays the same but total intrinsic value doubles.

2. Dividend Impact:

   • Calculate present value of dividends using $e^{-rT}$.
   • Recall that calls lose more value than puts due to dividends.

3. Equity Swaps:

   • Understand how dividend yields replace fixed payments in swaps.
   • Practice net cash flow calculations for exam questions.

4. Option Exercise:

   • American options may be exercised early for dividends; European options cannot.

Question Types:

• Numerical: Adjust option prices post-split/dividend (e.g., "A stock splits 3-for-1; recalculate the call’s intrinsic value").
• Conceptual: "Why does a dividend reduce a call’s value more than a put’s?" (Answer: Calls benefit less from dividends than puts).
• Application: "How would a pension fund hedge dividend risk using options?" (Answer: Buy puts or use equity swaps).

Final Note: Stock splits and dividends are critical for option pricing in real-world markets like NEPSE. Always adjust strike prices and dividends before calculating option values, and remember that American options offer flexibility to capture dividends early. Practice with Nepali business examples (e.g., a Kathmandu retail shop’s stock split) to master the mechanics.