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Explain how a stock option's terms may be altered by dividends and stock splits.

FRM® Part I · Financial Markets and Products · Options Markets · FRM1.FM.12.c

The idea

Exchange-traded stock options are adjusted for stock splits and stock dividends, but not for ordinary cash dividends. Each adjustment leaves the holder's total exercise cost, strike × number of shares, unchanged. After an n-for-m split, the shares covered are multiplied by n/m. New strike = old strike × m/n. A 2-for-1 split halves the strike and doubles the shares. A 25% stock dividend is treated like a 5-for-4 split, so a call on 100 shares at 40 becomes a call on 125 shares at 32. Ordinary cash dividends are not adjusted for, so the stock falls by about the dividend on the ex-dividend date, which hurts call holders and helps put holders. Very large special dividends are the exception and are sometimes adjusted for. For an ordinary cash dividend, do not adjust the strike.

Formulas

Strike after an n-for-m stock split

new strike = old strike × m ÷ n

old strike
the strike before the split
n, m
the split ratio, n new shares for every m old

Shares covered are multiplied by n ÷ m, so strike × shares is unchanged. A stock dividend is treated as a split; ordinary cash dividends get no adjustment.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which event normally leads to an adjustment of the terms of an exchange-traded stock option?

  1. A stock split - correct
  2. An ordinary quarterly cash dividendWhy not: Ordinary cash dividends do not adjust exchange-traded options; the stock simply falls on the ex-dividend date.
  3. A rise in the stock price of 20 percentWhy not: Price moves change option value but never its contractual terms.
  4. A change in the company's credit ratingWhy not: Rating changes affect prices, not the strike or the number of shares the option covers.

Exchange-traded options are adjusted for splits and stock dividends so that the holder's position is unchanged, but not for ordinary cash dividends.

A harder one

A company declares a 25 percent stock dividend. A call option covers 100 shares with strike 40. What are the adjusted terms?

  1. 100 shares with strike 32Why not: Adjusts the strike but leaves the number of shares unchanged.
  2. 125 shares with strike 40Why not: Increases the shares but leaves the strike unchanged.
  3. 125 shares with strike 32 - correct
  4. 125 shares with strike 50Why not: Multiplies the strike by 1.25 instead of dividing by it, moving it in the wrong direction.

A 25 percent stock dividend equals a 5-for-4 split: shares x 1.25 = 125, strike x 4/5 = 32. Total exercise cost 4,000 is unchanged (125 x 32).

The hardest tier

A call covers 300 shares with strike 45, and the stock trades at 54. The stock then splits 3-for-2, so the price becomes 36. What is the total intrinsic value of the call after the split?

  1. USD 1,800Why not: Adjusts the strike to 30 but keeps the original 300 shares instead of the adjusted 450.
  2. USD 4,050Why not: Uses the adjusted 450 shares but keeps the old strike of 45 in the per-share gain (54 - 45).
  3. USD 0Why not: Compares the new price (36) with the unadjusted strike 45 and concludes the call is out of the money.
  4. USD 2,700 - correct

After the split: 450 shares, strike 45 x 2/3 = 30. Intrinsic value = 450 x (36 - 30) = 2,700, the same as before (300 x 9). A correct adjustment leaves value unchanged.

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