Computing Adjustment Factors for Price History

Pull up an unadjusted chart of a stock that did a 2-for-1 split, and you will see the price fall by half overnight with no news, no crash, nothing. Nobody actually lost half their money that day — the company simply doubled the number of shares outstanding, so each one is worth half as much, and shareholders now hold twice as many of them. If a backtest reads that raw price series directly, it will think the stock crashed 50% and might even generate a spurious sell signal.

Where the jumps come from

Two very different events both cause a visible break in a raw price series, and they need to be treated differently:

• Splits (mechanical): a 2-for-1 split doubles share count and halves the price. Nothing about the company changed; the pie is just cut into more slices. Every price before the split needs to be halved, and every share count before it needs to be doubled, to keep the series comparable.
• Dividends (economic): a cash dividend actually removes cash from the company and hands it to shareholders, so the ex-date price genuinely should drop by roughly the dividend amount. If you want a "total return" series that reflects what a holder actually earned, you need to add that cash back in as if it were reinvested.

The calculation

For a split, the adjustment factor is simply the split ratio. A 2-for-1 split multiplies all prior prices by $1/2$ and all prior share counts by $2$.

For a cash dividend, the standard textbook adjustment factor on the ex-date is:

$$f = \frac{P_{close} - D}{P_{close}}$$

Read in words: take the closing price the day before the ex-date, subtract the dividend, and divide by that same closing price. Every price before the ex-date gets multiplied by this factor, which is always a little less than 1, to bring the pre-dividend history down onto the same scale as the post-dividend series.

Worked example

A stock closes at $100 the day before its ex-date, then pays a $2 dividend and opens at $98.

1. Compute the factor: $f = (100 - 2) / 100 = 0.98$.
2. Apply it backwards: every historical close before the ex-date is multiplied by 0.98. A price of $80 three months earlier becomes an adjusted $78.40.
3. Chain multiple events: if the stock later does a 2-for-1 split, that period's prices get multiplied by both the dividend factor (0.98) and the split factor (0.5), compounding back through time. A stock with five dividends and two splits over ten years has an adjustment factor for early history that is the product of all seven individual factors.

Event	Raw close before	Factor	Adjusted close
$2 dividend	$100.00	0.98	$98.00
2-for-1 split	$196.00 (grown since)	0.50	$98.00
Combined (both events, earliest history)	$100.00	0.98 × 0.50 = 0.49	$49.00

Two adjustment styles, two answers

Data vendors typically offer two different adjusted series, and mixing them up quietly breaks a backtest:

• Split-adjusted (price return): corrects for splits only. Good for reading a clean-looking chart, but a long-only strategy will understate real returns because dividends are ignored entirely.
• Total-return adjusted: corrects for splits and dividends, as if every dividend were reinvested in the stock on the ex-date. This is the series that matches what a buy-and-hold investor actually earned, and it is the one that belongs in a backtest measuring strategy performance.