Why does the adjusted closing price take into account dividends?

I'm trying to get an intuition as to why the adjusted closing price includes a dividend adjustment:

\begin{equation} 1 - \frac{dividend}{close} \end{equation}

I understand why the adjusted closing price "undoes" the effect of a split on a stock. A stock split hasn't changed the economics of a company so the adjustment effectively removes the split so that the adjusted closing prices before and after the split can be compared.

A dividend does change the underlying economics however so why does the adjusted price account for it? Lastly, the formula also doesn't make sense.

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– chrisaycock♦ Sep 21 '12 at 3:42

3 Answers

Let's assume there is no adjustment and that a stock's price is the same after a dividend payment as before. Then I could get free money simply by buying a stock the day before the ex-date and then selling the stock right after the dividend distribution. Clearly no such arbitrage opportunity exists. Therefore, the price of the stock after the dividend payment must be the same as the price before the payment minus the dividend amount. That is, the adjusted price is

\begin{equation} adj = close - dividend \end{equation}

The other argument, as you point-out in your question, is that the fundamentals have indeed changed and that a company with less cash on hand must have a lower market cap. That is, the number of shares outstanding hasn't changed (unlike in a split), so the share price must change.

To get the ratio you asked about, divide both sides of the above equation by $close$:

\begin{equation} \frac{adj}{close} = \frac{close}{close} - \frac{dividend}{close} = 1 - \frac{dividend}{close} \end{equation}

Therefore, I can get the adjusted price simply by multiplying the closing price by $1 - \frac{dividend}{close}$.

To conclude: when looking at a stock's returns from one day to the next, the historical share price must be adjusted for all corporate actions (splits, dividends, and name changes) to present a coherent picture of returns. Otherwise, the returns will appear to have unrealistic gaps.

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It's just a convention, a way to account for the total return of the stock including dividends. This method is for simplicity's sake. It'd be "impossible" to try to take into account all of the infinite possibilities of dividend investment elsewhere.

You could think of it as "the dividend is fully reinvested cost-free", but that's just a short-hand way to visualize it.

If the stock increases by X and a dividend paid is Y then today's return is X+Y. It carries on to each new day, so that's why a dividend paying stock has higher adjusted prices than the true price.

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Often you're more interested in what your overall return would have been (or has been) over a certain holding period rather than how much the stock price has changed. In that case, you'd need to have some way to account for the dividends, and calculating adjusted stock price is a convenient way of doing it.

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