It is known that stock prices will fall by the amount of the dividend on the ex-dividend date:
- Do stock prices drop due to dividends?
- Does a stock really dip in price on the ex-dividend date? And why would it do this?
- Why does the price of a stock really drop on ex-dividend date?
My question here is related but different: in the period before the dividend is paid, do stock prices rise by the expected amount of the dividend, before dropping by the amount of the dividend on the ex-dividend date?
Suppose the risk-free rate is a constant 5%. Suppose a company has no liabilities, no expenses, pays no tax, has $100,000 in invested in a risk-free 5% bond that pays a coupon at the beginning of each calendar year, and has 10,000 shares outstanding. The company pays out all its earnings from the bond coupons — $5000 per year or $0.50 per share per year — as dividends to its shareholders at the beginning of each calendar year. The stock price at the beginning of 2022 is $10. Does this mean that over the course of 2022, the stock price will slowly rise to $10.50, and then suddenly fall to $10 at the beginning of 2023 when the next $0.50 dividend is paid?
In other words, do the stock prices of dividend-paying stocks have a similar behavior to the zig-zag dirty price of bonds, where the dirty price steadily increases due to accrued interest before suddenly dropping on the date a coupon is paid? In the case of dividend-paying stocks, does this mean that stock prices steadily increase due to "accrued dividends" before suddenly dropping on the ex-dividend date?
This question is partially motivated by Jay's controversial answer to If stock price drops by the amount of dividend paid, what is the use of a dividend.