It's been another rough day so far this Thursday for ASX investors and the Australian share market. At the time of writing, the ASX 200 has sunk by another 0.47%, bringing down the index to around 8,100 points. But let's talk about the share price of Medibank Private Ltd (ASX: MPL).

Medibank shares are faring even worse than the broader market at this time. Yesterday, the ASX 200 private health insurance stock closed at $4.44 a share. But this morning, those shares opened at $4.35, where they remain. That's a fall worth a meaty 2.03%.

So why are Medibank shares down by more than four times the broader market's drop today?

Well, Medibank investors shouldn't be too disappointed to see this drop. In fact, they should be welcoming it. That's because Medibank shares are falling for perhaps the best reason to see a share price fall – the company has just traded ex-dividend for its latest shareholder payment.

Medibank shares drop as stock trades ex-dividend

Last month, we covered Medibank's latest half-year earnings report.

As we reported at the time, Medibank revealed a 6.1% increase in revenues for the six months to 31 December. Underlying net profits rose by 13.8% to $298.7 million, enabling the company to hike its interim dividend by 8.3% to 7.8 cents per share, fully franked.

That's a pleasing improvement from last year's interim dividend, which was worth 7.2 cents per share. With September's final dividend of 9.4 cents per share, Medibank's annual dividend is now fully franked at 16.6 cents per share.

However, this latest interim dividend is now closed to new investors. As of today, anyone buying Medibank shares will leave the right to receive this latest dividend behind with the seller.

As such, Medibank shares have inherently become less valuable. All new investors will have to wait until Medibank's final dividend later this year to receive income from their shares.

That's why we see a sizeable sell-down in the Medibank share price this Thursday. It's a normal reaction to an ASX share trading ex-dividend.

Eligible investors can now look forward to receiving this latest payout from Medibank on 26 March. Medibank does not currently offer a dividend reinvestment plan (DRP) though, so shareholders have no option but to receive this dividend in cash.

At the current Medibank share price, this ASX 200 stock has a dividend yield of 3.95%. Medibank shares have increased 14.65% over the past 12 months.