# How does income tax affect the Ex-dividend behavior of a stock?

If there are no taxes and no volatility, I would expect the the move in a stock on the Ex-dividend date to be equal to the gross value of the dividend.

However, if I am taxed, I find the problem gets somewhat complicated, because I need to consider that

1. I may be less inclined to hold a dividend-paying stock, but
2. I could just sell out and buy back across the Ex-dividend date, and
3. ultimately, a company that just paid out \$1 in dividends should be worth \$1 less, regardless of who ended up with the cash.

Based on the first 2 considerations I'd say that the drop on the ex-dividend date gradually reduces as taxes increase, but this is complicated by the 3rd point, which suggests to me that the stock should still drop by the value of the dividend.

Mixing these together suggests that increasing taxes should lower the price of stocks, but I can't put my finger on how much.

In my simple scenario, what would the price drop across the ex dividend date be assuming rational market participants?

• You have two $ symobls in your question and they're acting like a latex block - escape them: \$. – will May 18 '17 at 11:08

If you assume the same tax rate $\alpha$ for all shareholders, then out of a dividend $D$ the amount $\alpha D$ goes to the government and the amount $(1-\alpha) D$ goes to the shareholders. In a theoretical pure no arbitrage environment, and assuming no interest rate discounting for the sake of simplicity, this would imply that the stock price would go down by $\alpha D$ on the day the dividend is voted by the board, and $(1-\alpha) D$ on the ex-dividend date.

• why $\alpha D$ the day it is voted on? – will May 18 '17 at 11:49
• Because on the day the board votes the dividend $D$ the government becomes entitled to getting the sum $\alpha D$ out of the company, even though the actual flow of money will be first the shareholders getting the gross dividend $D$ on the dividend payment date, and then the shareholders transferring $\alpha D$ to the government. – Antoine Conze May 18 '17 at 11:56
• Again this is all theoretical but if they then announced that they would scrap the dividend the price should go up by $\alpha D$. And in fact if there is a possibility of the dividend being scraped, on the day the dividend is voted the price should go down by $p \alpha D$ where $p$ is the market participants estimation of the probability of the dividend being scraped... – Antoine Conze May 18 '17 at 12:02
• Just to add an analogy the same thing happens when a company issues a warrant : some people think the stock price goes down the day the warrant is exercised because of dilution, but that analysis is wrong. Equilibrium tells you that the stock price should go down the day the company announced the issuance if of the warrant, because that’s when the market becomes aware of the likelihood of the dilution. – Antoine Conze May 18 '17 at 12:10
• Say you're the single shareholder of the company. Yesterday you decided that you will pay the shareholder a dividend in one year, and assume that decision is somehow legally binding ($p=1$). Today you're selling the company to somebody else. That somebody will receive the dividend $D$ in 1 year but he/she already knows he/she's liable for paying $\alpha D$ to the government in 1 year, hence the transaction price is reduced today by $\alpha D$. – Antoine Conze May 18 '17 at 12:27

I would have put this in a comment, but it was too long. I wouldn't really classify it as an answer though.

You are correct that the company paying out \$1 in dividends drops the value of the company by \$1.

You are also correct that it is more complicated than this.

Here are some things to consider:

1. The dividend yields of stocks also drive demand for them, which changes the price.
2. Capital gains tax. If you can sell before the dividend and buyback after, yielding a profit of the dividend amount, then you'll have to pay capital gains tax on that.
3. There are different tax rates in different countries - so why not lend your shares to someone who pays no dividend tax (for a fee), and then get them back after the dividend? Guess what, this happens already (dividend tax arbitrage). And guess what rate people will charge you for this - that's right, it's a bit less than your dividend tax rate.
4. There is actually another even more amazing/ridiculous. Sometimes you have strange local (i.e. per country) laws that influence dividend values even more. here's a paper about a 42.86% tax credit on German dividends for German shareholders. So guess what, you lend your German shares to a German bank, they collect a larger dividend than you, and share some of the profits with you.
• Also, pension funds and other institutions are exempt from income tax, so there is lot of heterogeneity in the shareholder population, the effect of taxes is hard to predict. Arbitrage messes up the equation $[\alpha D, (1-\alpha)D]$ given in the other answer to this question. – noob2 May 18 '17 at 12:05
• In 1970 Elton and Gruber published the paper "Marginal stockholder rates and the clientele effect" which claimed to identify $\alpha$ from stock dividend drop data. Today it is realized that analysis is too simplistic because of the complications will mentions. There is no such thing as "the typical shareholder". – noob2 May 18 '17 at 12:15
• Yes, and taxation / tax credit depends on the issuing company's country as well as on the shareholder's country, with often specific bilateral tax treaty so the situation becomes complex. This is why many equity derivative deals are in fact tax deals masquerading as derivatives. – Antoine Conze May 18 '17 at 12:17
• @AntoineConze yes, especialyl stock loan desks. – will May 19 '17 at 9:26