Consider a dividend paying stock $S$ and suppose that its value just before a dividend payment of $D >0$ at time $t$ is denoted by $S(t−)$. The price after the payment should be $S(t)=S(t-)-D$?
How can I justify that. Is there an arbitrage argument?
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I am confused by the question. Suppose that you go into a store to buy corn flakes, priced at $P$ with a $$0.50$ off coupon. Then the effective price is $(P - 0.50)$ and the price, without the coupon is $P$. Doesn't this situation analogize to the dividend representing the coupon? – user2661923 Feb 04 '21 at 23:28
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Yes but I was looking for a rigorous proof, although the situation might be trivial? – Alif Feb 04 '21 at 23:33
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If a stock price is the discounted value of future income, then immediately before the dividend, the future income is the amount $S(t-)$, and immediately after the dividend, the future income is the amount $S(t) = S(t-)-D$. It's lessened by $D$ because that's no longer part of the stream of future income. There's nothing more to it than that.
Amaan M
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Not necessarily, because of tax considerations. Depending on the jurisdiction, capital gains may be taxed at a different rate than dividends. Depending on these rates, selling a stock before the dividend at $S(t-)$ may be a better or a worse deal than getting the dividend $D$ and selling at $S(t-)-D$. If enough investors prefer one to the other, it will affect the stock prices.
Robert Israel
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