As for dividends the effect you are describing it is usually factored in to the price. So the day after the dividend is declared the price drops by an equivalent amount. If the dividend is only a few cents per share the effect may not be noticeable on a volatile stock.

Most bonds are traded so that interest is figured daily and the buyer has to pay the seller the proportionate amount of accrued interest which they get back along with the interest from the rest of the period at the next payment date.

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---- Daily Landscape