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Stock duration of an equity stock is the average of the times until its dividends are received, weighted by their present values.[citation needed]
The interval between dividends can affect the attractiveness of a stock to stock holders.
In some cases there are legal regulations determining when stock dividends have to be paid.
As per Dividend Discount Model: Formula for the duration of stock is as follows-
where
is the Macaulay duration of stock under the DDM model
is the discount rate
is the expected growth rate in perpetuity
The modified duration is the percentage change in price in response to a 1% change in the long-term return that the stock is priced to deliver. Per the relationship between Macaulay duration and Modified duration:
The other formula for the same is - D = saa[citation needed]
is the time in years until the th payment will be received,
is the present value of all future cash payments from the asset.
The present value of dividends per the Dividend Discount Model is:
The numerator in the Macaulay duration formula becomes:
Multiplying by :
Subtracting :
Applying the Dividend Discount Model to the right side:
Simplifying:
Combining (1), (2) and (5):
Modified duration[]
For the stock market as a whole, the modified duration is the price/dividend ratio, which for the S&P 500 was about 62 in February 2004.[citation needed]