Stock duration

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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]

Duration[edit]

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]

Derivation[edit]

The Macaulay duration is defined as:

where:

  • indexes the cash flows,
  • is the present value of the th cash payment from an asset,
  • 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[edit]

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]

See also[edit]

External links[edit]