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Converting a Discrete Dividend Yield to a Continuous Annual Yield

Article Quant Q&A · Author: foshizzle
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Summary

The document asks how to express a stock’s quarterly or annual dividend as an annualized continuous dividend yield. Its answer relates the annual dividend amount to the current stock price, first forming a simple dividend-to-price ratio and then applying a logarithmic transformation. This reflects the general conversion from a discrete growth or return factor to a continuously compounded rate.

The response is brief and gives no derivation, example, or discussion of alternative dividend conventions. Its formula uses an annual dividend amount, so quarterly payments would need to be aggregated consistently before applying it. The expression also assumes a particular treatment of dividends relative to the current share price; it does not address changing future dividends, payment timing, or whether the stock price should be adjusted for ex-dividend effects. It is best read as a basic conversion under simplified assumptions rather than a complete dividend-yield model.

Key ideas

  • The answer converts an annual dividend-to-price ratio into a continuously compounded yield using a logarithm.
  • Quarterly payments must be represented consistently as an annual dividend amount.
  • The formula assumes a simplified relationship between current price and dividend cash flow.
  • Dividend timing and future changes in distributions are not addressed.

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Full text
# Calculating annualized continuous dividend yield


# Calculating annualized continuous dividend yield












What would be a formula for calculating the annualized continuous dividend yield of a stock? Given the quarterly or annual dividend

## Answer by nbbo2 (score 0, accepted)

https://quant.stackexchange.com/a/22916

$r=\ln(1+\frac{D}{S_o})$ where D is the annual dividend and $S_0$ is the current stock price$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.