Why Dividend Adjustment Factors Use the Ex-Date Price

Summary

The document examines a backward adjustment factor used to account for cash dividends in historical equity prices. It asks whether multiplying pre-ex-date prices by a factor based on the dividend and the price immediately before the ex-date preserves total return when comparing those prices with a later market value.

The author derives a different factor using the later price as the denominator and concludes that the fixed pre-ex-date price factor would not preserve total return to an arbitrary later date. The document is posed as a question and supplies no answer, evidence, or resolution of whether dividend adjustment instead serves another purpose, such as producing a consistent price series around the ex-date. Its algebra identifies the issue for investigation, but does not settle the interpretation or establish a generally valid adjustment method.

Key ideas

• The question concerns backward adjustment of historical equity prices for a cash dividend.
• The author tests total-return preservation between a pre-ex-date price and a later price.
• The proposed factor from the derivation depends on the later price rather than only on the ex-date reference price.
• The document leaves open the purpose and interpretation of the conventional adjustment factor.

Tags

# Dividend Adjustment Factor


# Dividend Adjustment Factor












I am trying to understand this backward dividend adjustment factor for equity prices:

$$ \frac{1}{1+\frac{d}{p}} $$

where $d$ is the dividend and $p$ the price before the ex-dividend date.

I thought the point of this adjustment was to preserve the total return of prices spanning the ex-date.

But this factor does not preserve the total return until any arbitrary date after the ex-date; let’s say I have an unadjusted price $x$ before the ex-date and a price $y$ after the ex-date, and I want to find the adjustment factor $f$ to preserve total returns.

$$ \frac{y+d-x}{x} = \frac{y-fx}{fx} \implies f = \frac{1}{1+\frac{d}{y}} $$

So if the objective is to preserve total return, a factor with the fixed $p$ does not do it, we need to consider the terminal $y$.

So is my understanding of the adjustment factor incorrect - it’s not supposed to preserve total return but serves another function?

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