I want to derive the dividend discount model from the asset pricing formula described in "Efficient Capital Markets: A Review of Theory and Empirical Work" by Eugene Fama 1970. The formula that I am referring to is equation number 1:

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What I could do so far is the following:

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As you can see I separated the asset price today as a function of future price discounted. The phi represents the information in the market about the price, risk etc. If we are pricing a share, we can consider the future price the sum of all the discounted dividends to today, therefore we can rewrite to the following: enter image description here

Is this correct? If extra information is needed I will provide. Thank you!

  • $\begingroup$ Line (4) is true, but it does not follow from line (3) since $\frac{\operatorname{E}[A]}{\operatorname{E}[B]} = c$ does not imply $\operatorname{E}[\frac{A}{B}] = c$. Line (5) is missing the the expectation operator and has a got a confused notion of discounting going on inconsistent with previous definitions for $r_{j, t+1}$. $\endgroup$ – Matthew Gunn Feb 26 '19 at 16:42

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