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I'm not sure if I understand you perfectly, but basically, you have: $$\mathbb{E}(S_1)= p S_0 u + (1-p) S_0 d = S_0\left[p (u-d) +d \right]$$ This is simply the expectation (i.e. there is no pricing here). Notice that this means that: $$\mathbb{E}\left[\frac{S_1}{S_0}\right]=p (u-d) + d$$ So the expected rate of return is $1+R_S=p (u-d) + d$. If the ...