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In small sample, there is no reason why $x' \epsilon$ will be 0. In fact, there is no real reason why $\epsilon$ should be independent. The fact that you are assuming a linear specification for the returns means you are to some extent making assumptions of linear regression. Justifying the errors being uncorrelated with the independent variables is justified ...


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Always take care that you got the compounding frequency right. I recommend you take a deeper look at http://breakingdownfinance.com/finance-topics/derivative-valuation/forward-contract/ . You can download an excel file here and take a deeper look at the formula. You can also give in the compounding frequency as input. In case of doubt, or as a standard ...


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If we compound semi-annually and we have half year to go, then the current forward price is $$F = S \left(1+\frac{r}{2}\right) = 125 \left(1+\frac{0.10}{2}\right)$$ Isn't it as simple as that?



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