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1) I'm going from memory here so someone may want to confirm that I'm thinking about this correctly - but the two models will end up with the same results and significance levels - in the first model, the intercept acts as the reference day, such that the average effect of $D_d=\beta_0+\beta_d$. In the second model you should get the same effect, however, it ...

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SMB is controlling for small stocks. Small and thinly traded are not equivalent. For instance, for most of its history, Berkshire Hathaway was a large stock, but thinly traded (b/c of its high price). There are a number of ways to handle liquidity risk. If you're looking to supplement a Fama-French regression, Pastor and Stambaugh (2003) uses order flow ...

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I would personally go for a normal returns, because you do not make any assumptions about the data or returns. When we use log returns we assume that prices are distributed log normally (which, usually is very far from the truth). Moreover if you will investigate different distribution you will not use the log returns features like time additivity or ...

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The correct formula is to compute multi period gross returns as products of single period gross returns. Conceptually it is equivalent to calculating the return on a self-financing portfolio initially made of 1 unit of stock, with each cash dividend reinvested in more stocks at the ex-dividend price.

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There's no industry standard for calculating returns on derivative contracts. The reason is that derivative contract assets are different from what I'll call real assets. Examples of real assets are an ounce of gold, or an equity. Derivatives require you to invest, or allocate some amount of cash (i.e. margin), to accommodate losses. But this allocation is ...

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