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The paper is not trying to say that equation (10) is derived from equation (8). Equation (8) tells us how household makes its optimal consumption and 'saving' decision (it gives us demand for investing the wealth into bonds/risky assets). The equation (10) then tells us that given the household optimal decisions (which depend on utility (8)), those ...


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There are two ways I could think of to answer this question. First, and I think this is what you are asking, "what is the covariance structure of two assets under the Fama-French 3-factor model?" Consider two assets $i$ and $j$. Let's start with their returns under the Fama-French factor model: $$ r_{i,t} = \alpha_{i} + \beta_{1,i} MKT_{t} + \beta_{2,i} ...


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