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Well, this is broad but something simple and projected oriented would be testing Theory of Capital Structure. All that would be required is testing WACC against market value of assets. This would give good exposure to CAPM, Data Analysis and hypothesis testing all in one. Just a suggestion


Your reasoning for the first property does not look correct or at least I do not understand it. Your arguments for the second property seem sound. But your wording of the second property is a bit fuzzy. You should state this more clearly, for example: $C(1,\ldots,1,u_j,1,\ldots,1) = u_j$ for all $u_j\in [0,1]$ and $j\in 1,\ldots, d.$ You don't mention it ...


Fix u, obtain derivative of v. And do it again for fixing v. To get marginal density of v, one has to do the integration w.r.t. u


The Leverage is calculated with the Debt-to-equity ratio: $\frac{Total Liabilities}{Total Equity}$ In your example this would be: $\frac{500,000}{100,000}$ This ratio is not a common one when dealing with mortgages (like loan-to-value), so it might be a case of an unfortunate example. The reason it is not 4:1 is because the ratio doesn't call for '...

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