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You have a portfolio, $P$, filled with many positions, which are specifically dependent upon various asset price movements, say $X,Y and Z$. These price movements are random variables, but they may contain some inherent correlations. Suppose $X$ and $Y$ are highly correlated but $Z$ has small correlation to both $X$ and $Y$. Now by asking "what is the ...


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High level Answer: Trading Book: All the books held in Capital Markets or Investment Banking Division of a Bank. Instruments will include:Swaps, Stocks, Bonds, etc. Banking Book: All the books held in Commercial or Retail Banking Division of a Bank. Instruments will include:Loans to corporates, Bank Guarantees, etc. Market Risk Measure: Sensitivities like ...


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I don't know how common this is, but I've seen it done. Many risk model vendors (Northfield, Axioma) allow the blending of different risk models with different periodicity (e.g. a shorter horizon risk model blended with a longer horizon risk model). Here's a Northfield deck about this: https://www.northinfo.com/documents/779.pdf


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Some people like to play for the "big win." Their utility function involves the excitement of the gamble, and they don't mind the negative expectation, or even the big loss, as long as there is a chance for the big win. Investments like lottery tickets and penny stocks exhibit extremely high kurtosis. So, for a person with a "gambling", "shoot the moon" - ...


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Choose John Deere. Some firms provide minimal disclosures, other firms are very good at making investors aware of every detail. Deere provides excellent and complete disclosures, well beyond what the law requires. It is a great firm to teach and learn with. As to what should you look for, that depends on the industry. Consider the electric utility ...


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I will try to provide a complete answer, although valuation can get way too far. So let's stick to the essentials. Balance Sheet Cash & Cash Equivalents: Cash in bank and short-term securities, that can be used to settle short-term liabilities. Can be used to quantify liquidity risk (e.g Cash Ratio) Tangible and Intangible assets: What is their portion ...


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There are waaaaayyy better estimators than $Var(log(Close_{t+1}/Close_{t}))$. This close-close estimator is unbiased, and has a data efficiency defined as $1$. The Parkinson estimator uses high and low prices only (useful when you don't trust your open and close prices, or don't have them). It has a data efficiency of about $4$. The expected variance from "...


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Note that \begin{align*} f(m) &= \int d_{\gamma}(m,x)\mu(dx)\\ &=\int \big[\gamma(m)-\gamma(x)-\gamma'(x)(m-x)\big]\mu(dx)\\ &=\gamma(m) - \int \big[\gamma(x)+\gamma'(x)(m-x)\big]\mu(dx). \end{align*} Then, \begin{align*} \frac{df}{dm} = \gamma'(m) - \int \gamma'(x)\mu(dx), \end{align*} and the critical point is given by \begin{align*} b = \big(\...


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As I know, I think that spectral risk measure is a new kind of measure developed from the CVaR (weighted average value of VaR) and in the framework of coherent risk measures. If you can prove that a risk measure is coherent then you can add any types of weighted function $\phi$ to make it a spectral risk measure. The underlying idea is that the sum of any ...


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If you can prove that $\kappa_{\alpha}(X,t)=a_X(\alpha,t^{-1})=t\ln(\frac{E[e^{t^{-1}X}]}{\alpha})$ is convex and apply the property of positive homogeneity, then the sub-additivity follows. In original paper, authors show that $\kappa_{\alpha}(X,t)=a_X(\alpha,t^{-1})$ is convex in $(X,t)$. Lemma: For fixed $\alpha$, all $\lambda\in[0,1],X,Y\in L_{M^+}$ ...


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For the first question: Let me ask you a question. Do the risk-neutral investor have a feeling of risk? For the second question: Sharpe Ratio tries to capture the excess return over the risk free rate. But you need to adjust it with the risk associated with your portfolio. So it depends on the type of risk measure you employ.


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