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They are not riskless and a TBill is not the right benchmark comparison. While a dollar neutral long/short portfolio does provide enhanced risk management, the extent is dependant upon the composition of the portfolio. For example, if long 10M IBM and short 10M XOM, what have you hedged ? What is the relationship between IBM and XOM ? In this example you ...


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Long-short strategy is generally used by hedge funds. In simple words, an equity long-short strategy means buying an undervalued stock and selling(shorting) an overvalued stock. In normal circumstances, the long position will increase in value and the short position will decline in value. In this situation, the hedge fund will benefit. This strategy would ...


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What is risk? If one defines risk heuristically as deviation from expectation, then (assuming returns have finite variance) standard deviation can be considered a first approximation for risk. For most distributions the mean and variance do not fully parameterize the distribution. Some standard measures of risk for general distributions include Value at ...


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Compare these two links: https://en.wikipedia.org/wiki/Distortion_risk_measure https://en.wikipedia.org/wiki/Spectral_risk_measure Then these risk measures are only different by their assumptions on the distortion function: $\tilde{g}$ is the dual distortion function $\tilde{g}(u) = 1 - g(1-u)$ with $g: [0,1] \to [0,1]$. $\phi$ is non-negative, ...


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I can't comment yet on the topic due to my reputation level (so I will throw an answer up) but having just done my MFE capstone research on EVT implementation for VaR. According to my advisor who was a director of a quant research group at Citi before returning to academia, not many people are doing this. My research was to start collecting data comparing ...


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Let's discuss what a PFE is before looking at the equation. PFE is a common statistical measure for the amount of money you'll lose if your counterparty defaults. Let's give an example, say if you were to long 1000 far-in-the-money call options with a bank. Those options worth a lot to you because they're all in-the-money, it's something that you want to ...


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When you enter into a derivative trade, such as a swap, the intial value is zero; as interest rates change the value may become positive or negative. If it is positive and the counterparty defaults you could be out a big sum of money (imagine that you are trading with Lehman Brothers in 2008). The idea of PFE is to estimate at some time in the future the ...


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If certain broad assumptions are correct (eg, asset prices are continuous in time, markets are efficient) then asset returns must follow a Levy process. Both the Gaussian and Stable distributions are subsets of Levy processes. The question should not be whether Gaussian or Stable is better. Neither are adequate (in fact, many Stable distributions imply ...


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I think, the use of stable distributions in Finance (and, probably, in Economics) is a big mistake. It is essential that the intuitive fact that the stable distributed observations possess a large number of big deviations from empirical mean is not true (see, Lev B. Klebanov, Irina Volchenkova (2015) "Heavy Tailed Distributions in Finance: Reality or Mith? ...


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Translation invariance of a risk measure $\rho$ is defined as $$ \rho(X+k) = \rho(X)-k, $$ where $X$ is a random variable such that $\rho(X)$ exists and $k$ is a constant. The meaning is that if I add an amount $k$ to my risky positions then the risk is reduced by this amount. For VaR we consider the case that $X$ has a continuous distribution and that it ...


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Very hard to tell from the given context but I would assume that "risk numbers" refers to the risk of a position (e.g. trading desk) which is typically measured in terms of a VaR (value-at-risk) or a similar measure (ES - expected shortfall). "Modeling risk" is the task of identifying your sources of risk (risk types like e.g. interest rate risk, volatility ...



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