# Tag Info

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Well, if you assume $X$ has volatility $\sigma_X$ and $Y$ has volatility $\sigma_Y$, then $$\sigma_{X+Y} = \sqrt{ Var( X + Y) } = \sqrt{ \sigma_X^2+\sigma_Y^2 + 2 \sigma_X \sigma_Y \rho }$$ Then, you want to show $$\sigma_{X+Y} = \sqrt{ \sigma_X^2+\sigma_Y^2 + 2 \sigma_X \sigma_Y \rho } \leq \sigma_X + \sigma_Y$$ Squaring both sides: ...

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I think what you are missing is simply the Vega-Gamma relation in the Black-Scholes model. Namely: $$Vega = \frac{\partial v}{\partial \sigma} = \sigma(T-t)S^2 \frac{\partial^2 v}{\partial S^2} = \sigma \tau S^2 \Gamma$$ Plugging this into your coverage error, you get its expression in terms of the Vega which is the most natural measurement of your ...

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2) you only take trading days for your analysis because taking in account days on which no price changes took place would shift results in a wrong direction. For exmple, you mostly take 250 trading days p.a. 3) Your time interval up to 2007 is okay and excludes the financial crisis, which is a non-normal circumstance. Therefore, your time interval can be ...

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From Ziegel (2013) : The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical decision theory, risk measures for which such verification and comparison is possible, are called ...

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Did the portfolio manager have the option of investing in emerging markets? If yes, use MSCI All-World. If the portfolio has holdings based in countries with "developed markets" yet has has emerging markets exposure to revenue/earnings, the convention is to use MSCI World.

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I have never seen such an adjustment. While monthly data are irregularly sampled in time (in every way...calendar days, trading days, seconds, etc), that irregularity is likely to be a smaller effect than your choice of data frequency (monthly, weekly, daily data). That said, your question is intriguing because in other fields they do have to deal with ...

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Normalize for trading days if possible.

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