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Consider a position consisting of a $$\$ 100,000$$ investment in asset $$\mathrm{A}$$ and a $$\$ 100,000$$ investment in asset B. Assume that the daily volatilities of both assets are $$1 \%$$ and that the coefficient of correlation between their returns is 0.3 . Estimate the 5 -day $$99 \% \mathrm{VaR}$$ and ES for the portfolio assuming normally distributed returns.

   Consider a position consisting of a $$\$ 100,000$$ investment in asset $$\mathrm{A}$$ and a $$\$ 100,000$$ investment in asset B. Assume that the daily volatilities of both assets are $$1 \%$$ and that the coefficient of correlation between their returns is 0.3 . Estimate the 5 -day $$99 \% \mathrm{VaR}$$ and ES for the portfolio assuming normally distributed returns.

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 22, Problem 1

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Step 1

The daily volatility of the portfolio can be calculated using the formula for the volatility of a portfolio: $$\sigma_{\text{portfolio}} = \sqrt{w_A^2 \cdot \sigma_A^2 + w_B^2 \cdot \sigma_B^2 + 2 \cdot w_A \cdot w_B \cdot \rho_{AB} \cdot \sigma_A \cdot Show more…

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Consider a position consisting of a $$\$ 100,000$$ investment in asset $$\mathrm{A}$$ and a $$\$ 100,000$$ investment in asset B. Assume that the daily volatilities of both assets are $$1 \%$$ and that the coefficient of correlation between their returns is 0.3 . Estimate the 5 -day $$99 \% \mathrm{VaR}$$ and ES for the portfolio assuming normally distributed returns.

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