Question

Suppose that the daily volatility of the FTSE 100 stock index (measured in pounds sterling) is $1.8 \%$ and the daily volatility of the dollar/sterling exchange rate is $0.9 \%$. Suppose further that the correlation between the FTSE 100 and the dollar/sterling exchange rate is 0.4 . What is the volatility of the FTSE 100 when it is translated to U.S. dollars? Assume that the dollar/sterling exchange rate is expressed as the number of U.S. dollars per pound sterling. (Hint: When $Z=X Y$, the percentage daily change in $Z$ is approximately equal to the percentage daily change in $X$ plus the percentage daily change in $Y_{\text {) }}$

   Suppose that the daily volatility of the FTSE 100 stock index (measured in pounds sterling) is $1.8 \%$ and the daily volatility of the dollar/sterling exchange rate is $0.9 \%$. Suppose further that the correlation between the FTSE 100 and the dollar/sterling exchange rate is 0.4 . What is the volatility of the FTSE 100 when it is translated to U.S. dollars? Assume that the dollar/sterling exchange rate is expressed as the number of U.S. dollars per pound sterling. (Hint: When $Z=X Y$, the percentage daily change in $Z$ is approximately equal to the percentage daily change in $X$ plus the percentage daily change in $Y_{\text {) }}$

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 23, Problem 12

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S. dollars. We can use the formula: $\text{Volatility of Z} = \sqrt{\text{Volatility of X}^2 + \text{Volatility of Y}^2 + 2 \times \text{Correlation} \times \text{Volatility of X} \times \text{Volatility of Y}}$ In this case, X represents the FTSE 100 in pounds Show more…

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Suppose that the daily volatility of the FTSE 100 stock index (measured in pounds sterling) is $1.8 \%$ and the daily volatility of the dollar/sterling exchange rate is $0.9 \%$. Suppose further that the correlation between the FTSE 100 and the dollar/sterling exchange rate is 0.4 . What is the volatility of the FTSE 100 when it is translated to U.S. dollars? Assume that the dollar/sterling exchange rate is expressed as the number of U.S. dollars per pound sterling. (Hint: When $Z=X Y$, the percentage daily change in $Z$ is approximately equal to the percentage daily change in $X$ plus the percentage daily change in $Y_{\text {) }}$

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