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Consider that the daily standard deviation of the NZX50 index (in New Zealand Dollar, NZD) is 2% and the daily standard deviation of the USD/NZD exchange rate is 1%. Assume that the correlation between the NZX50 and the USD/NZD exchange rate is 0.5.

a What is the standard deviation of the NZX50 when it is translated to USD? Assume that the USD/NZD exchange rate is expressed as the number of U.S. dollars per one New Zealand Dollar. (Hint: NZX50 in USD = NZX50 in NZD x USD/NZD, hence, the percentage daily change in NZX50 in USD is approximately equal to the percentage daily change in NZX50 in NZD plus the percentage daily change in USD/NZD.)

b. Assume that the correlation between the S&P 500 Index (in USD) and the NZX50 Index (in NZD) is 0.7, the correlation between the S&P 500 index (in USD) and the USD/NZD exchange rate is 0.3. The daily standard deviation of the S&P 500 Index is 1.6%. What is the correlation between the S&P 500 Index (in USD) and the NZX50 Index when it is translated to USD? (Hint: Let denote the percentage daily change as r, then Covariance (r_NZX50 in USD, r_S&P in USD) = Covariance(r_NZX50 in NZD + r_USD/NZD, r_S&P in USD) = Covariance(r_NZX50 in NZD , r_S&P in USD) + Covariance(r_USD/NZD, r_S&P in USD). Note that, r_NZX50 in USD = r_NZX50 in NZD + r_USD/NZD is from the Hint in question a).

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