On December 31, 2015 Historic Bank had long positions of 200,000,000 Japanese Yen and 50,000,000 Swiss Francs.The closing exchange rates were ¥92/$ and Swf1.89/$. What is the value of delta for the respective positions of the two currencies in dollars?

Question

Quizplus · Accepted Answer

To find the value of delta for each currency position in dollars, we convert the positions from their respective currencies to dollars using the provided exchange rates. For the Japanese Yen: $200,000,000 \, \text{Yen} \div 92 \, \text{Yen/$} = \$2,173,913.04$. The delta is the change in value for a one unit change in the exchange rate, so for a \$1 change, the delta is $-200,000,000$ Yen because the position is in Yen and we're considering its value in dollars. However, since we're asked for the value in dollars, we need to convert this change correctly. The correct approach is to consider the impact of a small change in the exchange rate on the dollar value of the position, which is not directly given by the numbers provided. For the Swiss Francs: $50,000,000 \, \text{Swf} \div 1.89 \, \text{Swf/$} = \$26,455,026.46$. Similarly, the delta for the Swiss Francs would reflect the change in the dollar value of this position for a one unit change in the exchange rate. The provided options seem to misunderstand the calculation of delta, which involves the sensitivity of the position's value to changes in the exchange rate, not the direct conversion of the entire position's nominal value at the given rates. The correct calculation involves understanding how a small change in the exchange rate affects the dollar value of the position, which is not directly answered by the options provided. However, the closest option based on the misunderstanding of the question's requirement is B, which seems to attempt to reflect changes in value, but the explanation for why it's chosen is based on a misunderstanding of how delta is calculated in this context. The correct approach to calculating delta would involve derivatives of the conversion formula with respect to the exchange rate, which is not directly provided in the answer choices.

On December 31, 2015 Historic Bank Had Long Positions of 200,000,000