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Answer: ROI of -2.40% because the EUR depreciated against the USD
The EUR **depreciates** from 1.40 USD/EUR to 1.26 USD/EUR. - USD asset return: **+6.0%** - EUR asset return measured in USD: \[ \frac{1.08\times 1.26}{1.40}-1 = 0.972-1 = -2.8\% \] - Blended ROA: \[ \frac{6.0\% + (-2.8\%)}{2} \approx 1.6\% \] - Subtract cost of funds (4.0%): \[ 1.6\% - 4.0\% \approx -2.4\% \] So the realized ROI is approximately **-2.4%**, which corresponds to **D**.
Author: Manit Arora
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Question 193.1. A U.S. bank raises $200 million in liabilities that pay an interest rate of 4.0% in order to fund two investments: $100 million invested into U.S. dollar-denominated assets and the remaining $100 million invested into Euro (EUR) denominated assets. The expected net (of default risk) yield on the USD assets is 6.0%, and the net yield on the EUR assets is 8.0%. In this way, the expected return on the investment (ROI) is 3.0% as the difference between the blended ROA of 7.0% (average of 6.0% and 8.0%) and the cost of funds (COF) of 4.0%. However, the bank is un-hedged with respect to currency risk. At the beginning of the year, the exchange rate is EUR/USD $1.40. At the end of the year, the exchange rate has moved to EUR/USD $1.26. The nominal returns for the year were exactly as expected.
What is the one-year realized ROI if we account for the currency shift? Note: please assume all interest rates are effective annual rates (EARs), consistent with Saunders' illustrations in the assigned readings. For example, an effective annual rate of 8.0% is equivalent to 8.0% per annum with (discrete) annual compounding.
A
ROI of +5.90% because the EUR appreciated against the USD
B
ROI of -4.30% because the EUR appreciated against the USD
C
ROI of +1.90% because the EUR depreciated against the USD
D
ROI of -2.40% because the EUR depreciated against the USD
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