Math Problem Statement

Question 1

The following are the foreign currency positions of an FI, expressed in the foreign currency:

Currency

Assets

Liabilities

FX Bought

FX Sold

Swiss franc (Sf)

Sf 127,500

Sf 51,000

Sf 10,200

Sf 15,300

British pound (£)

£ 38,168

£ 16,794

£ 11,450

£ 15,267

Japanese yen (¥)

¥ 7,869,885

¥ 3,147,954

¥ 1,259,181

¥ 9,233,998

The exchange rate of dollars for Sf is 0.98, of dollars for British pound is 1.31, and of dollars for yen is 0.00953.

The following are the foreign currency positions converted to dollars:

Currency

Assets

Liabilities

FX Bought

FX Sold

Swiss franc (Sf)

$ 125,000

$ 50,000

$ 10,000

$ 15,000

British pound (£)

$ 50,000

$ 22,000

$ 15,000

$ 20,000

Japanese yen (¥)

$ 75,000

$ 30,000

$ 12,000

$ 88,000

a. What is the FI’s net exposure in Swiss francs stated in Swiss francs (Sf) and in dollars ($)?

Net Exposure (Swiss Francs): Sf

Net Exposure (US dollars): $

Solution

To find the Financial Institution's (FI's) net exposure in Swiss francs (Sf), both in Swiss francs and in dollars, we’ll follow these steps:

  1. Net Exposure Calculation in Swiss Francs (Sf): The net exposure in a particular currency can be calculated by summing the assets and foreign exchange (FX) bought, then subtracting the liabilities and FX sold.

    For Swiss francs: Net Exposure (Sf)=(Assets+FX Bought)(Liabilities+FX Sold)\text{Net Exposure (Sf)} = (\text{Assets} + \text{FX Bought}) - (\text{Liabilities} + \text{FX Sold})

    Plugging in the values: Net Exposure (Sf)=(127,500+10,200)(51,000+15,300)\text{Net Exposure (Sf)} = (127,500 + 10,200) - (51,000 + 15,300) =137,70066,300= 137,700 - 66,300 =71,400Sf= 71,400 \, \text{Sf}

  2. Net Exposure Calculation in Dollars ($): Convert the net exposure in Swiss francs to dollars using the exchange rate (Sf to $ is 0.98).

    Net Exposure (US dollars)=71,400×0.98\text{Net Exposure (US dollars)} = 71,400 \times 0.98 =69,972dollars= 69,972 \, \text{dollars}

Final Answer:

  • Net Exposure (Swiss Francs): 71,400 Sf
  • Net Exposure (US dollars): 69,972 $

Would you like further details on any of these calculations?

Here are 5 related questions to deepen understanding:

  1. How would the net exposure change if the Swiss franc exchange rate fluctuates?
  2. What impact would increasing the FX bought position have on net exposure?
  3. How can FI use hedging to manage its currency exposure?
  4. How do foreign assets and liabilities affect FI’s risk profile?
  5. What would happen if the Swiss franc depreciated against the dollar?

Tip: Exchange rates can have a significant effect on net exposures; monitoring rates is essential for managing currency risk.

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Math Problem Analysis

Mathematical Concepts

Currency conversion
Net exposure calculation
Foreign exchange rates

Formulas

Net Exposure = (Assets + FX Bought) - (Liabilities + FX Sold)
Dollar Conversion = Net Exposure (Foreign Currency) × Exchange Rate

Theorems

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Suitable Grade Level

Undergraduate finance or advanced high school economics