Suppose you are a British venture capitalist holding a major stake in an e-commerce start-up in Silicon Valley. As a British resident, you are concerned with the pound value of your U.S. equity position. Assume that if the American economy booms in the future, your equity stake will be worth $1,001,000, and the exchange rate will be $1.4/£. If the American economy experiences a recession, on the other hand, your American equity stake will be worth $501,120, and the exchange rate will be $1.6/£. You assess that the American economy will experience a boom with a 60 percent probability and a recession with a 40 percent probability. a. Estimate your exposure to the exchange risk. (Round final answer to nearest dollar.) Exposure b. Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty. (Round final answer to nearest dollar.) Variance
Suppose you are a British venture capitalist holding a major stake in an e-commerce start-up in Silicon Valley. As a British resident, you are concerned with the pound value of your U.S. equity position. Assume that if the American economy booms in the future, your equity stake will be worth $1,001,000, and the exchange rate will be $1.4/£. If the American economy experiences a recession, on the other hand, your American equity stake will be worth $501,120, and the exchange rate will be $1.6/£. You assess that the American economy will experience a boom with a 60 percent probability and a recession with a 40 percent probability. a. Estimate your exposure to the exchange risk. (Round final answer to nearest dollar.) Exposure b. Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty. (Round final answer to nearest dollar.) Variance
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![### Exchange Rate Risk: An Example for British Venture Capitalists
#### Scenario:
As a British venture capitalist holding a major stake in an e-commerce start-up in Silicon Valley, you are concerned with the pound value of your U.S. equity position. Assume the following:
- If the American economy booms, your equity stake will be worth $1,001,000, and the exchange rate will be $1.4/£.
- If the American economy experiences a recession, your American equity stake will be worth $501,120, and the exchange rate will be $1.6/£.
Your assessment indicates that the American economy has a 60 percent probability of booming and a 40 percent probability of experiencing a recession.
### Questions:
**a. Estimate your exposure to the exchange risk. (Round final answer to nearest dollar.)**
Please calculate your exposure to the exchange rate risk by filling in the value in the box provided.
**Exposure:**
\[ \boxed{\hspace{4.7cm}} \]
**b. Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty. (Round final answer to nearest dollar.)**
Please calculate the variance of the pound value by filling in the value in the box provided.
**Variance:**
\[ \boxed{\hspace{4.7cm}} \]
---
### Detailed Explanation of the Graphs/Diagrams:
In this specific task, there were no explicit graphs or diagrams provided in the image.
### Calculations:
To assist with understanding, here are the detailed steps to solve each part of the problem:
**a. Exposure Calculation**
First, convert the dollar values to pound values under each scenario:
- Boom: \(\frac{1,001,000 \text{ USD}}{1.4 \text{ USD/GBP}} = 715,000 \text{ GBP}\)
- Recession: \(\frac{501,120 \text{ USD}}{1.6 \text{ USD/GBP}} = 313,200 \text{ GBP}\)
Then calculate the expected pound value:
\[ \text{Expected Value} = (0.6 \times 715,000 \text{ GBP}) + (0.4 \times 313,200 \text{ GBP}) \]
\[ \text{Expected Value} = 429,000 \text{ GBP} + 125,280 \text{ GBP}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc0fe995-7680-4da1-9251-6315116f8ff1%2Fbc1a0c74-20d6-4a0c-82f7-eb57810dd72b%2Flq0gf88_processed.png&w=3840&q=75)
Transcribed Image Text:### Exchange Rate Risk: An Example for British Venture Capitalists
#### Scenario:
As a British venture capitalist holding a major stake in an e-commerce start-up in Silicon Valley, you are concerned with the pound value of your U.S. equity position. Assume the following:
- If the American economy booms, your equity stake will be worth $1,001,000, and the exchange rate will be $1.4/£.
- If the American economy experiences a recession, your American equity stake will be worth $501,120, and the exchange rate will be $1.6/£.
Your assessment indicates that the American economy has a 60 percent probability of booming and a 40 percent probability of experiencing a recession.
### Questions:
**a. Estimate your exposure to the exchange risk. (Round final answer to nearest dollar.)**
Please calculate your exposure to the exchange rate risk by filling in the value in the box provided.
**Exposure:**
\[ \boxed{\hspace{4.7cm}} \]
**b. Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty. (Round final answer to nearest dollar.)**
Please calculate the variance of the pound value by filling in the value in the box provided.
**Variance:**
\[ \boxed{\hspace{4.7cm}} \]
---
### Detailed Explanation of the Graphs/Diagrams:
In this specific task, there were no explicit graphs or diagrams provided in the image.
### Calculations:
To assist with understanding, here are the detailed steps to solve each part of the problem:
**a. Exposure Calculation**
First, convert the dollar values to pound values under each scenario:
- Boom: \(\frac{1,001,000 \text{ USD}}{1.4 \text{ USD/GBP}} = 715,000 \text{ GBP}\)
- Recession: \(\frac{501,120 \text{ USD}}{1.6 \text{ USD/GBP}} = 313,200 \text{ GBP}\)
Then calculate the expected pound value:
\[ \text{Expected Value} = (0.6 \times 715,000 \text{ GBP}) + (0.4 \times 313,200 \text{ GBP}) \]
\[ \text{Expected Value} = 429,000 \text{ GBP} + 125,280 \text{ GBP}
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