The promised cash flows of three securities are listed below. If the cash flows are risk-free, and the risk-free interest rate is 6.0%, determine the no-arbitrage price of each security before the first cash flow is paid. (Click on the following icon in order to copy its contents into a spreadsheet.) Security A B C Cash Flow Today ($) 500 0 1,000 Cash Flow in One Year ($) 500 1,000 0 The no-arbitrage price of security A is $971.7. (Round to the nearest cent.) The no-arbitrage price of security B is $ (Round to the nearest cent.)
The promised cash flows of three securities are listed below. If the cash flows are risk-free, and the risk-free interest rate is 6.0%, determine the no-arbitrage price of each security before the first cash flow is paid. (Click on the following icon in order to copy its contents into a spreadsheet.) Security A B C Cash Flow Today ($) 500 0 1,000 Cash Flow in One Year ($) 500 1,000 0 The no-arbitrage price of security A is $971.7. (Round to the nearest cent.) The no-arbitrage price of security B is $ (Round to the nearest cent.)
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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![### Understanding No-Arbitrage Pricing of Securities
In this scenario, we examine the no-arbitrage price of three securities based on their cash flows and a risk-free interest rate of 6.0%. For educational purposes, we will determine the no-arbitrage price for each security before the first cash flow is paid.
#### Cash Flow Table
The following table outlines the cash flows for three securities:
| **Security** | **Cash Flow Today ($)** | **Cash Flow in One Year ($)** |
|--------------|-------------------------|-----------------------------|
| A | 500 | 500 |
| B | 0 | 1,000 |
| C | 1,000 | 0 |
#### Calculation of No-Arbitrage Price
The no-arbitrage price of a security is the present value of its expected cash flows, discounted at the risk-free rate.
1. **Security A:**
- Cash Flow Today: $500
- Cash Flow in One Year: $500
- No-arbitrage price calculation includes discounting the future cash flow.
- The no-arbitrage price of security A is **$971.7**.
2. **Security B:**
- Cash Flow Today: $0
- Cash Flow in One Year: $1,000
- Apply the discount factor for the cash flows in one year.
- Fill in the calculated no-arbitrage price for Security B.
This exercise demonstrates how to determine fair pricing in a risk-free environment ensuring no arbitrage opportunities.
Note: The calculations should involve applying the formula for present value, which is:
\[ PV = \frac{CF}{(1 + r)^t} \]
Where:
- \( CF \) = Cash Flow
- \( r \) = Interest Rate
- \( t \) = Time in Years
#### Conclusion
Understanding the no-arbitrage pricing of securities helps in making informed investment decisions by evaluating fair prices against future cash flows with a given interest rate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55f59351-6cab-453e-87b8-764174a74643%2F39fe8265-d770-45b5-8739-dc0e6fb16749%2F01rwso_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding No-Arbitrage Pricing of Securities
In this scenario, we examine the no-arbitrage price of three securities based on their cash flows and a risk-free interest rate of 6.0%. For educational purposes, we will determine the no-arbitrage price for each security before the first cash flow is paid.
#### Cash Flow Table
The following table outlines the cash flows for three securities:
| **Security** | **Cash Flow Today ($)** | **Cash Flow in One Year ($)** |
|--------------|-------------------------|-----------------------------|
| A | 500 | 500 |
| B | 0 | 1,000 |
| C | 1,000 | 0 |
#### Calculation of No-Arbitrage Price
The no-arbitrage price of a security is the present value of its expected cash flows, discounted at the risk-free rate.
1. **Security A:**
- Cash Flow Today: $500
- Cash Flow in One Year: $500
- No-arbitrage price calculation includes discounting the future cash flow.
- The no-arbitrage price of security A is **$971.7**.
2. **Security B:**
- Cash Flow Today: $0
- Cash Flow in One Year: $1,000
- Apply the discount factor for the cash flows in one year.
- Fill in the calculated no-arbitrage price for Security B.
This exercise demonstrates how to determine fair pricing in a risk-free environment ensuring no arbitrage opportunities.
Note: The calculations should involve applying the formula for present value, which is:
\[ PV = \frac{CF}{(1 + r)^t} \]
Where:
- \( CF \) = Cash Flow
- \( r \) = Interest Rate
- \( t \) = Time in Years
#### Conclusion
Understanding the no-arbitrage pricing of securities helps in making informed investment decisions by evaluating fair prices against future cash flows with a given interest rate.
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