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
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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.
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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