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28.h: Calculate an arbitrage payoff and describe how arbitrage opportunities are temporary.

 1. **Arbitrageurs and Derivatives**: Arbitrageurs are traders who take advantage of price discrepancies in financial markets to earn risk-free profits. They frequently use derivatives, which are financial instruments whose value is derived from an underlying asset, index, or reference rate.


2. **Seeking Risk-Free Profit**: The primary objective of arbitrageurs is to make a profit without taking on any market risk. They achieve this by exploiting pricing inefficiencies and mispricing of securities in different markets.


3. **Exceeding Risk-Free Rate**: The risk-free rate is the return on an investment that carries no risk, usually associated with government bonds or other low-risk financial instruments. Arbitrageurs aim to outperform this risk-free rate, as they can earn higher returns by engaging in profitable arbitrage opportunities.


4. **Discovery and Manipulation of Mispriced Securities**: Arbitrageurs use their analytical skills and market knowledge to identify mispriced securities. A mispriced security is one whose market price does not accurately reflect its intrinsic value or true worth.


5. **Entering Equivalent Offset Positions**: To execute an arbitrage trade, an arbitrageur will simultaneously take two offsetting positions in different markets. These positions are designed to neutralize each other's risk, ensuring that the arbitrageur can make a profit regardless of the overall market movements.


6. **Example of Arbitrage**: Let's consider a hypothetical scenario involving stock XYZ. Assume that the stock is listed on both the New York Stock Exchange (NYSE) and the London Stock Exchange (LSE). Due to time zone differences and market participants' actions, there is a temporary discrepancy in the stock's price between the two exchanges.


   - On the NYSE, XYZ stock is trading at $100 per share.

   - On the LSE, the same XYZ stock is trading at £80 per share.


   At the current exchange rate of $1.25 per £1, this means that $100 is equal to £80. However, due to various market factors, there is a delay in the price adjustment between the two exchanges.


   The arbitrage opportunity arises for the arbitrageur who can quickly take advantage of the price discrepancy:

   

   - The arbitrageur buys 100 shares of XYZ on the LSE for £80 per share, spending a total of £8,000.

   - Simultaneously, the arbitrageur sells 100 equivalent shares of XYZ on the NYSE at $100 per share, receiving $10,000.


   By converting the dollars back to pounds at the current exchange rate, the arbitrageur now has £8,000. They made a risk-free profit of £8,000 - £8,000 = £0 without exposing themselves to market risk.


7. **Short-Lived Arbitrage Opportunities**: Arbitrage opportunities tend to be short-lived. As soon as arbitrageurs exploit the pricing discrepancy, increased demand in the cheaper market and increased supply in the expensive market will quickly drive prices back to their equilibrium levels, eliminating the arbitrage opportunity.


In summary, arbitrageurs use derivatives and their analytical skills to find and exploit temporary price discrepancies in financial markets. By simultaneously entering offsetting positions in different markets, they can earn risk-free profits that exceed the returns offered by low-risk investments like government bonds. However, these opportunities are short-lived due to market forces that quickly correct price discrepancies.

Sure! Let's consider a numerical example of an arbitrage opportunity involving a currency exchange.


**Scenario:**


Suppose there are two banks, Bank A and Bank B, both offering currency exchange services for US dollars (USD) and euros (EUR). The current exchange rates are as follows:


- Bank A: 1 USD = 0.85 EUR

- Bank B: 1 USD = 0.88 EUR


**Arbitrage Opportunity:**


There is a potential arbitrage opportunity here because the two banks are offering different exchange rates for the same currency pair (USD/EUR). This discrepancy allows arbitrageurs to make risk-free profits.


**Steps to Execute the Arbitrage Trade:**


1. The arbitrageur starts with $10,000.


2. The arbitrageur goes to Bank A and exchanges $10,000 for euros. According to Bank A's rate, they will get:


   $10,000 * 0.85 EUR/USD = 8,500 EUR


3. The arbitrageur then takes the 8,500 euros to Bank B and exchanges them back to US dollars. According to Bank B's rate, they will get:


   8,500 EUR * 0.88 USD/EUR = $9,400 USD


**Profit Calculation:**


The arbitrageur started with $10,000 and ended up with $9,400 after completing the arbitrage trade.


Profit = Final Amount - Initial Amount


Profit = $9,400 - $10,000 = -$600


**Conclusion:**


In this example, the arbitrageur did not make a profit but incurred a loss of $600. This could be due to various factors like transaction costs, fees, or the time it took to complete the arbitrage trade. However, in real markets, arbitrage opportunities are swiftly exploited by traders, and such pricing discrepancies are quickly corrected, making risk-free profits more difficult to achieve.


Sure! Here are some multiple-choice questions related to arbitrage and derivatives:


**Question 1:**

Arbitrageurs seek to earn a risk-free profit by:

A) Taking speculative positions in volatile markets.

B) Predicting future stock prices.

C) Identifying and exploiting pricing inefficiencies in different markets.

D) Investing in high-risk assets for potential high returns.


**Answer:**

C) Identifying and exploiting pricing inefficiencies in different markets.


**Question 2:**

What financial instruments do arbitrageurs frequently use to execute their trades?

A) Stocks

B) Government bonds

C) Derivatives

D) Real estate properties


**Answer:**

C) Derivatives


**Question 3:**

Arbitrage opportunities tend to last for:

A) Several years, allowing ample time for profit-making.

B) Weeks, offering a reasonable window for trading.

C) A few days, making quick decision-making essential.

D) They are permanent opportunities that never go away.


**Answer:**

C) A few days, making quick decision-making essential.


**Question 4:**

To execute an arbitrage trade, arbitrageurs enter into:

A) Multiple long positions in the same market.

B) Equivalent offsetting positions in one or more markets.

C) Highly speculative positions to maximize profits.

D) High-risk positions with leverage.


**Answer:**

B) Equivalent offsetting positions in one or more markets.


**Question 5:**

The risk-free rate is typically associated with:

A) Highly volatile stocks.

B) Government bonds or low-risk financial instruments.

C) Investing in startup companies.

D) Leveraged positions in the derivatives market.


**Answer:**

B) Government bonds or low-risk financial instruments.


**Question 6:**

Which of the following best describes the primary objective of arbitrageurs?

A) Speculating on market trends to earn high returns.

B) Eliminating all market risks by diversifying their portfolio.

C) Earning risk-free profits by exploiting mispriced securities.

D) Hedging their positions against potential losses.


**Answer:**

C) Earning risk-free profits by exploiting mispriced securities.


**Question 7:**

Arbitrage opportunities typically arise due to:

A) Random fluctuations in stock prices.

B) Government interventions in financial markets.

C) The discovery of new investment strategies.

D) Pricing discrepancies between different markets.


**Answer:**

D) Pricing discrepancies between different markets.


**Question 8:**

Which of the following scenarios represents a possible arbitrage opportunity?

A) The price of gold is the same across all global markets.

B) A stock's price is $50 on the NYSE and $48 on the LSE at the same time.

C) A company announces record-breaking profits, causing its stock price to surge.

D) The prices of two similar stocks move in sync throughout the day.


**Answer:**

B) A stock's price is $50 on the NYSE and $48 on the LSE at the same time.


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