Practice Exercises and Solutions for Financial Instruments

22.2 Practice Exercises and Solutions

Welcome to the practice exercises section of our comprehensive guide on financial instruments. This section is designed to reinforce your understanding of options, futures, and derivatives through practical problems and detailed solutions. These exercises will help you apply theoretical concepts to real-world scenarios, preparing you for both exams and professional practice in the financial markets.

Exercise 1: Understanding Options

Problem:

You are considering purchasing a call option on XYZ Corporation’s stock. The stock is currently trading at $50 per share. The call option has a strike price of $55, an expiration date in three months, and is priced at a premium of $3 per option.

1. Calculate the intrinsic value of the option at the time of purchase.
2. Determine the time value of the option.
3. What is the breakeven price for this call option?

Solution:

1. Intrinsic Value:

   The intrinsic value of a call option is the difference between the stock price and the strike price, provided the stock price is above the strike price. In this case, the stock price ($50) is below the strike price ($55), so the intrinsic value is $0.

2. Time Value:

   The time value is calculated by subtracting the intrinsic value from the option premium. Here, the option premium is $3, and the intrinsic value is $0. Therefore, the time value is $3.

3. Breakeven Price:

   The breakeven price for a call option is the strike price plus the premium paid. Thus, the breakeven price is $55 + $3 = $58.

Exercise 2: Futures Contracts

Problem:

Suppose you are a wheat farmer expecting to harvest 10,000 bushels of wheat in three months. You want to hedge against the risk of falling wheat prices, so you decide to enter into a futures contract. The current futures price for wheat is $5 per bushel.

1. If the price of wheat falls to $4 per bushel at the time of harvest, calculate your gain or loss from the futures contract.
2. What would be your net selling price per bushel of wheat, including the futures contract?

Solution:

1. Gain or Loss from Futures Contract:

   You locked in a selling price of $5 per bushel through the futures contract. If the market price falls to $4, you gain $1 per bushel on the futures contract. For 10,000 bushels, your total gain is 10,000 bushels x $1 = $10,000.

2. Net Selling Price:

   Without the futures contract, you would sell at the market price of $4 per bushel. However, with the $1 gain from the futures contract, your net selling price is $4 + $1 = $5 per bushel.

Exercise 3: Hedging with Derivatives

Problem:

A company has a $1 million loan with a floating interest rate tied to the LIBOR, currently at 2%. To protect against rising interest rates, the company enters into an interest rate swap, agreeing to pay a fixed rate of 3% while receiving payments based on the LIBOR rate.

1. If the LIBOR increases to 4%, calculate the net interest payment the company will make.
2. Explain the benefit of the swap to the company.

Solution:

1. Net Interest Payment:

   Without the swap, the company would pay 4% on its $1 million loan, which amounts to $40,000 annually. With the swap, the company pays a fixed rate of 3%, equating to $30,000, and receives payments based on the 4% LIBOR, which is $40,000. The net payment is $30,000 - $40,000 = -$10,000, meaning the company effectively receives $10,000.

2. Benefit of the Swap:

   The interest rate swap protects the company from rising interest rates. By locking in a fixed rate, the company avoids the risk of increased payments due to rate hikes, ensuring more predictable financial planning.

Exercise 4: Speculating with Options

Problem:

An investor believes that the stock of ABC Corporation, currently trading at $100, will rise in the next month. They purchase a call option with a strike price of $105, expiring in one month, at a premium of $2.

1. If the stock price rises to $110 at expiration, calculate the investor’s profit or loss.
2. What is the maximum loss the investor can incur?

Solution:

1. Profit or Loss:

   At expiration, the intrinsic value of the call option is $110 (stock price) - $105 (strike price) = $5. The investor paid a $2 premium, so the profit is $5 - $2 = $3 per option.

2. Maximum Loss:

   The maximum loss is limited to the premium paid for the option, which is $2 per option.

Exercise 5: Arbitrage Opportunities

Problem:

You notice that the stock of DEF Corporation is trading at $50 on the New York Stock Exchange (NYSE) and $52 on the London Stock Exchange (LSE). Assume no transaction costs or currency exchange issues.

1. Explain how you could exploit this price difference through arbitrage.
2. Calculate the potential profit if you can trade 1,000 shares.

Solution:

1. Arbitrage Strategy:

   Buy 1,000 shares of DEF Corporation on the NYSE at $50 per share and simultaneously sell them on the LSE at $52 per share. This exploits the price difference between the two markets.

2. Potential Profit:

   The profit per share is $52 - $50 = $2. For 1,000 shares, the total profit is 1,000 x $2 = $2,000.

Exercise 6: Understanding Swaps

Problem:

A multinational corporation has revenues in euros but expenses in U.S. dollars. To manage currency risk, it enters into a currency swap, exchanging euros for dollars at a fixed exchange rate of 1 euro = $1.20.

1. If the euro depreciates to 1 euro = $1.10, calculate the benefit of the swap.
2. How does the swap mitigate currency risk for the corporation?

Solution:

1. Benefit of the Swap:

   Without the swap, the corporation would receive fewer dollars for its euros due to depreciation. With the swap, it still exchanges euros at the favorable rate of $1.20, avoiding the loss from the weaker euro.

2. Risk Mitigation:

   The currency swap locks in a fixed exchange rate, protecting the corporation from unfavorable currency fluctuations and ensuring stable cash flows.

Exercise 7: Calculating Margin Requirements

Problem:

You decide to trade futures contracts on crude oil, which requires a margin of $5,000 per contract. You have $20,000 in your account.

1. How many contracts can you trade with your available margin?
2. If the margin requirement increases to $6,000 per contract, how does this affect your trading capacity?

Solution:

1. Number of Contracts:

   With $20,000 and a $5,000 margin per contract, you can trade 20,000 / 5,000 = 4 contracts.

2. Effect of Increased Margin:

   If the margin requirement rises to $6,000, you can now trade 20,000 / 6,000 = 3 contracts, reducing your trading capacity.

Exercise 8: Credit Derivatives

Problem:

A bank holds a portfolio of corporate loans and wants to reduce its exposure to credit risk. It purchases a credit default swap (CDS) on one of the loans, paying a premium of 1% of the loan’s value annually.

1. If the loan defaults, explain how the CDS provides protection to the bank.
2. What is the cost of the CDS for a $10 million loan?

Solution:

1. Protection from CDS:

   The CDS acts as insurance. If the loan defaults, the bank receives a payout from the CDS seller, compensating for the loss on the loan.

2. Cost of the CDS:

   The annual premium is 1% of $10 million, which equals $100,000.

Exercise 9: Exotic Options

Problem:

An investor is considering a barrier option on a stock, which becomes active only if the stock price reaches $120. The current stock price is $110, and the barrier option has a strike price of $115.

1. If the stock price rises to $125, calculate the intrinsic value of the option.
2. Explain the advantage of using a barrier option.

Solution:

1. Intrinsic Value:

   Since the stock price reached $125, surpassing the $120 barrier, the option is active. The intrinsic value is $125 (stock price) - $115 (strike price) = $10.

2. Advantage of Barrier Option:

   Barrier options can be cheaper than standard options because they only become active under certain conditions, allowing investors to tailor risk exposure.

Exercise 10: Structured Products

Problem:

A structured product offers a 5% return if the S&P 500 index remains within a specified range over a year. If the index moves outside this range, the return is 0%.

1. Discuss the potential benefits and risks of investing in this structured product.
2. How might an investor use this product in their portfolio?

Solution:

1. Benefits and Risks:

   The structured product provides a potential return with limited risk if the index remains stable. However, if the index moves outside the range, the investor earns nothing, posing a risk of opportunity cost.

2. Portfolio Use:

   An investor might use this product for diversification, seeking stable returns without direct exposure to the index’s volatility.

Quiz Time!