Posted: August 24th, 2022

Derivatives Assignment

Week 3 Assignment Questions

Calculate your pre-tax rate of return (profit divided by investment) in each of these scenarios (show your calculations):

1. buy 1,000 shares of ABC common stock at $50 and sell at $60 one year later.

2. buy 1,000 shares of ABC common stock at $50, borrowing 50% of the amount necessary to buy it, at a 2% interest rate, sell the stock at $60 one year later, paying back the loan at the same time.

3. buy listed options at $400 for 1,000 shares of ABC, giving you the right but not the obligation to buy the shares at $50 one year later, you exercise the option one year later when the stock price is $60. Also, use the Long Call chart (from the CBOE material in the lesson) to explain what is going on.

2. Some airlines hedge jet fuel prices and some do not. When oil prices declined, some airlines that had hedged jet fuel prices were worse off than those that did not hedge. Using a numerical example, show your understanding of hedging by explaining why they were worse off. Then, explain if this situation is an argument against hedging in no more than half page (double spaced).
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Pre-tax rate of return = (Profit / Investment)

Profit = (Selling Price – Purchase Price) x Shares = (60 – 50) x 1000 = $10,000
Investment = Purchase Price x Shares = 50 x 1000 = $50,000
Pre-tax rate of return = $10,000/$50,000 = 20%
Pre-tax rate of return = (Profit / Investment)

Profit = (Selling Price – Purchase Price) x Shares = (60 – 50) x 1000 = $10,000
Loan = Investment x (1 – Loan Percentage) = $50,000 x (1 – 0.5) = $25,000
Interest = Loan x Interest Rate x Time = $25,000 x 0.02 x 1 = $500
Investment = Loan + Interest + Purchase Price = $25,000 + $500 + $50,000 = $75,500
Pre-tax rate of return = $10,000/$75,500 = 13.21%
The Long Call chart shows the profit and loss for a call option holder. If the stock price is below the strike price, the option holder will not exercise the option and will let it expire worthless. If the stock price is above the strike price, the option holder will exercise the option and will buy the stock at the strike price, then sell the stock at the current market price. The profit is the difference between the selling price and the strike price, minus the option premium paid. In this scenario, the pre-tax rate of return would be the profit divided by the option premium paid.

Option Premium Paid = Option Price x Shares = 400 x 1000 = $400,000
Profit = (Selling Price – Strike Price) x Shares = (60 – 50) x 1000 = $10,000
Pre-tax rate of return = $10,000/$400,000 = 2.5%
In the case of the airlines that hedged jet fuel prices, they locked in a fixed price for their fuel for a certain period, which protected them from price increases but also left them exposed to price decreases. When oil prices declined, they still had to pay the higher, locked-in price for their fuel, while airlines that did not hedge were able to take advantage of the lower prices in the market. This situation is not an argument against hedging in general, as hedging can be an effective risk management tool when used properly. The key is to understand the nature of the risks being hedged and to carefully evaluate the cost and benefits of different hedging strategies.

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