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Chapter 1: Problem 7

Suppose you own 5,000 shares that are worth \(\$ 25\) each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next four months?

Short Answer

Expert verified
Buy 50 put options to insure against a decline over the next four months.

Step by step solution

01

Understand Put Options

A put option gives the holder the right, but not the obligation, to sell a stock at a predetermined price (the strike price) before the option expires. By purchasing put options, you can protect your shares from falling below this strike price.
02

Calculate Total Value of Shares

You own 5,000 shares, each worth \(25. The total value of your shares is calculated as follows: \[ 5,000 \text{ shares} \times \\) 25 = \$ 125,000.\] This is the total value you want to protect against a decline.
03

Determine the Amount of Put Options Needed

Each option typically covers 100 shares. To determine how many put options you need to buy, divide the total number of shares by the number of shares each option covers: \[ \frac{5,000}{100} = 50 \text{ put options}. \]Thus, you need to purchase 50 put options to cover all of your shares.
04

Choose the Strike Price and Expiry

Select a strike price at which you would be comfortable selling your shares if necessary, and choose an expiry date for the options, in this case, four months from now. The strike price should reasonably reflect the minimum price you are willing to accept.
05

Purchase the Put Options

Buy 50 put options with your chosen strike price and a four-month expiration. By doing this, you ensure that you can sell your 5,000 shares at the strike price, regardless of any market decline over the next four months.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Put Options
Put options are financial contracts that provide the holder the right, but not the obligation, to sell an underlying asset at a designated price until a specific expiration date. This price is known as the "strike price." When you purchase put options for your stocks, you're essentially buying insurance against a drop in their value.

Here are a few key points about put options:
  • You have the right to sell your shares at the strike price before expiration, even if the market value drops below it.
  • Put options are flexible and can be tailored to your risk tolerance and market expectations by selecting different strike prices and expiration dates.
  • This strategic tool requires an initial premium payment, which is the price you pay for the option.
In the context of the exercise, buying put options allows you to lock in a predetermined selling price for your shares, ensuring protection against unfavorable price movements over the set time frame.
Risk Management
Risk management involves strategies to minimize potential losses within financial markets. In options trading, like in the original exercise, one can use put options as an effective risk management tool to protect investments.

Why use put options for risk management?
  • Stability: They provide a safety net for stockholders worried about downturns, allowing them to withstand volatile markets with more peace of mind.
  • Cost-Efficiency: While there is a premium for purchasing options, this cost may be far less than potential losses if the stock's value plummets.
  • Flexibility: Investors can decide how much of their portfolio they wish to hedge, tailoring strategies to fit their risk appetite.
By strategically buying put options, investors can confidently hold onto their stocks even as market fluctuations occur, knowing they have a fallback plan.
Strike Price
The strike price is a key element of any options contract, including put options. It is the price at which you can sell the underlying stock. Choosing the right strike price is crucial when forming your options strategy.

Considerations for selecting a strike price:
  • Comfort Level: Choose a price that meets your minimum acceptance level for sale. It should reflect a value that is acceptable in worst-case scenarios.
  • Premium Cost: Lower strike prices generally result in lower premiums, but they also mean less protection.
  • Market Analysis: Consider market conditions and forecasts to choose a strike price that aligns with your expectations and risk management plan.
In the exercise, selecting a strike price involves deciding at which point you'd prefer to sell your shares should the market fall, ensuring your financial goals are met while reducing downside risk.

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Most popular questions from this chapter

On May \(8,2000,\) an investor owns 100 Cisco shares. As indicated in Table 1.2 the share price is \(62 \frac{3}{4}\) and an October put option with a strike price 50 costs \(4 \frac{5}{8} .\) The investor is comparing two alternatives to limit downside risk. The first involves buying one October put option contract with a strike price of \(50 .\) The second involves instructing a broker to sell the 100 shares as soon as Cisco's price reaches \(50 .\) Discuss the advantages and disadvantages of the two strategies.

It is now July \(2001 .\) A mining company has just discovered a small deposit of gold. It will take six months to construct the mine. The gold will then be extracted on a more or less continuous basis for one year. Futures contracts on gold are available on the New York Commodity Exchange. There are delivery months every two months from August 2001 to December 2002 . Each contract is for the delivery of 100 ounces. Discuss how the mining company might use futures markets for hedging.

The price of gold is currently \(\$ 500\) per ounce. Forward contracts are available to buy or sell gold at \(\$ 700\) for delivery in one year. An arbitrageur can borrow money at \(10 \%\) per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero.

The current price of a stock is \(\$ 94,\) and three-month call options with a strike price of \(\$ 95\) currently sell for \(\$ 4.70 .\) An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options \((20\) contracts). Both strategies involve an investment of \(\$ 9,400 .\) What advice would you give? How high does the stock price have to rise for the option strategy to be more profitable?

Suppose that a March call option with a strike price of \(\$ 50\) costs \(\$ 2.50\) and is held until March. Under what circumstances will the holder of the option make a gain? Under what circumstances will the option be exercised?
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