L26: Risk management with options

Risk management with options

Options can be used to increase the risk of your portfolio (in hopes of a higher return) as well as to decrease the risk of your portfolio (at the expense of a lower return). Below, we work through a couple of examples that show how this can be achieved.

Example 1: Using options to increase risk

This usually involves buying option on stocks instead of buying/shorting the stocks themselves.

To see the difference, consider the following two strategies:

  • Stategy A: invest $9000 in stock A by buying 100 shares at $90 each
  • Stategy B: Use the $9000 to buy 900 call options on stock A (trading at $10 an option). The strike price is $90 and the options expire in a year.

Calculate what your (%) return would be for each strategy, if the price a year from now is:

  • $75
  • $90
  • $105
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Example 2: Using options to decrease risk

You can limit your losses from buying a particular stock by also purchasing put options on that stock. This is called the protective put strategy.

To see how this works, consider the following two strategies:

  • Strategy A: buy one share of AMZN for $100
  • Strategy B: you buy one share of AMZN for $100 and a put option on AMZN that costs you an additional $5. The put option has a strike price of $95 and it expires in 3 months.

Q1: What is your % return for each strategy, if the price of AMZN 3 months from now is:

  • $0
  • $95
  • $105
  • $150
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Q2: Draw the payoff and profit for this protective put, as functions of the price of AMZN

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Volatility bets with options

You can use options to trade based on your opinions about volatility. Below are two examples that show you how this would work.

Example 3: Betting on volatility

You buy a call option on stock X for $10 an option and you also buy a put option on stock X for $5 an option. Both options have strike price of $100. For what values of the price of the underlying asset X would you make a positive profit? Draw the payoff and profit of this strategy as a function of the underlying stock price.

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Example 4: Betting against volatility

You sell a call option on stock X for $10 an option and you also sell a put option on stock X for $5 an option. Both options have strike price of $100. For what values of the price of the underlying asset X would you make a positive profit? Draw the payoff and profit of this strategy as a function of the underlying stock price.

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