Options

A derivative in finance is a financial product that derives its value from another financial product.

An option in finance is a product that provides the right but not the obligation to buy or sell another financial product.

A call option provides an investor with the right to buy a share of stock at the strike price.

If you buy a call option, you are hoping that the price of a stock will go up. The more the stock price goes up, the more money you make.

When the stock price is above the strike price, this is referred to as In The Money.

If the stock price is below the strike price, then it is referred to as Out of the Money. 

A put option provides an investor with the right to sell a share of stock at the strike price. Think of it as the opposite of a call option.

A put option increases in value when the price of the stock drops below the strike price because you are buying the option to sell the stock at a given price.

An investor can hedge against a drop in the value of a large, undiversified stock position by buying a put option, which provides the right but not the obligation to sell a stock at a particular price. If the stock price drops considerably, the put option allows the investor to sell at a particular price, which can provide a high payout when the stock loses money.

Both an insurance policy and a put option are derivatives because their values depend on the performance of the underlying asset.

Think of options as a contract between two parties. 

One party writes an option, that they make available for sale for a premium, the price to purchase the option.

The other party buys the option, thereby paying for the right, but not the obligation to buy or sell a share of stock at a certain price, called the strike price or exercise price.

Although options are often written on stocks, they can also derive their value from other things like stock market indices. Regardless of the underlying asset, the concept is the same.

The contract also includes an expiration date, and depending on the type of option, it can either be exercised anytime before the expiration date (American Option), or only on the expiration date (European Option).

First, options are what's known in economics as a zero-sum game, meaning that for every winner, there must be a loser. Every positive payout is equally offset by a negative payout. 

As a result, the average return to those who invest in options is zero.

Well, in reality, it is actually negative because there are transaction costs to buy options. As a result, investing in options is not a good long-term strategy if your goal is to maximize returns for a given level of risk.

Another Important thing to remember about options is the Black-Scholes model. Occasionally, you will hear about an investment strategy that involves investing in stocks while also buying options that protect against a drop in the price of stocks.

This sounds like a pretty good deal, all of the upside with protection against the downside. Unfortunately, this cannot work in an efficient market. The Black-Scholes model states that a perfectly hedged investment in risky assets has no risk, so the expected return on a perfectly hedged stock investment should equal the risk-free rate.

In fact, the Black-Scholes model is used in this way to price options. Options should be seen as a way to reduce risk while also reducing expected wealth because most options expire out of the money.

In this sense, options are no different than insurance contracts. Insurance reduces expected wealth but also reduces the risk of a big drop in spending. This tradeoff makes sense when an investor holds a large idiosyncratic risk to wealth, like a home.

It is rare that a household will benefit from buying financial options. An investor who holds a diversified portfolio and wants to reduce risk can receive a higher than expected return by simply increasing their allocation to safe assets.

This is because the transaction costs on options are higher than the transaction costs on a low-cost portfolio of safe assets.

Options won't buy you a free lunch by reducing risk without also reducing expected return.

Options can be useful for investors who hold an undiversified portfolio.

For example, investors may be restricted in their ability to sell shares of a stock in an Initial Public Offering (IPO). 

They may also have exercised incentive stock options and want to hold onto the concentrated position for a while in order to reduce their tax liability.

There may also be investors who have a large capital gain in a stock investment that they would prefer not to sell so that their heirs or a charity can receive the benefit of a step-up in basis at death.

Regardless of the reason, when an investor maintains a large concentrated stock position in a portfolio, this represents a significant source of idiosyncratic risk, and portfolio inefficiency.

Options can help reduce this risk by providing a hedge for the portfolio.

The Black-Scholes model suggests that options based on more volatile stocks should be more expensive than options based on less volatile stocks. 

Why? Because a more volatile stock is more likely to see its price fluctuate widely than less volatile stocks, which means it is more likely to rise above the strike price, in the case of call options, or fall below the strike price, in the case of put options, before the option expires. 

As a result, you will pay more for a call option on a stock that could jump in price from $50 to $70 than a stock that has been hanging steadily around $50 for the last year.

Since options for more volatile stocks are more expensive than options for less volatile stocks, it is possible to estimate the amount of expected volatility of a stock from the price of its options. 

For example, if a 3-month call option with a strike price of $55 costs $2 for Stock A and $1 for Stock B, then we can assume that the implied volatility of Stock A is higher than the implied volatility of Stock B.

There is an index that shows the change in implied volatility of U.S. stocks over time, known as the Volatility Index, or VIX. This index was developed by the Chicago Board Options Exchange to estimate the expected market volatility over the next 30 days, based on the Black-Scholes model and current option prices of the S&P 500 index. When the implied volatility goes up, option prices become more expensive.

The VIX is a pretty good indicator of how panicked investors are about stock prices at a given point in time, but it’s not a very good predictor of how volatile stocks are going to be in the future.