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**Fence** (also known as a Dutch Rudder) is an investment strategy that uses options to limit the range of possible returns on a financial instrument.^{ [1] }

In finance, an **investment strategy** is a set of rules, behaviors or procedures, designed to guide an investor's selection of an investment portfolio. Individuals have different profit objectives, and their individual skills make different tactics and strategies appropriate. Some choices involve a tradeoff between risk and return. Most investors fall somewhere in between, accepting some risk for the expectation of higher returns.

In finance, an **option** is a contract which gives the buyer the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price prior to or on a specified date, depending on the form of the option. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed.

**Financial instruments** are monetary contracts between parties. They can be created, traded, modified and settled. They can be cash (currency), evidence of an ownership interest in an entity (share), or a contractual right to receive or deliver cash (bond).

A fence consists of the following elements:

- long position in a financial instrument (e.g. a share, index or currency)
- long put (normally with a strike price close to or at the current spot price of the financial instrument)
- short put (with a strike price lower than the bought put - e.g. 80% of the current spot price)
- short call (with a strike price higher than the current spot price).

In finance, a **long** position in a financial instrument, means the holder of the position owns a positive amount of the instrument. It is contrasted with *going short*.

In financial markets, a share is a unit used as mutual funds, limited partnerships, and real estate investment trusts. The owner of shares in the corporation/company is a shareholder of the corporation. A share is an indivisible unit of capital, expressing the ownership relationship between the company and the shareholder. The denominated value of a share is its face value, and the total of the face value of issued shares represent the capital of a company, which may not reflect the market value of those shares.

In economics and finance, an **index** is a statistical measure of changes in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and employment. Economic indices track economic health from different perspectives. Influential global financial indices such as the Global Dow, and the NASDAQ Composite track the performance of selected large and powerful companies in order to evaluate and predict economic trends. The Dow Jones Industrial Average and the S&P 500 primarily track U.S. markets, though some legacy international companies are included. The consumer price index tracks the variation in prices for different consumer goods and services over time in a constant geographical location, and is integral to calculations used to adjust salaries, bond interest rates, and tax thresholds for inflation. The GDP Deflator Index, or real GDP, measures the level of prices of all new, domestically produced, final goods and services in an economy. Market performance indices include the labour market index/job index and proprietary stock market index investment instruments offered by brokerage houses.

The expiration dates of all the options are usually the same. The call strike is normally chosen in such a way that the sum total of the three option premiums are equal to zero.

In finance, the **expiration** date of an option contract is the last date on which the holder of the option may exercise it according to its terms. In the case of options with "automatic exercise" the net value of the option is credited to the long and debited to the short position holders.

This investment strategy will ensure that the value of the investment at expiry will be between the strike price on the short call and the strike price on the long put. Thus possible gains and losses (the value of the financial instrument minus the cost of acquiring it) are confined to a specified range.

In finance, the **strike price** of an option is the fixed price at which the owner of the option can buy, or sell, the underlying security or commodity. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium.

However, if the price of the financial instrument falls below the strike level of the sold put the investor will start participating in any further price declines of the financial instrument.

The **Black–Scholes** or **Black–Scholes–Merton model** is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the **Black–Scholes formula**, which gives a theoretical estimate of the price of European-style options and shows that the option has a *unique* price regardless of the risk of the security and its expected return. The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with adjustments and corrections, by options market participants.

In finance, a **put** or **put option** is a stock market device which gives the owner the right, but not the obligation, to sell an asset, at a specified price, by a predetermined date to a given party. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock. The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.

In financial mathematics, **put–call parity** defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract.

In mathematical finance, the **Greeks** are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters. Collectively these have also been called the **risk sensitivities**, **risk measures** or **hedge parameters**.

In finance, **moneyness** is the relative position of the current price of an underlying asset with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a three-fold classification: if the derivative would have positive intrinsic value if it were to expire today, it is said to be **in the money**; if it would be worthless if expiring at the current price it is said to be **out of the money**, and if the current price and strike price are equal, it is said to be **at the money**. There are two slightly different definitions, according to whether one uses the current price (spot) or future price (forward), specified as "at the money spot" or "at the money forward", etc.

A **hedge** is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, gambles, many types of over-the-counter and derivative products, and futures contracts.

**Rational pricing** is the assumption in financial economics that asset prices will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

In finance, a price (premium) is paid or received for purchasing or selling options. This price can be split into two components.

In finance, a **butterfly** is a limited risk, non-directional options strategy that is designed to have a high probability of earning a limited profit when the future volatility of the underlying asset is expected to be lower or higher than the implied volatility when long or short respectively.

A **covered call** is a financial market transaction in which the seller of call options owns the corresponding amount of the underlying instrument, such as shares of a stock or other securities. If a trader buys the underlying instrument at the same time the trader sells the call, the strategy is often called a "buy-write" strategy. In equilibrium, the strategy has the same payoffs as writing a put option.

In options trading, a **box spread** is a combination of positions that has a certain payoff, considered to be simply "delta neutral interest rate position". For example, a bull spread constructed from calls combined with a bear spread constructed from puts has a constant payoff of the difference in exercise prices assuming that the underlying stock does not go ex-dividend before the expiration of the options. If the underlying asset has a dividend of x, then the settled value of the box will be 10+x. Under the no-arbitrage assumption, the net premium paid out to acquire this position should be equal to the present value of the payoff.

In finance, a **collar** is an option strategy that limits the range of possible positive or negative returns on an underlying to a specific range. A **collar** strategy is used as one of the ways to hedge against possible losses and it represents long put options financed with short call options.

The **iron condor** is an option trading strategy utilizing two vertical spreads – a put spread and a call spread with the same expiration and four different strikes. A long iron condor is essentially selling both sides of the underlying instrument by simultaneously shorting the same number of calls and puts, then covering each position with the purchase of further out of the money call(s) and put(s) respectively. The converse produces a short iron condor.

In finance an **iron butterfly,** also known as the ironfly, is the name of an advanced, neutral-outlook, options trading strategy that involves buying and holding four different options at three different strike prices. It is a limited-risk, limited-profit trading strategy that is structured for a larger probability of earning smaller limited profit when the underlying stock is perceived to have a low volatility.

**Option strategies** are the simultaneous, and often mixed, buying or selling of one or more options that differ in one or more of the options' variables. Call options, simply known as calls, give the buyer a right to buy a particular stock at that option's strike price. Conversely, put options, simply known as puts, give the buyer the right to sell a particular stock at the option's strike price. This is often done to gain exposure to a specific type of opportunity or risk while eliminating other risks as part of a trading strategy. A very straightforward strategy might simply be the buying or selling of a single option, however option strategies often refer to a combination of simultaneous buying and or selling of options.

**Options spreads** are the basic building blocks of many options trading strategies. A spread position is entered by buying and selling equal number of options of the same class on the same underlying security but with different strike prices or expiration dates.

The **backspread** is the converse strategy to the ratio spread and is also known as reverse ratio spread. Using calls, a bullish strategy known as the call backspread can be constructed and with puts, a strategy known as the put backspread can be constructed.

In finance, a **strangle** is an investment strategy involving the purchase or sale of particular option derivatives that allows the holder to profit based on how much the price of the underlying security moves, with relatively minimal exposure to the *direction* of price movement. A purchase of particular options is known as a long strangle, while a sale of the same options is known as a short strangle. As an options position **strangle** is a variation of a more generic straddle position. **Strangle's** key difference from a straddle is in giving investor choice of balancing cost of opening a strangle versus a probability of profit. For example, given the same underlying security, strangle positions can be constructed with low cost and low probability of profit. Low cost is relative and comparable to a cost of straddle on the same underlying. Strangles can be used with equity options, index options or options on futures.

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