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The notional amount (or notional principal amount or notional value) on a financial instrument is the nominal or face amount that is used to calculate payments made on that instrument. This amount generally does not change hands and is thus referred to as notional.
Contrast a bond with an interest rate swap:
- In a bond, the buyer pays the principal amount at issue (start), then receives coupons (computed off this principal) over the life of the bond, then receives the principal back at maturity (end).
- In a swap, no principal changes hands at inception (start) or expiry (end), and in the meantime, interest payments are computed based on a notional amount, which acts as if it were the principal amount of a bond, hence the term notional principal amount, abbreviated to notional.
In simple terms the notional principal amount is essentially how much of the asset or bonds a person has. For example, if a premium bond was bought for £1 then the notional principal amount would be £1. Hence the notional principal amount is the quantity of the assets and bonds.
Interest rate swaps 
In the context of an interest rate swap, the notional principal amount is the specified amount on which the exchanged interest payments are based; this could be 8000 US dollars, or 2.7 million pounds sterling, or any other combination of a number and a currency. Each period's rates are multiplied by the notional principal amount to determine the height and currency of each counter-party's payment. A notional principal amount is the amount used as a reference to calculate the amount of interest due on an 'interest only class' which is not entitled to any principal.
Total return swaps 
In a typical total return swap, one party pays a fixed or floating rate multiplied by a notional principal amount plus the depreciation, if any, in a notional amount of property in exchange for payments by the other party of the appreciation, if any, on the same notional amount of property. For example, assume the underlying property is the S&P 500 stock index. A would pay B LIBOR times a $100 notional amount plus depreciation, if any, on a $100 notional investment in the S&P 500 index. B would pay A the appreciation, if any, in the same notional S&P 500 investment.
Equity options 
Shares also have a notional principal amount but it is called nominal instead of notional.
If you are buying stock option contracts, for example, those contracts could potentially give you a lot more shares than you could control by buying shares outright. So the Notional Value is the value of what you control rather than the value of what you own.
So, for instance, if you purchase 100 equity call option with a strike of $60 for a stock that is currently trading at $60, then you have the same upside potential as someone who holds $6,000 of stock (1 option * 100 multiplier * $60), but you may have paid only $5/option (for a total of $500), so by this measure you have achieved leverage of $6,000/$500 = 12x. Note that if the stock price moves to $70, your dollar notional is now $7,000 (- cost of option and commission differential), but your quantity (unit notional) is still 1 contract.
Foreign Currency/Exchange or "FX" derivatives 
In FX derivatives, such as forwards or options, there are two notionals. Suppose you have a call option on USD/JPY struck at 110, and you buy one of these. Then this gives you the option to pay 100 USD and receive 110 x 100 = 11,000 JPY, so the USD notional is 100 USD, and the JPY notional is 11,000 JPY.
Note that the ratio of notionals is exactly the strike, and thus if you move the strike, you must change one or the other notional. For instance, if you move the strike to 100, then if you hold the USD fixed at 100, the JPY notional becomes 10,000: you will pay the same number of USD, and receive fewer JPY. Alternatively, you could hold JPY constant at 11,000 and change the USD notional to 110: you pay more USD and receive the same number of JPY (you've changed the price of JPY, denominated in USD).
When hedging a foreign currency exposure, (say for an American USD business, an outflow of 11,000 JPY) it is the foreign currency notional that must be fixed.
Exchange-traded funds track underlying positions, so an investment performs equivalently to purchasing that number of physical positions, though the fund may in fact not directly purchase the positions, and instead use derivatives (especially futures) to produce the position.
Levered ETFs, notably inverse exchange-traded funds, have the unusual property that their notional changes every day: this is because they pay the compounded daily return, so it is as if one were re-investing each day's earnings at the new daily price: if one has an inverse ETF in an asset that goes down, one has more money, which one uses to short a cheaper asset, hence one's unit notional goes up, and conversely if the asset has gone up in value. See inverse exchange-traded fund for mathematical details.
- Notional amount - Definition from Investor Dictionary - Define meaning of the word Notional amount
- Sold at par.
- A different measure of leverage would be your Delta.