Leverage is using given resources in such a way that the potential positive or negative outcome is magnified.
Business
A profitable business with good credit and cash flow may be able to borrow at rates well below the rate at which they can earn money in their core business or other projects by utilizing the borrowed capital. Several methods are used to look at what rate of return a corporation can earn money. See return on assets and return on equity. Any time a business can earn more money than what they can borrow at, the corporation will be more profitable over the period of time in which they can do so.
Finance
In financial leverage leverage takes the form of borrowing money and reinvesting it with the hope to earn a greater rate of return than the cost of interest. Leverage allows greater potential return to the investor than otherwise would have been available. The potential for loss is greater because if the investment becomes worthless, not only is that money lost, but the loan still needs to be repaid. A margin account is a common way of utilizing the concept of leverage in investing.
Derivatives
Another form of creating leverage using financial instruments is through the use of options. The purchase of a call option on a security gives the buyer the right to purchase the underlying security at a given price in the future. If the price of the underlying security rises, the value of the call option will rise at a rate much greater than the value of the underlying security. However if the rate of the call option falls or does not rise, the call option may be worthless, involving a much greater loss than if the same money had been invested in the underlying instrument.
Leverage and risk
Utilizing leverage amplifies the potential gain from an investment or project, but also increases the potential loss. This increased risk may be perfectly acceptable or even necessary to reach the goals of the entity or person making the investment. In fact, precisely managing risk utilizing strategies including leverage and securities purchases, is the subject of a discipline known as financial engineering
"Slippage"
In a rising market, the compounding associated with a leveraged portfolio leads to greater gains; in a declining market, the compounding of a leveraged portfolio may lead to larger losses. However, in a flat market with volatility, the compounding of a leveraged portfolio will cause the portfolio to under perform an identical unleveraged portfolio. Because the percentage increase in a leveraged portfolio is higher by the same ratio as the decrease is higher.
Example
A 100 index going to 110 is a 10% increase. A 110 index going to 100 is a 9.09% decrease. In a 200% leveraged index it's a 20% increase, to 120, and a 18.17% (9.09*2) decrease to 98.2.
If a target index gains 10% on one day before returning to the original level the next day, a 2.0 beta portfolio will lose 1.8% of its value, and a 1.25 beta portfolio will lose 0.3% of its value.
Real world
During the 1970s the stock market were "flat". On 31-Dec-79 the Dow Jones Industrial Average closed at 838.74, on 19-Nov-69 it closed at 839.96 ([1]). An unleveraged portfolio of DJIA would have ended with the same price as it began the decade (and would have lost value through inflation). A 200% leveraged portfolio holding the DJIA during that period would have lost all of its value.
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