Leverage

In finance, **leverage** (sometimes referred to as **gearing** in the United Kingdom and Australia) is any technique involving the use of debt (borrowed funds) rather than fresh equity in the purchase of an asset, with the expectation that the after-tax profit to equity holders from the transaction will exceed the borrowing cost, frequently by several multiples⁠ ⁠— hence the provenance of the word from the effect of a lever in physics, a simple machine which amplifies the application of a comparatively small input force into a correspondingly greater output force. Normally, the lender (finance provider) will set a limit on how much risk it is prepared to take and will set a limit on how much leverage it will permit, and would require the acquired asset to be provided as collateral security for the loan. For example, for a residential property the finance provider may lend up to, say, 80% of the property's market value, for a commercial property it may be 70%, while on shares it may lend up to, say, 60% or none at all on certain volatile shares.

Leveraging enables gains to be multiplied. On the other hand, losses are also multiplied, and there is a risk that leveraging will result in a loss if financing costs exceed the income from the asset, or the value of the asset falls.

## Sources

Leverage can arise in a number of situations, such as:

* leverage their savings when buying a home by financing a portion of the purchase price with mortgage debt. Thus if they buy a house 50% financed by debt, 50% by equity (own funds), when they sell the house for double the purchase price, they repay the lender not half the gain as would be the case for equity financing, but only the nominal value of the loan (plus interest). Thus the investor from a 50% leveraging by debt-finance, has increased his wealth by 200% (before interest cost). If he had financed the purchase by further equity, his own or that of a third-party, his gain would only be 100%.
* individuals leverage their exposure to financial investments by use of margins (borrowing from their broker).
* securities like options and futures are effectively bets between parties where the principal is implicitly borrowed/lent at interest rates of very short treasury bills.
* equity owners of businesses leverage their investment by having the business borrow a portion of its needed financing. The more it borrows, the less equity it needs, so any profits or losses are shared among a smaller base and are proportionately larger as a result.
* businesses leverage their operations by using fixed cost inputs when revenues are expected to be variable. An increase in revenue will result in a larger increase in operating profit.
* hedge funds may leverage their assets by financing a portion of their portfolios with the cash proceeds from the short sale of other positions.

## Risk

While leverage magnifies profits when the returns from the asset more than offset the costs of borrowing, leverage may also magnify losses. A corporation that borrows too much money might face bankruptcy or default during a business downturn, while a less-leveraged corporation might survive. An investor who buys a stock on 50% margin will lose 40% if the stock declines 20%.

Risk may depend on the volatility in value of collateral assets. Brokers may demand additional funds when the value of securities held declines. Banks may decline to renew mortgages when the value of real estate declines below the debt's principal. Even if cash flows and profits are sufficient to maintain the ongoing borrowing costs, loans may be called-in.

This may happen exactly at a time when there is little market liquidity, i.e. a paucity of buyers, and sales by others are depressing prices. It means that as market price falls, leverage goes up in relation to the revised equity value, multiplying losses as prices continue to go down. This can lead to rapid ruin, for even if the underlying asset value decline is mild or temporary the debt-financing may be only short-term, and thus due for immediate repayment. The risk can be mitigated by negotiating the terms of leverage, by maintaining unused capacity for additional borrowing, and by leveraging only liquid assets which may rapidly be converted to cash.

On the other hand, the high level of leverage afforded to borrowers involved in forex trading presents relatively low risk per unit due to the relative stability of that market. Compared with other trading markets, forex traders must trade a much higher volume of units in order to make any considerable profit. For example, many brokers offer 100:1 leverage for investors, meaning that someone bringing $1,000 of equity can control a further $100,000 while taking responsibility/ownership for any losses or gains their investments incur. A 1% gain in the value of $101,000 currency purchased will thus generate a profit of $1,010 (ignoring interest), which is a 101% profit on the equity invested. Without the benefit of leverage, the investor would have invested $101,000 of equity and would have gained a profit of only 1%. However, with leverage, if the currency depreciated by 1% the loss would be -101% on the equity invested.

There is an implicit assumption in that account, however, which is that the underlying leveraged asset is the same as the unlevereged one. If a company borrows money to modernize, add to its product line or expand internationally, the extra trading profit from the additional diversification might more than offset the additional risk from leverage. Or if an investor uses a fraction of his portfolio to margin stock index futures (high risk) and puts the rest in a low-risk money-market fund, he might have the same volatility and expected return as an investor in an unlevered low-risk equity-index fund. Or if both long and short positions are held by a pairs-trading stock strategy the matching and off-setting economic leverage may lower overall risk levels.

So while adding leverage to a given asset always adds risk, it is not the case that a levered company or investment is always riskier than an unlevered one. In fact, many highly levered hedge funds have less return volatility than unlevered bond funds, and normally low-risk public utilities with lots of debt are usually less risky stocks than unlevered high-risk technology companies.

## Effect on rates of return

Here is an example showing the calculation of the expected return resulting from leverage. There is a short-form calculation and a long-form that is more intuitive. Given:

The following example is for an investor who seeks to purchase shares of a well performing asset (+5% expected growth). The investor seeks to increase the total amount purchased by leveraging the purchase with borrowed money. A lender and the investor establish the following terms: the lender will permit the investor to leverage the purchase by agreeing to a loan that is equal to eight times the equity investment; for every 1 dollar invested (equity), the lender will lend 8 (leverage). The cost of the loan is 4% of the loan amount.
+5% asset return

−4% leverage cost

8:1 leverage ratio

LONG-FORM math

The gross total amount of asset performance following the leveraged purchase is equal to the total quantity of asset purchased multiplied by the Asset Return. In this case, the quantity of asset purchased is equal to 9 (8 from loan funds + 1 from equity funds) and the Asset Return is +5%. So the gross total profit from the leveraged asset purchase = 9 times +5% = +45% gross total profit from leveraged asset purchase. To arrive at net profit, the leverage cost is subtracted from the gross total costs. The cost of the loan is 4% of the loan amount, and the loan is 8 per dollar of equity or 8 times −4% = −32% cost. So the sum of total profit and total cost is +45% profit minus 32% cost = 13% net profit from the leveraged purchase per dollar of equity investment = expected leverage return on equity investment.

SHORT-FORM math

Asset Leverage Differential = sum of Asset's Return and the Cost of Leverage Debt = +5% − 4% = +1% Rate Leveraged Asset Return

Leveraged Debt to Equity Investment Ratio = 8 divided by 1 = 8 Leverage Factor

Multiply first two lines = Rate of Leveraged Asset Return x Leverage Factor = + 1% × 8 = +8% Return on Leverage

Add Return on Asset's = 5%
Equals Rate of Leveraged Asset Return = sum of Asset Return and Leverage 8% + 5% = **13%**

## Measuring

A good deal of confusion arises in discussions among people who use different definitions of leverage. The term is used differently in investments and corporate finance, and has multiple definitions in each field.

### Investments

**Accounting leverage** is total assets divided by the total assets minus total liabilities. **Notional leverage** is total notional amount of assets plus total notional amount of liabilities divided by equity. **Economic leverage** is volatility of equity divided by volatility of an unlevered investment in the same assets. To understand the differences, consider the following positions, all funded with $100 of cash equity:

* Buy $100 of crude oil with money out of pocket. Assets are $100 ($100 of oil), there are no liabilities, and assets minus liabilities equals owners' equity. Accounting leverage is 1 to 1. The notional amount is $100 ($100 of oil), there are no liabilities, and there is $100 of equity, so notional leverage is 1 to 1. The volatility of the equity is equal to the volatility of oil, since oil is the only asset and you own the same amount as your equity, so economic leverage is 1 to 1.
* Borrow $100 and buy $200 of crude oil. Assets are $200, liabilities are $100 so accounting leverage is 2 to 1. The notional amount is $200 and equity is $100, so notional leverage is 2 to 1. The volatility of the position is twice the volatility of an unlevered position in the same assets, so economic leverage is 2 to 1.
* Buy $100 of crude oil, borrow $100 worth of gasoline, and sell the gasoline for $100. The seller now has $100 cash and $100 of crude oil, and owes $100 worth of gasoline. Your assets are $200, and liabilities are $100, so accounting leverage is 2 to 1. You have $200 in notional assets plus $100 in notional liabilities, with $100 of equity, so your notional leverage is 3 to 1. The volatility of your position might be half the volatility of an unlevered investment in the same assets, since the price of oil and the price of gasoline are positively correlated, so your economic leverage might be 0.5 to 1.
* Buy $100 of a 10-year fixed-rate treasury bond, and enter into a fixed-for-floating 10-year interest rate swap to convert the payments to floating rate. The derivative is off-balance sheet, so it is ignored for accounting leverage. Accounting leverage is therefore 1 to 1. The notional amount of the swap does count for notional leverage, so notional leverage is 2 to 1. The swap removes most of the economic risk of the treasury bond, so economic leverage is near zero.

### Abbreviations

* EBIT means Earnings before interest and taxes.
* DOL is Degree of Operating Leverage
* DFL is Degree of Financial Leverage
* DCL is Degree of Combined Leverage
* ROE is Return on equity
* ROA is Return on assets

### Corporate finance

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{\displaystyle \mathrm{DOL} = \frac{\mathrm{EBIT\;+\;Fixed\;Costs}}{\mathrm{EBIT}}}

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{\displaystyle \mathrm{DFL} = \frac{\mathrm{EBIT}}{\mathrm{EBIT} -
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{\displaystyle \mathrm{DCL} = \text{DOL} \times \text{DFL} = \frac{\mathrm{EBIT} + \text{Fixed Costs}}{\mathrm{EBIT} - \text{Total Interest Expense}}}

Accounting leverage has the same definition as in investments. There are several ways to define operating leverage, the most common. is:

Operating leverage

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Operating Income

{\displaystyle
\begin{align}
\text{Operating leverage} & = \frac{\text{Revenue} - \text{Variable Cost}}{\text{Revenue} - \text{Variable Cost} - \text{Fixed Cost}} \\[8pt]
& = \frac{\text{Revenue} - \text{Variable Cost}}{\text{Operating Income}}
\end{align}
}

Financial leverage is usually defined as:

# Financial leverage

Total Debt
Shareholders' Equity

{\displaystyle \text{Financial leverage}= \frac{\text{Total Debt}}{\text{Shareholders' Equity}}}

For outsiders, it is hard to calculate operating leverage as fixed and variable costs are usually not disclosed. In an attempt to estimate operating leverage, one can use the percentage change in operating income for a one-percent change in revenue.
The product of the two is called Total leverage, and estimates the percentage change in net income for a one-percent change in revenue.

There are several variants of each of these definitions, and the financial statements are usually adjusted before the values are computed. Moreover, there are industry-specific conventions that differ somewhat from the treatment above.

## Bank regulation

Before the 1980s, quantitative limits on bank leverage were rare. Banks in most countries had a reserve requirement, a fraction of deposits that was required to be held in liquid form, generally precious metals or government notes or deposits. This does not limit leverage. A capital requirement is a fraction of assets that is required to be funded in the form of equity or equity-like securities. Although these two are often confused, they are in fact opposite. A reserve requirement is a fraction of certain liabilities (from the right hand side of the balance sheet) that must be held as a certain kind of asset (from the left hand side of the balance sheet). A capital requirement is a fraction of assets (from the left hand side of the balance sheet) that must be held as a certain kind of liability or equity (from the right hand side of the balance sheet). Before the 1980s, regulators typically imposed judgmental capital requirements, a bank was supposed to be "adequately capitalized," but these were not objective rules.

National regulators began imposing formal capital requirements in the 1980s, and by 1988 most large multinational banks were held to the Basel I standard. Basel I categorized assets into five risk buckets, and mandated minimum capital requirements for each. This limits accounting leverage. If a bank is required to hold 8% capital against an asset, that is the same as an accounting leverage limit of 1/.08 or 12.5 to 1.

While Basel I is generally credited with improving bank risk management it suffered from two main defects. It did not require capital for all off-balance sheet risks (there was a clumsy provisions for derivatives, but not for certain other off-balance sheet exposures) and it encouraged banks to pick the riskiest assets in each bucket (for example, the capital requirement was the same for all corporate loans, whether to solid companies or ones near bankruptcy, and the requirement for government loans was zero).

Work on Basel II began in the early 1990s and it was implemented in stages beginning in 2005. Basel II attempted to limit economic leverage rather than accounting leverage. It required advanced banks to estimate the risk of their positions and allocate capital accordingly. While this is much more rational in theory, it is more subject to estimation error, both honest and opportunitistic. The poor performance of many banks during the financial crisis of 2007–2009 led to calls to reimpose leverage limits, by which most people meant accounting leverage limits, if they understood the distinction at all. However, in view of the problems with Basel I, it seems likely that some hybrid of accounting and notional leverage will be used, and the leverage limits will be imposed in addition to, not instead of, Basel II economic leverage limits.

## Financial crisis of 2007–2008

The financial crisis of 2007–2008, like many previous financial crises, was blamed in part on "excessive leverage".

* Consumers in the United States and many other developed countries had high levels of debt relative to their wages, and relative to the value of collateral assets. When home prices fell, and debt interest rates reset higher, and business laid off employees, borrowers could no longer afford debt payments, and lenders could not recover their principal by selling collateral.
* Financial institutions were highly levered. Lehman Brothers, for example, in its last annual financial statements, showed accounting leverage of 31.4 times ($691 billion in assets divided by $22 billion in stockholders’ equity). Bankruptcy examiner Anton R. Valukas determined that the true accounting leverage was higher: it had been understated due to dubious accounting treatments including the so-called repo 105 (allowed by Ernst & Young).
* Banks' notional leverage was more than twice as high, due to off-balance sheet transactions. At the end of 2007, Lehman had $738 billion of notional derivatives in addition to the assets above, plus significant off-balance sheet exposures to special purpose entities, structured investment vehicles and conduits, plus various lending commitments, contractual payments and contingent obligations.
* On the other hand, almost half of Lehman’s balance sheet consisted of closely offsetting positions and very-low-risk assets, such as regulatory deposits. The company emphasized "net leverage", which excluded these assets. On that basis, Lehman held $373 billion of "net assets" and a "net leverage ratio" of 16.1. This is not a standardized computation, but it probably corresponds more closely to what most people think of when they hear of a leverage ratio.

## Use of language

Levering has come to be known as "leveraging", in financial communities; this may have originally been a slang adaptation, since leverage was a noun. However, modern dictionaries (such as *Random House Dictionary* and *Merriam-Webster's Dictionary of Law*) refer to its use as a verb, as well. It was first adopted for use as a verb in American English in 1957.