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# Financial leverage

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### Financial leverage

In finance, leverage (sometimes referred to as gearing in the United Kingdom and Australia) is a general term for any technique to multiply gains and losses.[1] Leverage exists when an investor achieves the right to a return on a capital base that exceeds the investment which the investor has personally contributed to the entity or instrument achieving a return.[2] Common ways to attain leverage are borrowing money, buying fixed assets and using derivatives.[3] Important examples are:

• A public corporation may leverage its equity by borrowing money. The more it borrows, the less equity capital it needs, so any profits or losses are shared among a smaller base and are proportionately larger as a result.[4]
• A business entity can leverage its revenue by buying fixed assets. This will increase the proportion of fixed, as opposed to variable, costs, meaning that a change in revenue will result in a larger change in operating income.[5][6]
• Hedge funds often leverage their assets by using derivatives. A fund might get any gains or losses on $20 million worth of crude oil by posting$1 million of cash as margin.[7]

## Measuring leverage

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.[8]

### Investments

Accounting leverage is total assets divided by the total assets minus total liabilities.[9] Notional leverage is total notional amount of assets plus total notional amount of liabilities divided by equity.[1] 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:[10] • 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. You now have $100 cash,$100 of crude oil, and owe $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.

### Model risk

Main article: Model risk

Another risk of leverage is model risk. Many investors run high levels of notional leverage but low levels of economic leverage (in fact, these are the type of strategies hedge funds are named for, although not all hedge funds pursue them). Economic leverage depends on model assumptions.[7] For example, a fund with $100 might feel comfortable holding$1,000 long positions in crude oil futures and $1,000 of short positions in gasoline futures. The notional leverage is 20 to 1 (accounting leverage is zero) but the fund might estimate economic leverage is only 1 to 1, that is the fund may assume a 10% fall in the price of oil will cause a 9% fall in the price of gasoline, so the fund will lose only 10% net ($100 loss on the oil long and $90 profit on the gasoline short). If that assumption is incorrect, the fund may have much more economic leverage than it thinks. For example, if refinery capacity is shut down by a hurricane, the price of oil may fall (less demand from refineries) while the price of gasoline might rise (less supply from refineries). A 5% fall in the price of oil and a 5% rise in the price of gasoline could wipe out the fund.[10] ### Counterparty risk Leverage may involve a counterparty, either a creditor or a derivative counterparty. It doesn't always do that, for example a company levering by acquiring a fixed asset has no further reliance on a counterparty.[3] In the case of a creditor, most of the risk is usually on the creditor's side, but there can be risks to the borrower, such as demand repayment clauses or rights to seize collateral.[10] If a derivative counterparty fails, unrealized gains on the contract may be jeopardized. These risks can be mitigated by negotiating terms, including mark-to-market collateral.[7] ## Worked example [20] Calculate equity return given: 5% Projected Return on Investment 4% Cost of Debt 8:1 Leverage Debt:Equity = Investment in Asset of 9 LONG-FORM MATH Profit from investment = Size of asset * Return on investment = 9 * 5% = 0.45 less Interest on debt = Size of debt * Cost of debt = 8 * 4% = 0.32 Equals equity's profit = 0.45 - 0.32 = 0.13 Return on Equity = Profit divided by Equity portion = (0.13 / 1) = 13% SHORT-FORM GENERIC CALCULATION Interest rate differential = Return on investment less Cost of debt = 5% - 4% = 1% Debt to equity multiple = 8 divided by 1 = 8 Multiply first two lines = 1% * 8 = 8% Add return on investment = 5% Equals return on equity = 8% + 5% = 13% ## Leverage and 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 not objective rules.[21] 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.[22] 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).[21] 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.[22] 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.[23] ## Leverage and the financial crisis of 2007–2009 The financial crisis of 2007–2009, like many previous financial crises, was blamed in part on "excessive leverage." However, the word is used in several different senses. • Consumers in the United States and many other developed countries borrowed large amounts of money,$2.6 trillion in the United States alone.[24] For most of this, "leverage" is a euphemism, as the borrowing was used to support consumption rather than to lever anything.[25] Only people who borrowed for investment, such as speculative house purchases or buying stocks, were using leverage in the financial sense.
• Financial institutions were highly levered. Lehman Brothers, for example, in its last annual financial statements, showed accounting leverage of 30.7 times ($691 billion in assets divided by$22 billion in stockholders’ equity).[26] 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).[27] Accounting leverage is the ratio usually cited by the press.
• Notional leverage 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.[26] • 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.[26] This is not a standardized computation, but it probably corresponds more closely to what most people think of when they hear 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[28]) refer to its use as a verb, as well.[29] It was first adopted for use as a verb in American English in 1957.[30]

## References

Template:Financial ratios
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