Leverage (finance)

In finance, leverage (sometimes referred to as gearing in the United Kingdom and Australia) is any technique involving the use of borrowed funds in the purchase of an asset, with the expectation that the after tax income from the asset and asset price appreciation will exceed the borrowing cost. Normally, the finance provider would 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 some shares.

Leveraging enables gains and losses to be multiplied.[1] On the other hand, there is a risk that leveraging will result in a loss — ie., it actually turns out that financing costs exceed the income from the asset, or because the value of the asset has fallen.


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


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% of the money invested if the stock declines 20%.[6]

Risk may be attributed to a loss in value of collateral assets. Brokers may require the addition of funds when the value of securities hold declines. Banks may fail 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.

This may happen exactly when there is little market liquidity and sales by others are depressing prices. It means that as things get bad, leverage goes up, multiplying losses as things continue to go down. This can lead to rapid ruin, even if the underlying asset value decline is mild or temporary.[6] The risk can be mitigated by negotiating the terms of leverage, by maintaining unused room for additional borrowing, and by leveraging only liquid assets.[7]

On the other hand, the extreme level of leverage afforded in forex trading presents relatively low risk per unit due to its relative stability when compared with other markets. 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 can control $100,000 while taking responsibility for any losses or gains their investments incur. This intense level of leverage presents equal parts risk and reward.

There is an implicit assumption in that account, however, which is that the underlying levered asset is the same as the unlevered one. If a company borrows money to modernize, or add to its product line, or expand internationally, the additional diversification might more than offset the additional risk from leverage.[6] Or if an investor uses a fraction of his or her portfolio to margin stock index futures and puts the rest in a money market fund, he or she might have the same volatility and expected return as an investor in an unlevered equity index fund, with a limited downside.[7] 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,[7] and public utilities with lots of debt are usually less risky stocks than unlevered technology companies.[6]

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.[8] 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

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.

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% x 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%


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.[9]


Accounting leverage is total assets divided by the total assets minus total liabilities.[10] 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:[6]


Corporate finance

Accounting leverage has the same definition as in investments.[11] There are several ways to define operating leverage, the most common.[12] is:

Financial leverage is usually defined[10][13] as:

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.[14] The product of the two is called Total leverage,[15] and estimates the percentage change in net income for a one-percent change in revenue.[16]

There are several variants of each of these definitions,[17] and the financial statements are usually adjusted before the values are computed.[10] Moreover, there are industry-specific conventions that differ somewhat from the treatment above.[18]

Bank regulation

After 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.[19]

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.[20]

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).[19]

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.[20] 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.[21]

Financial crisis of 2007–2009

The financial crisis of 2007–2009, like many previous financial crises, was blamed in part on "excessive leverage".

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[24]) refer to its use as a verb, as well.[25] It was first adopted for use as a verb in American English in 1957.[26]

See also


  1. 1 2 Brigham, Eugene F., Fundamentals of Financial Management (1995).
  2. Mock, E. J., R. E. Schultz, R. G. Schultz, and D. H. Shuckett, Basic Financial Management (1968).
  3. Grunewald, Adolph E. and Erwin E. Nemmers, Basic Managerial Finance (1970).
  4. Ghosh, Dilip K. and Robert G. Sherman (June 1993). "Leverage, Resource Allocation and Growth". Journal of Business Finance & Accounting. pp. 575–582.
  5. Lang, Larry, Eli Ofek, and Rene M. Stulz (January 1996). "Leverage, Investment, and Firm Growth". Journal of Financial Economics. pp. 3–29.
  6. 1 2 3 4 5 Bodie, Zvi, Alex Kane and Alan J. Marcus, Investments, McGraw-Hill/Irwin (June 18, 2008)
  7. 1 2 3 Chew, Lillian (July 1996). Managing Derivative Risks: The Use and Abuse of Leverage. John Wiley & Sons.
  8. Math for calculating leverage effects
  9. Van Horne (1971). Financial Management and Policy.
  10. 1 2 3 Weston, J. Fred and Eugene F. Brigham, Managerial Finance (1969).
  11. Weston, J. Fred and Eugene F. Brigham, Managerial Finance (2010).
  12. Brigham, Eugene F., Fundamentals of Financial Management (1995)
  13. "Financial Leverage". Retrieved 16 December 2012.
  14. Damodaran (2011), Applied Corporate Finance, 3rd ed., pp. 132-133>
  15. Li, Rong-Jen and Glenn V. Henderson, Jr., "Combined Leverage and Stock Risk," Quarterly Journal of Business & Finance (Winter 1991), p. 18-39.
  16. Huffman, Stephen P., "The Impact of Degrees of Operating and Financial Leverage on the Systematic Risk of Common Stock: Another Look," Quarterly Journal of Business & Economics (Winter 1989), p. 83-100.
  17. Dugan, Michael T., Donald Minyard, and Keith A. Shriver, "A Re-examination of the Operating Leverage-Financial Leverage Tradeoff," Quarterly Review of Economics & Finance (Fall 1994), p. 327-334.
  18. Darrat, Ali F.d and Tarun K. Mukherjee, "Inter-Industry Differences and the Impact of Operating and Financial Leverages on Equity Risk," Review of Financial Economics (Spring 1995), p. 141–155.
  19. 1 2 Ong, Michael K., The Basel Handbook: A Guide for Financial Practitioners, Risk Books (December 2003)
  20. 1 2 Saita, Francesco, Value at Risk and Bank Capital Management: Risk Adjusted Performances, Capital Management and Capital Allocation Decision Making, Academic Press (February 3, 2007)
  21. Tarullo, Daniel K., Banking on Basel: The Future of International Financial Regulation, Peterson Institute for International Economics (September 30, 2008)
  22. 1 2 3 Lehman Brothers Holdings Inc Annual Report for year ended November 30, 2007 http://www.sec.gov/Archives/edgar/data/806085/000110465908005476/a08-3530_110k.htm#Item6_SelectedFinancialData_003911.
  23. Report of Anton R. Valukas, Examiner, to the United States Bankruptcy Court, Southern District of New York, Chapter 11 Case No. 08-13555 (JMP).
  24. Merrian-Webster's Dictionary of Law. Merriam-Webster. June 2011. ISBN 978-0877797197.
  25. "leverage." Merriam-Webster's Dictionary of Law. Merriam-Webster, Inc. 7 June 2011. Dictionary.com
  26. "leverage." Online Etymology Dictionary. Douglas Harper, Historian. 7 June 2011. Dictionary.com

Further reading

  1. Bartram, Söhnke M.; Brown, Gregory W.; Waller, William (August 2013). "How Important is Financial Risk?". Journal of Financial and Quantitative Analysis. forthcoming. 
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