A public corporation may leverage its equity by borrowing money, The more it borrows, less equity capital it needs, so any profits - losses are shared among smaller base & are proportionately larger as result,

A business entity can leverage its revenue by buying fixed assets, This will increase proportion of fixed, as opposed to variable, costs, meaning that change în revenue will result în larger change în operating income,

Hedge funds often leverage their assets by using derivatives, A fund might get any gains - losses on $20 million worth of crude oil by posting $1 million of cash as margin,

__Measuring leverage__A good deal of confusion arises în discussions among people who use different definitions of leverage, The term îs used differently în investments & corporate finance, & has multiple definitions în each field,

__Investments__Accounting leverage îs total assets divided by total assets minus total liabilities, Notional leverage îs total notional amount of assets plus total notional amount of liabilities divided by equity, Economic leverage îs volatility of equity divided by volatility of unlevered investment în same assets, To understand differences, consider following positions, all funded with $100 of cash equity,

(1) Buy $100 of crude oil, Assets are $100 ($100 of oil), there are no liabilities, Accounting leverage îs 1 to 1, Notional amount îs $100 ($100 of oil), there are no liabilities & there îs $100 of equity, Notional leverage îs 1 to 1, The volatility of equity îs equal to volatility of oil, since oil îs only asset & you own same amount as your equity, so economic leverage îs 1 to 1,

(2) Borrow $100 & buy $200 of crude oil, Assets are $200, liabilities are $100 so accounting leverage îs 2 to 1, Notional amount îs $200, equity îs $100 so notional leverage îs 2 to 1, The volatility of position îs twice volatility of unlevered position în same assets, so economic leverage îs 2 to 1,

(3) Buy $100 of crude oil, borrow $100 worth of gasoline & sell gasoline for $100, You now have $100 cash, $100 of crude oil & owe $100 worth of gasoline, Your assets are $200, liabilities are $100 so accounting leverage îs 2 to 1, You have $200 notional amount of assets plus $100 notional amount of liabilities, with $100 of equity, so your notional leverage îs 3 to 1, The volatility of your position might be half volatility of unlevered investment în same assets, since price of oil & price of gasoline are positively correlated, so your economic leverage might be 0,5 to 1,

(4) Buy $100 of 10-year fixed-rate treasury bond, & enter into fixed-for-floating 10-year interest rate swap to convert payments to floating rate, The derivative îs off-balance sheet, so it îs ignored for accounting leverage, Accounting leverage îs therefore 1 to 1, The notional amount of swap does count for notional leverage, so notional leverage îs 2 to 1, The swap removes most of economic risk of treasury bond, so economic leverage îs near zero,

__Corporate finance__Degree of Operating Leverage (DOL)= (EBIT + Fixed costs) / EBIT; Degree of Financial Leverage (DFL)= EBIT / ( EBIT - Total Interest expense ); Degree of Combined Leverage (DCL)= DOL * DFL

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

__Financial leverage îs usually defined as:__Operating leverage îs attempt to estimate percentage change în operating income (earnings before interest & taxes - EBIT) for one percent change în revenue,

Financial leverage tries to estimate percentage change în net income for one percent change în operating income,

The product of two îs called Total leverage, & estimates percentage change în net income for one percent change în revenue,

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

__Leverage & ROE__If we have to check real effect of leverage on ROE, we have to study financial leverage, Financial leverage refers to use of debt to acquire additional assets, Financial leverage may decrease - increase return on equity în different conditions, Financial over-leveraging means incurring huge debt by borrowing funds at lower rate of interest & using excess funds în high risk investments în order to maximize returns,

__Leverage & risk__The most obvious risk of leverage îs that it multiplies losses, A corporation that borrows too much money might face bankruptcy during business downturn, while less-levered corporation might survive, An investor who buys stock on 50% margin will lose 40% of his money if stock declines 20%,

There îs important implicit assumption în that account, however, which îs that underlying levered asset îs same as unlevered one, If company borrows money to modernize, - add to its product line, - expand internationally, additional diversification might more than offset additional risk from leverage, Or if investor uses fraction of his - her portfolio to margin stock index futures & puts rest în money market fund, he - she might have same volatility & expected return as investor în unlevered equity index fund, with limited downside, So while adding leverage to given asset always adds risk, it îs not case that levered company - investment îs always riskier than unlevered one, In fact, many highly-levered hedge funds have less return volatility than unlevered bond funds, & public utilities with lots of debt are usually less risky stocks than unlevered technology companies,

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