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Leverage (finance)

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167:, 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 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. 230:
more than offset the additional risk from leverage. Or if an investor uses a fraction of his or her portfolio to margin stock index futures (high risk) and puts the rest in a low-risk money-market fund, he or she 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.
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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.
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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.
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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
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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
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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
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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
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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
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There is an implicit assumption in that account, however, which is that the underlying leveraged asset is the same as the unleveraged 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
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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
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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
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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
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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 heavily indebted low-risk
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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.
547: 748:{\displaystyle {\begin{aligned}{\text{Operating leverage}}&={\frac {{\text{Revenue}}-{\text{Variable Cost}}}{{\text{Revenue}}-{\text{Variable Cost}}-{\text{Fixed Cost}}}}={\frac {{\text{Revenue}}-{\text{Variable Cost}}}{\text{Operating Income}}}\end{aligned}}} 477: 555: 794: 57:
in physics, which amplifies a small input force into a greater output force, because successful leverage amplifies the smaller amounts of money needed for borrowing into large amounts of profit. However, the technique also involves the high
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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.
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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.
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of not being able to pay back a large loan. Normally, a lender 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
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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).
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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), pp. 83–100.
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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), pp. 327–334.
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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
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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), pp. 141–155.
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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
171:, 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 187:
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,
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Saita, Francesco, Value at Risk and Bank Capital Management: Risk Adjusted Performances, Capital Management and Capital Allocation Decision Making, Academic Press (February 3, 2007)
638:{\displaystyle {\text{Degree of Combined Leverage}}={\text{DOL}}\times {\text{DFL}}={\frac {\mathrm {EBIT} +{\text{Fixed Costs}}}{\mathrm {EBIT} -{\text{Total Interest Expense}}}}} 803:
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.
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Li, Rong-Jen and Glenn V. Henderson, Jr., "Combined Leverage and Stock Risk," Quarterly Journal of Business & Finance (Winter 1991), pp. 18–39.
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are effectively leveraged bets between parties where the principal is implicitly borrowed and lent at interest rates of very short treasury bills.
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will lose 40% if the stock declines 20%.; also in this case the involved subject might be unable to refund the incurred significant total loss.
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Report of Anton R. Valukas, Examiner, to the United States Bankruptcy Court, Southern District of New York, Chapter 11 Case No. 08-13555 (JMP).
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of equity divided by volatility of an unlevered investment in the same assets. For example, assume a party buys $ 100 of a 10-year fixed-rate
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determined that the true accounting leverage was higher: it had been understated due to dubious accounting treatments including the so-called
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rational in theory, it is more subject to estimation error, both honest and opportunitistic. The poor performance of many banks during the
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National regulators began imposing formal capital requirements in the 1980s, and by 1988 most large multinational banks were held to the
542:{\displaystyle {\text{Degree of Financial Leverage}}={\frac {\mathrm {EBIT} }{\mathrm {EBIT} -{\text{Total Interest Expense}}}}} 214:
or default during a business downturn, while a less-leveraged corporation might survive. An investor who buys a stock on 50%
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excluded these assets. On that basis, Lehman held $ 373 billion of "net assets" and a "net leverage ratio" of 16.1.
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leverage is total notional amount of assets plus total notional amount of liabilities divided by equity.
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may leverage their assets by financing a portion of their portfolios with the cash proceeds from the
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Ong, Michael K., The Basel Handbook: A Guide for Financial Practitioners, Risk Books (December 2003)
789:{\displaystyle {\text{Financial leverage}}={\frac {\text{Total Debt}}{\text{Shareholders' Equity}}}} 201: 1792: 1769: 1707: 1533: 1458: 1418: 1398: 151: 1503: 1493: 1463: 1433: 1373: 875:
Mock, E. J., R. E. Schultz, R. G. Schultz, and D. H. Shuckett, Basic Financial Management (1968).
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Before the 1980s, quantitative limits on bank leverage were rare. Banks in most countries had a
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Lang, Larry; Eli Ofek; Rene M. Stulz (January 1996). "Leverage, Investment, and Firm Growth".
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Ghosh, Dilip K.; Robert G. Sherman (June 1993). "Leverage, Resource Allocation and Growth".
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Bodie, Zvi, Alex Kane and Alan J. Marcus, Investments, McGraw-Hill/Irwin (June 18, 2008)
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Tarullo, Daniel K., Banking on Basel: The Future of International Financial Regulation,
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are expected to maintain a leverage ratio in excess of 3%. The ratio is defined as
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Lehman Brothers Holdings Inc Annual Report for year ended November 30, 2007
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Grunewald, Adolph E. and Erwin E. Nemmers, Basic Managerial Finance (1970).
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imposed in addition to, not instead of, Basel II economic leverage limits.
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There are several ways to define operating leverage, the most common. is:
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Bartram, Söhnke M.; Brown, Gregory W.; Waller, William (August 2015).
319:{\displaystyle {\frac {\mbox{Tier 1 Capital}}{\mbox{Total exposure}}}} 1498: 1361: 1098:
Damodaran (2011), Applied Corporate Finance, 3rd ed., pp. 132–133>
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Weston, J. Fred and Eugene F. Brigham, Managerial Finance (1969).
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inputs when revenues are expected to be variable. An increase in
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Brigham, Eugene F., Fundamentals of Financial Management (1995)
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maintain the ongoing borrowing costs, loans may be called-in.
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Leverage can arise in a number of situations. Securities like
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to convert the payments to floating rate. The derivative is
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Accounting leverage is total assets divided by the total
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Managing Derivative Risks: The Use and Abuse of Leverage
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are usually less risky stocks than unlevered high-risk
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The use of borrowed funds in the purchase of an asset
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Englewood Cliffs, N.J., Prentice-Hall. 1025: 250:The term leverage is used differently in 336:items and derivative "add-ons", whereas 206:Financial risk management § Banking 121:Financial risk management § Banking 14: 1816: 261: 1185: 864:Fundamentals of Financial Management 381: 357: 346: 202:Derivative (finance) § Leverage 99:will result in a larger increase in 53:Financial leverage is named after a 24: 1149:"How Important is Financial Risk?" 1140: 620: 617: 614: 611: 596: 593: 590: 587: 524: 521: 518: 515: 509: 506: 503: 500: 463: 460: 457: 454: 449: 446: 443: 440: 437: 433: 430: 427: 424: 421: 413: 410: 407: 404: 25: 1840: 1797: 1787: 1128: 1119: 1110: 1101: 1092: 1071: 1062: 1030:Financial Management and Policy 972: 342:Basel III § Leverage ratio 1584:Debtor-in-possession financing 943: 913:Journal of Financial Economics 904: 887: 878: 245: 189:structured investment vehicles 13: 1: 847: 165:financial crisis of 2007–2008 159:Financial crisis of 2007–2008 152:financial crisis of 2007–2009 1524:Staggered board of directors 491:Degree of Financial Leverage 395:Degree of Operating Leverage 7: 1641:Accretion/dilution analysis 1011:Chew, Lillian (July 1996). 810: 561:Degree of Combined Leverage 42:is any technique involving 10: 1845: 1604:Leveraged recapitalization 277: 199: 118: 114: 1829:Financial risk management 1783: 1775:Valuation using multiples 1760:Sum-of-the-parts analysis 1730:Modigliani–Miller theorem 1631: 1589:Dividend recapitalization 1569: 1417: 1404:Secondary market offering 1307: 1296: 1223: 1166:10.1017/S0022109015000216 111:sale of other positions. 1793:List of investment banks 1708:Free cash flow to equity 1534:Super-majority amendment 1459:Management due diligence 1399:Seasoned equity offering 1015:. John Wiley & Sons. 1504:Shareholder rights plan 1494:Post-merger integration 1464:Managerial entrenchment 1434:Contingent value rights 1374:Initial public offering 195: 1646:Adjusted present value 1509:Special-purpose entity 1347:Direct public offering 1317:At-the-market offering 790: 749: 639: 629:Total Interest Expense 543: 533:Total Interest Expense 473: 320: 1661:Conglomerate discount 791: 750: 640: 544: 474: 362:Economic leverage is 321: 200:Further information: 1683:Economic value added 1678:Discounted cash flow 1079:"Financial Leverage" 953:(September 30, 2008) 862:Brigham, Eugene F., 842:Repurchase agreement 782:Shareholders' Equity 765: 655: 556: 486: 390: 299: 1268:Senior secured debt 900:. pp. 575–582. 262:Accounting leverage 131:capital requirement 127:reserve requirement 65:collateral security 1803:Outline of finance 1715:Market value added 1698:Financial modeling 1656:Business valuation 1579:Debt restructuring 1357:Follow-on offering 1342:Corporate spin-off 1300:(terms/conditions) 1217:investment banking 1026:Van Horne (1971). 837:Operating leverage 786: 770:Financial leverage 745: 743: 664:Operating leverage 635: 539: 469: 372:interest rate swap 316: 313: 308: 1811: 1810: 1735:Net present value 1720:Minority interest 1651:Associate company 1627: 1626: 1594:Financial sponsor 1514:Special situation 1484:Pre-emption right 1474:Minority discount 1384:Private placement 1283:Subordinated debt 1238:Exchangeable debt 1225:Capital structure 1213:Corporate finance 822:Homemade leverage 784: 783: 780: 771: 739: 738: 733: 725: 714: 711: 703: 695: 688: 680: 665: 633: 630: 606: 578: 570: 562: 537: 534: 492: 467: 396: 382:Corporate finance 376:off-balance sheet 358:Economic leverage 347:Notional leverage 334:off-balance sheet 314: 312: 307: 256:corporate finance 185:off-balance sheet 181:Ernst & Young 18:Equity multiplier 16:(Redirected from 1836: 1801: 1800: 1791: 1790: 1693:Fairness opinion 1688:Enterprise value 1671:Weighted average 1599:Leveraged buyout 1454:Drag-along right 1352:Equity carve-out 1309:Equity offerings 1305: 1304: 1301: 1273:Shareholder loan 1258:Second lien debt 1253:Preferred equity 1233:Convertible debt 1206: 1199: 1192: 1183: 1182: 1178: 1168: 1135: 1132: 1126: 1123: 1117: 1114: 1108: 1105: 1099: 1096: 1090: 1089: 1087: 1085: 1075: 1069: 1066: 1060: 1057: 1046: 1045: 1033: 1023: 1017: 1016: 1008: 997: 994: 979: 976: 970: 965: 954: 947: 941: 938: 929: 926: 917: 916: 915:. pp. 3–29. 908: 902: 901: 891: 885: 882: 876: 873: 867: 860: 832:Margin (finance) 827:Leveraged buyout 801:operating income 795: 793: 792: 787: 785: 781: 778: 777: 772: 769: 754: 752: 751: 746: 744: 740: 737:Operating Income 736: 735: 734: 731: 726: 723: 720: 715: 713: 712: 709: 704: 701: 696: 693: 690: 689: 686: 681: 678: 675: 666: 663: 644: 642: 641: 636: 634: 632: 631: 628: 623: 608: 607: 604: 599: 584: 579: 576: 571: 568: 563: 560: 548: 546: 545: 540: 538: 536: 535: 532: 527: 512: 498: 493: 490: 478: 476: 475: 470: 468: 466: 452: 402: 397: 394: 325: 323: 322: 317: 315: 310: 305: 303: 236:public utilities 173:Anton R. Valukas 101:operating profit 21: 1844: 1843: 1839: 1838: 1837: 1835: 1834: 1833: 1814: 1813: 1812: 1807: 1779: 1755:Stock valuation 1750:Residual income 1666:Cost of capital 1623: 1619:Project finance 1609:High-yield debt 1565: 1544:Tag-along right 1469:Mandatory offer 1439:Control premium 1420: 1413: 1389:Public offering 1337:Bought out deal 1299: 1298: 1292: 1219: 1210: 1143: 1141:Further reading 1138: 1133: 1129: 1124: 1120: 1115: 1111: 1106: 1102: 1097: 1093: 1083: 1081: 1077: 1076: 1072: 1067: 1063: 1058: 1049: 1042: 1024: 1020: 1009: 1000: 995: 982: 977: 973: 966: 957: 948: 944: 939: 932: 927: 920: 909: 905: 892: 888: 883: 879: 874: 870: 861: 854: 850: 817:Coupon leverage 813: 776: 768: 766: 763: 762: 742: 741: 730: 722: 721: 719: 708: 700: 692: 691: 685: 677: 676: 674: 667: 662: 658: 656: 653: 652: 627: 610: 609: 603: 586: 585: 583: 575: 567: 559: 557: 554: 553: 531: 514: 513: 499: 497: 489: 487: 484: 483: 453: 403: 401: 393: 391: 388: 387: 384: 360: 349: 302: 300: 297: 296: 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1306: 1303: 1295: 1289: 1286: 1284: 1281: 1279: 1276: 1274: 1271: 1269: 1266: 1264: 1261: 1259: 1256: 1254: 1251: 1249: 1246: 1244: 1241: 1239: 1236: 1234: 1231: 1230: 1228: 1226: 1222: 1218: 1214: 1207: 1202: 1200: 1195: 1193: 1188: 1187: 1184: 1176: 1172: 1167: 1162: 1158: 1154: 1150: 1145: 1144: 1131: 1122: 1113: 1104: 1095: 1080: 1074: 1065: 1056: 1054: 1052: 1043: 1041:9780133153095 1037: 1032: 1031: 1022: 1014: 1007: 1005: 1003: 993: 991: 989: 987: 985: 975: 969: 964: 962: 960: 952: 946: 937: 935: 925: 923: 914: 907: 899: 898: 890: 881: 872: 865: 859: 857: 852: 843: 840: 838: 835: 833: 830: 828: 825: 823: 820: 818: 815: 814: 808: 804: 802: 773: 761: 760: 759: 732:Variable Cost 727: 716: 705: 702:Variable Cost 697: 687:Variable Cost 682: 671: 669: 651: 650: 649: 624: 600: 580: 572: 564: 552: 551: 528: 494: 482: 481: 417: 398: 386: 385: 379: 377: 373: 369: 368:treasury bond 365: 355: 353: 344: 343: 339: 335: 295: 294: 293: 292: 291: 289: 285: 275: 273: 269: 259: 257: 253: 243: 241: 237: 231: 227: 223: 219: 217: 213: 207: 203: 193: 190: 186: 182: 178: 174: 170: 166: 156: 153: 147: 143: 140: 135: 132: 128: 122: 112: 110: 106: 102: 98: 94: 89: 85: 81: 76: 72: 70: 66: 61: 56: 51: 49: 45: 41: 37: 33: 19: 1745:Real options 1570: 1561:Tender offer 1421:acquisitions 1409:Underwriting 1394:Rights issue 1297:Transactions 1156: 1152: 1130: 1121: 1112: 1103: 1094: 1082:. Retrieved 1073: 1064: 1029: 1021: 1012: 974: 945: 912: 906: 895: 889: 880: 871: 863: 805: 798: 757: 647: 361: 350: 331: 281: 270:minus total 265: 249: 232: 228: 224: 220: 209: 179:(allowed by 162: 148: 144: 136: 124: 77: 73: 52: 39: 35: 29: 1519:Squeeze-out 1489:Proxy fight 1419:Mergers and 1332:Bought deal 1263:Senior debt 1084:16 December 605:Fixed Costs 272:liabilities 252:investments 246:Definitions 242:companies. 105:Hedge funds 1818:Categories 1765:Tax shield 1725:Mismarking 1529:Stock swap 1479:Pitch book 1449:Divestment 1327:Bookrunner 1248:Pari passu 848:References 779:Total Debt 710:Fixed Cost 364:volatility 240:technology 212:bankruptcy 119:See also: 93:fixed cost 48:investment 46:to buy an 1740:Pure play 1633:Valuation 1499:Sell side 1362:Greenshoe 728:− 706:− 698:− 683:− 625:− 573:× 529:− 284:Basel III 36:leverage, 1571:Leverage 1549:Takeover 1444:Demerger 1429:Buy side 811:See also 352:Notional 177:repo 105 67:for the 40:gearing, 1554:Reverse 1539:Synergy 1379:Pre-IPO 1367:Reverse 1288:Warrant 1175:2307939 866:(1995). 724:Revenue 694:Revenue 679:Revenue 278:Banking 139:Basel I 115:History 97:revenue 84:futures 80:options 32:finance 1173:  1038:  282:Under 268:assets 216:margin 204:, and 91:using 88:Equity 1278:Stock 288:banks 109:short 55:lever 1824:Debt 1215:and 1171:SSRN 1086:2012 1036:ISBN 254:and 196:Risk 163:The 82:and 69:loan 60:risk 1161:doi 577:DFL 569:DOL 274:. 50:. 30:In 1820:: 1169:. 1157:50 1155:. 1151:. 1050:^ 1001:^ 983:^ 958:^ 933:^ 921:^ 855:^ 286:, 103:. 71:. 34:, 1205:e 1198:t 1191:v 1177:. 1163:: 1088:. 1044:. 774:= 717:= 672:= 621:T 618:I 615:B 612:E 601:+ 597:T 594:I 591:B 588:E 581:= 565:= 525:T 522:I 519:B 516:E 510:T 507:I 504:B 501:E 495:= 464:T 461:I 458:B 455:E 450:s 447:t 444:s 441:o 438:C 434:d 431:e 428:x 425:i 422:F 418:+ 414:T 411:I 408:B 405:E 399:= 326:. 20:)

Index

Equity multiplier
finance
borrowing funds
investment
lever
risk
collateral security
loan
options
futures
Equity
fixed cost
revenue
operating profit
Hedge funds
short
Financial risk management § Banking
reserve requirement
capital requirement
Basel I
financial crisis of 2007–2009
financial crisis of 2007–2008
Lehman Brothers
Anton R. Valukas
repo 105
Ernst & Young
off-balance sheet
structured investment vehicles
Derivative (finance) § Leverage
Financial risk management § Banking

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