Bank for International Settlements, 1999, Central Bank Survey of Foreign Exchange and Derivatives Market Activity 1998 (Basel, May).
Bank for International Settlements, 2000, Press Release: The Global OTC Derivatives Market at End-June 2000 (Basel, November 13).
Basel Committee on Banking Supervision, 1988, International Convergence of Capital Measurement and Capital Standards (Basel: Bank for International Settlements, July).
Basel Committee on Banking Supervision, 1995, Basel Capital Accord: Treatment of Potential Exposure for Off-Balance-Sheet Items (Basel: Bank for International Settlements, April).
Basel Committee on Banking Supervision, 1996, Amendment to the Capital Accord to Incorporate Market Risks, (Basel: Bank for International Settlements, January).
Basel Committee on Banking Supervision, 1999a, Banks’ Interactions with Highly Leveraged Institutions (Basel: Bank for International Settlements, January).
Basel Committee on Banking Supervision, 1999b, Sound Practices for Banks’ Interactions with Highly Leveraged Institutions (Basel: Bank for International Settlements, January).
Basel Committee on Banking Supervision, 1999c, A New Capital Adequacy Framework (Basel: Bank for International Settlements, June).
Caxton Corporation, Kingdon Capital Management, LLC, Moore Capital Management, Inc., Soros Fund Management LLC, and Tudor Investment Corporation, 2000, Sound Practices for Hedge Fund Managers (New York, February).
Jackson, Patricia, 1999, “Capital Requirements and Bank Behaviour: The Impact of the Basel Accord,” Working Paper No. 1 (Basel: Basel Committee on Baking Supervision, April).
Schinasi, Garry. J. and R. Todd Smith, 1999, Portfolio Diversification, Leverage, and Financial Contagion, IMF Working Paper 99/136 (Washington: International Monetary Fund, October).
United States, President’s Working Group on Financial Markets, 1999, Hedge Funds, Leverage, and the Lessons of Long-Term Capital Management (Washington, April).
The author is particularly indebted to Garry Schinasi for inspiring this research and to Burkhard Drees for his intense involvement with this paper. The author is also grateful for helpful comments and suggestions provided by an anonymous referee, Sean Craig, Peter Garber, Jim Gordon, Charles Kramer, Richard MacMinn, David Robinson, Stephen Smith, Todd Smith, Bent Sørensen and seminar participants at the IMF Asia and Pacific Department, the 2000 Asia Pacific Finance Association meetings, the 2000 Symposium on Risk Management in the Global Economy at the Federal Reserve Bank of Chicago, and at the 2000 Australasian Finance and Banking Conference.
For example, LTCM’s on-balance sheet leverage may have conveyed a misleading picture: News reports indicate that its on-balance-sheet leverage ratio moved from a factor of 25 to 167 at the height of the collapse while its (undefined) off-balance-sheet leverage ratio moved from a factor of 270 to 2100 (Section VI discusses the construction of off-balance-sheet ratios).
Value-at-Risk is a measure of the maximum potential change in value of a portfolio of financial instruments with a given probability over a preset horizon.
Leverage also has benefits. It enables borrowers to invest in projects requiring a certain minimum investment but subject to increasing returns. Leverage can also be usefully employed to hedge an existing commitment in a cost-saving manner. Furthermore, leverage facilitates speculation, which is necessary for the efficient functioning of markets and tends to enhance liquidity. Some firms, such as banks, need to be leveraged by the nature of their business.
While the simultaneous build up of leveraged positions could have a similar impact, this tends to occur over a longer period than the abrupt reversal of these positions, and hence the impact is more gradual.
Since assets are the sum of debt and equity, the leverage ratio can be expressed as the debtequity ratio plus unity.
The VaR measure is kept generic here, but can be defined for different pre-set probabilities.
It is interesting to note that a highly leveraged portfolio of low risk assets can imply less risk to equity than an unleveraged portfolio of very risky assets.
Two important shortcomings of the risk coverage ratio and the off-balance-sheet leverage ratio are that these ratios need to be reported by the financial institutions themselves in order to assure the privacy of their individual position taking. In addition, the Value-at-Risk data are based on very specific assumptions. Nevertheless, an independent outside auditor can certify periodically the consistency of the data with a computation method that has been agreed with the supervisor.
However, they increase the cost of capital to the extent that they are reflected on the balance sheet.
Margin payments in the form of cash are just one way of posting collateral. In the following example, securities are frequently used to post collateral.
On-the-run securities are the latest issue of a particular maturity. Usually they are the most actively traded issues for a particular maturity. Off-the-run securities are the previous issues of the same maturity. For example, in October 1998 the on-the-run 30-year treasury bond matured in August 2028; the most recent off-the-run 30-year treasury bond matured in November 2027.
The lender of cash in a repo may also demand a “haircut” (margin payment) to limit his credit exposure resulting from a decline in price of the collateral. This margin payment would reduce leverage. While stock margins are 50 percent and exchange-traded futures margins are between 2 and 8 percent, haircuts on repos are between 1 and 2 percent. Hedge funds have in some cases been able to negotiate a zero margin. Without any cushion to accommodate fluctuations, a 4 percent price movement (as occurred in the fall of 1998) on a few trillion dollars of assets serving as collateral in a repo would cause massive margin calls and result in a major market movement.
Balance sheet leverage is limited by two factors: underlying equity and requirements to hold capital against the assets created from the equity, which limits the number of times equity can be leveraged up. Leverage accumulated through off-balance-sheet derivative contracts is limited by the amount of margin payments counterparties require. If there is no margin payment, leverage can be unlimited.
Many forward contracts are written so that they have no value at their inception.
The short position in the money market is indicated by the minus sign in the forward pricing equation.
To the extent that the long forward contract has a positive value at inception, it can be purchased in part with (on-balance sheet) debt, thereby increasing the overall degree of leverage of the investor. Methods for calculating total leverage are considered in the following section.
Note that the definition of leverage used in this paper makes the leverage ratio remain at infinity when losses exceed equity, even though the mathematical ratio would change signs.
Even though changes in the price of the underlying asset result in changes in the value of equity in the position of the same size, the leverage ratio varies between infinity and 1 as the price of the asset increases.
An alternative approach to measuring leverage, which takes the posted margin as the investor’s equity position, does not take into account the constantly changing degree of leverage and subsequent margin adjustments.
The “delta” of the option is defined as the rate of change of the option price with respect to the price of the underlying asset. It is also called the “hedge ratio”.
This ratio is sometimes referred to in the literature as the ‘lambda’ of an option.
This statement simply indicates that the value of an option cannot be less than its intrinsic value, even if its time value is zero.
The delta of a put option,
Even though not all repurchase agreements take place off-balance sheet, they are such an important tool to acquiring leverage that they have been included here.
Alternatively, the “off-balance-sheet gross” and “off-balance-sheet net leverage ratios” could be calculated by dividing the sum of asset equivalent components implicit in off-balance-sheet items by the sum of their equity equivalent components. Positions that have an infinite leverage ratio will only contribute to the numerator, but not to the denominator. Both ratios do not take into account that portions of the equity equivalent components of derivatives, in turn, may be financed by on-balance-sheet leverage.
Various other ways of combining (on-balance-sheet) asset positions are considered in Counterparty Risk Management Group (1999).
Due to the quarterly nature of the data and reporting lags, there may not be precise relationship between events and the observed leverage indicator.
One globally active bank reached a ratio as high as 579.
This compares to a ratio of 36 for the top 7 US commercial banks at the end of the second quarter in 1998.
The consultation paper for a new Basel Accord (Basel Committee on Banking Supervision, 1999c) abolishes the limit on risk weightings for exposures to counterparties in OTC derivatives transactions.
Note: The term ‘credit equivalent’ refers to the amount of a derivative contract that exposes the holder to credit risk and is typically the contract’s positive market value. The term ‘debt equivalent’ refers to the portion of the exposure of a derivative contract (the current notional amount) that would have to be borrowed to replicate the derivative in the spot market.
Derivatives containing credit risk are mostly traded over-the-counter. Exchange traded derivatives with relatively little credit risk may be considered under the 1996 Amendment to the Capital Accord to Incorporate Market Risk.
While derivatives are often referred to as off-balance-sheet financial transactions because the notional amounts of their contracts are not recorded on the balance sheet, the market values on trading derivatives, which—as pointed out above—generally represent a small fraction of the notional amount, are recorded on the balance sheet and are therefore captured by capital adequacy requirements.
The 1996 Market Risk Amendment does base capital requirements on an improved representation of exposure for some instruments. However, it ignores exposure beyond the market value for others, and requires capital charges against the full notional amount of another set of instruments.