Market Risk Budgeting with Value-at-Risk-Limits for Linear Positions

Posted: 1 Mar 1999

See all articles by Helmut Beeck

Helmut Beeck

Bayerische Vereinsbank

Lutz Johanning

WHU - Otto Beisheim School of Management

Bernd Rudolph

Ludwig Maximilian University of Munich (LMU) - Faculty of Business Administration (Munich School of Management)

Abstract

Value-at-Risk limits shall be used for allocating capital within financial institutions. Commonly the management decides on an annual basis about the amount of capital a stock trader can loose with a prespecified probability within the year. Since the holding period for trading business is much shorter (we assume a day), the annual limit is transformed into a daily VaR limit by the "square root of time" rule. In particular, we explore three different Value-at-Risk-Limits. The first limit is called "fixed limit" The trader has the same limit each day the year. The second limit is called "stop loss limit" because realized losses during the year reduce trader's daily limit. Third, the "dynamic limit" differs from the "stop loss limit" in that realized profits can increase the daily limit. We show in a simulation study for real german stock returns from 1974-1995 that the "fixed limit" outperforms the "stop loss limit". It yields slightly higher profits combined with a smaller standard deviation. Under the "dynamic limit" a trader can earn higher annual profits, but the standard deviation and the probability of losses increase as well. The frequency of violations of the annual VaR limit is much smaller than the expected probability. This shows that the application of the "square root of time" rule leads to an overestimation of risk on an annual basis.

JEL Classification: G31, G32

Suggested Citation

Beeck, Helmut and Johanning, Lutz and Rudolph, Bernd, Market Risk Budgeting with Value-at-Risk-Limits for Linear Positions. Available at SSRN: https://ssrn.com/abstract=150697

Helmut Beeck (Contact Author)

Bayerische Vereinsbank

RCO 3, Arabellastrasse 12
D-81925 Munich
Germany

Lutz Johanning

WHU - Otto Beisheim School of Management ( email )

Burgplatz 2
Vallendar, 56179
Germany
+49 261 6509 720 (Phone)

Bernd Rudolph

Ludwig Maximilian University of Munich (LMU) - Faculty of Business Administration (Munich School of Management)

Kaulbachstr. 45
Munich, DE 80539
Germany

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