Procyclical Leverage and Endogenous Risk

43 Pages Posted: 17 Mar 2009 Last revised: 5 Oct 2012

See all articles by Jon Danielsson

Jon Danielsson

London School of Economics - Systemic Risk Centre

Hyun Song Shin

Bank for International Settlements (BIS)

Jean-Pierre Zigrand

London School of Economics - Department of Finance, Systemic Risk Centre, and Financial Markets Group

Date Written: October 4, 2012

Abstract

Market volatility reflects traders' actions, while their actions depend on perceptions of risk. Equilibrium volatility is the fixed point of the mapping that takes perceived risk to actual risk. We solve for equilibrium stochastic volatility in a dynamic setting where risk-neutral traders operate under Value-at-Risk constraints. We derive a closed form solution for the stochastic volatility function in the benchmark model with a single risky asset. Even though the underlying fundamental risks remain constant, the resulting dynamics generate stochastic volatility through traders' reactions in equilibrium. Volatilities, expected returns and Sharpe ratios are shown to be countercyclical. If the purpose of financial regulation is to shield the financial system from collapse, then basing regulation on individually optimal risk management may not be enough.

Keywords: Liquidity, Endogenous Risk, Financial Crises

JEL Classification: G11, G13, G21

Suggested Citation

Danielsson, Jon and Shin, Hyun Song and Zigrand, Jean-Pierre, Procyclical Leverage and Endogenous Risk (October 4, 2012). Available at SSRN: https://ssrn.com/abstract=1360866 or http://dx.doi.org/10.2139/ssrn.1360866

Jon Danielsson

London School of Economics - Systemic Risk Centre ( email )

Houghton Street
London WC2A 2AE
United Kingdom
+44.207.955.6056 (Phone)

HOME PAGE: http://www.riskreasearch.org

Hyun Song Shin (Contact Author)

Bank for International Settlements (BIS) ( email )

Centralbahnplatz 2
Basel, Basel-Stadt 4002
Switzerland

HOME PAGE: http://www.bis.org/author/hyun_song_shin.htm

Jean-Pierre Zigrand

London School of Economics - Department of Finance, Systemic Risk Centre, and Financial Markets Group ( email )

Houghton Street
London WC2A 2AE
United Kingdom
+44 20 7955 6201 (Phone)
+44 20 7955 7420 (Fax)

Register to save articles to
your library

Register

Paper statistics

Downloads
842
rank
25,891
Abstract Views
3,395
PlumX Metrics