Contagion as a Wealth Effect of Financial Intermediaries

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Abstract
This paper models financial contagion as a wealth effect of financial intermediaries in a market with two risky assets and three types of traders: noise traders who trade in one market, financial intermediaries who partially arbitrage away noise trading, and long-term investors who provide liquidity. Contagion is characterized as decreased liquidity, increased volatility in both markets, and increased correlation between returns on the two assets occurring simultaneously with financial intermediaries suffering losses on positions. When financial intermediaries have reduced capital as a result of trading losses, they have a reduced capacity for bearing risks. This motivates them to liquidate positions in both markets, resulting in reduced market liquidity, increased price volatility in both markets, and increased correlation. Through this mechanism, the wealth effect leads to contagion. Financial intermediaries are assumed to follow consumption and portfolio rules which make them look like a log-utility investor: the volatility of their portfolio equals the Sharpe ratio available in the market and the dividend rate (i.e., consumption rate) equals the rate of time preference. They trade in two markets with independent fundamentals and constant dollar total risk. As the financial intermediaries partially arbitrage away the effects of noise trading in one market, they take large risky arbitrage positions. Long-term investors provide some liquidity, which makes it possible for financial intermediaries to liquidate positions when they suffer losses. The equilibrium has two state variables, the wealth of financial intermediaries and noise trading. A system of two simultaneous partial differential equations is solved numerically using a projection method. This model cautions risk managers to evaluate risks using information about the capitalization and positions of other market participants.

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