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The authors investigate the conditional covariances of stock returns using bivariate exponential ARCH models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., 'leverage' effects. Using monthly data, the authors find strong evidence of conditional heteroscedasticity in both market and nonmarket components of returns, and weaker evidence of time-varying conditional betas. Surprisingly, while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk.