This paper examines the role of time-varying jump intensities in forming meanvariance portfolios. We find that compared with the no-jump or constant-jump models, the model which incorporates time-varying jump intensities better fits the dynamics of the assets returns, and yields mean-variance portfolios with higher Sharpe ratios. Our research suggests that using a better econometric model that captures non-normal features in the data has benefits for portfolio allocation even for a mean-variance investor.mean-variance, optimal portfolio, time-varying jump intensities the S&P 500 index and NIKKEI 225 index traded in Chicago mercantile exchange (CME) are considered in our analysis. 2 We capture the time-varying jump intensities in two risky asset returns using the bivariate Baba-Engle-Kraft-Kroner with autoregressive jump intensity (BAJI) model. Like Chan (2004) and M.-C. Lee and Cheng (2007), we allow different assets prices to jump simultaneously or independently, where the simultaneous jumps capture the timevarying systematic jump risks while the independent jumps capture the time-varying idiosyncratic jump risks. The estimation results show that the jump intensities are time-varying and persistent. The individual jump intensities of S&P 500 index future are high during the early 2000s recession in the United States, and the individual jump intensities of NIKKEI 225 index future are large during the 1990s recession in Japan. The individual jump intensities of the two futures are relatively low during the 2008 subprime crisis in the United States, but their common jump intensities are large, indicating that the U.S. subprime crisis has major influence on both the S&P 500 index futures and the NIKKEI 225 index futures.We solve the portfolio optimization problem based on the mean-variance framework of Markowitz (1952). That is, the investors aim to minimize the portfolio variance for a given level of target expected return. To examine whether it is important to consider time-varying jump intensities in mean-variance portfolio decisions, we describe the dynamics of asset returns based on the BAJI model. We consider three alternative models, including the static model in which the covariance matrix is calculated using the in-sample covariance matrix estimate, the Baba-Engle-Kraft-Kroner (BEKK) model (Engle & Kroner, 1995) and Baba-Engle-Kraft-Kroner with constant jump intensity (BCJI) model.The in-sample and out-of-sample results show that the BAJI model which incorporates time-varying jump intensities performs better, and produces higher Sharpe ratios than the other three models. The Sharpe ratios of BAJI model remain highest after considering the trading cost. Based on the bootstrapping method, we find that the superiority of BAJI model over the other three models is robust to the parameter uncertainties of expected returns, and increases when the uncertainty level decreases.Our paper is related to the previous literature regarding volatility timing. For instance, Fleming et al. (2001), Fleminga, Kirby, andOstdiek...