A risk-constrained generation asset scheduling model for generation companies (GENCOs) in the electricity markets is proposed in this paper. The model embodies the arbitrage opportunities for GENCOs through an optimization procedure. The risk exposure of GENCOs is managed by explicitly adding the downside risk constraints into the optimization problem. To avoid the inaccuracy of downside risk, the variance of expected profit is calculated to measure the fluctuation of GENCO's profit. The sensitivity of GENCOs' profit to risk is also calculated in the form of Sharpe ratio. The downside risk constraint will keep tightening iteratively until the risk exposure tolerance is satisfied. Consequently the profit and risk will be balanced automatically.