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The financial crisis of 2008 brought with it a great interest in downside risk. This dissertation focus on portfolio optimization under downside risk constraints. We maximize the expected return subject to the level of risk, which is defined as Value at Risk (VaR) or Conditional Value at Risk (CVaR) above the risk free rate on the initial wealth. Since this model does not depend on distributional assumptions for the returns, we are able to evade the shortcomings of overestimation or underestimation of risk. In an out-of-sample exercise between 1994 and 2014, we show that our VaR and CVaR strategies yield an annualized Sharpe ratio of 0.67 and 0.63, respectively, which compares well to the S&P500 that yields an annualized Sharpe ratio of 0.47. Additionally, we find evidence that our downside risk model for portfolio optimization exhibits better results during recessions when comparing its performance with several benchmarks. This implies that our model can be viewed as a risk mitigation strategy.