Abstract: Extreme risk is very important for bank asset allocation. Especially after the subprime mortgage crisis, the tail risk has drawn great attention from financial institutions. The traditional Conditional Value at Risk (CVaR) and Value at Risk (VaR) cann't measure the tail extreme risk effectively. Therefore, Power Spectral Risk Measure and Monte Carlo simulation are combined to build a portfolio selection model, while controlling tail extreme risk and credit risk. First, through the idea that loss X_i is larger while the risk weight φ_i is larger, the extreme risk is controlled by minimizing the Power Spectral Risk of loan portfolio. This method makes up the shortcoming of CVaR that ignoring the risky losses should be greater weight deficiencies and the shortcoming of VaR that only provides a maximum confidence level of asset loss without reflecting the potential loss more than the confidence level. Second, Monte Carlo simulation is implemented for estimating portfolio credit risk which caused by the credit rating migration. Then, through the idea that the greater the loss of loan portfolio after the credit rating migration, the greater the risk aversion weight is, establish the objective by minimizing the PSR of loan portfolio. The portfolio selection model is constructed by combining the objective of PSR and the constraints that the return of portfolio is greater than the target revenue. The proposed model makes up for the lack of control of credit risk and tail risk in the existing researches. The empirical evidence is based on the historical data of 12 loans. The empirical results show that the proposed model can achieve higher yield risk ratio than CVaR and VaR model, that is, the proposed model can achieve higher profit under the unit power spectral risk. This paper expands the idea of combining loan extreme risk and credit risk for loan allocation

Key words: power spectral risk, Monte Carlo simulation, credit rating migration, loan portfolio