Abstract: Taking the loan’s yields as the profit of financial asset,taking the volatility of loan’s yields as reflection of loan’s risk,under the constraint of Value at Risk(VaR),based on the solution of quadratic programming,a decision-making model of loan-risk portfolio optimization is set up with the minimum risk within the feasible range of definite portfolio yield.There are three characteristics of the model:Using yield rate of maximum loss but yield amount reflects VaR,so it becomes convenient to the decision analysis.Taking risk correlation into account,it controls risk limitation with the maximum loss on yield rate of VaR,so the ability for risk tolerance of commercial bank is reflected by loan’s distribution or allocation.If given the objective in the feasible range,and given the yield rate as decision-maker expected,the loan’s portfolio to the minimum risk always can be found.The efficient boundary which was given by this model provides a scientific method for the decision-making of the loan’s portfolio.

Key words: loan’s portfolio, loan’s decision-making, quadratic programming, Value at Risk, Lagrange multiplier, efficient boundary