Interest Rate Risk Management and Dynamic Portfolio Selections

The dynamic portfolio selections in the sense of Markowitz’s mean-variance are addressed in an incomplete market and the effect of interest rate risk on them is discussed. According to Markowitz’s measure risk approach, the interest rate risk is divided into the controllable risk and the uncontrollable risk. The former can be hedged, but the latter cannot. The zero-coupon bond is an efficient tool to avoid the interest rate risk. The optimal payoff resulting from self-financed strategies and the mean-variance efficient frontier are expressed explicitly. The results show that the optimal payoff and the efficient frontier are not affected by the controllable risk of interest rate, but by the uncontrollable risk. The efficient frontier is a part of a hyperbola if there exists the uncontrollable risk. The expected optimal payoff grows with the increase of risk; however, the margin expected optimal payoff lowers. The efficient frontier is a straight line if and only if there is no uncontrollable risk.