Asset Allocation Strategy under Rate of Return, Rate of Inflation and Credit Spread Rate in Finite-Time Horizon

Abstract

The global financial crisis has given a very tremendous financial market chaos in the world. Beside the reason that it caused mostly by the bubble economic, it also caused by the ignorance of default risk from bond derivatives such as CDO, CDS and SWAP. Those portfolio of bond ignored the risk of the low rating bonds, which gives a very high risk of having default. This research aims to find an optimal solution for dynamic portfolio in finite-time horizon under defaultable assets. Defaultable assets mean that the assets has a chance to be liquidated in a finite time horizon, e.g stock and corporate bond. The assets that will be used here are limited to the equity, corporate bond and money account. In this study, beside for having the risk of default, the investor will also consider the risk of market such as inflation into her investment. The indirect utility function will be used as the reference for investment decision. Further the asset allocation will be obtained by maximizing the total expected discounted utility in the time span during the investment is executed.To determine the financial defaulty assets, there are two methods that can be used, namely the reduced form and the structural methods. The first method is more applicable because the assets price can be linked with the market risk and credit risk and the latter method. The interest rate and the rate of inflation will be allowed as a representation of market risk, while the credit spread will be used as a representation of credit risk. Furthermore, the dynamic of asset prices can be derived analytically by using Ito Calculus in the form of the movement of the three risk factors above.The dynamic process of investor wealth will be derived from the dynamics of asset prices and budget constraints, which will be linked with portfolio composition. This problem will be solved using the stochastic dynamic programming method. Depending on the chosen utility function, the optimal solution of the portfolio composition can be found explicitly in the form of feedback control. The closed form solution will give the proportion of wealth between bond and money account. Furthermore, the composition of the portfolio will be given as the result. The complicated equation of bond pricing will follow recovery market value (RMV) methods. The finding model is later simulated with different possible values of the parameters. The result shows that the optimal asset allocation will depend on various parameters such as correlation between the risks, the chosen utility function and also recovery rate.