In today's rapidly changing economic environments, global portfolio investors are invariably confronted with dynamic and fluid choice of criteria that enable them to exercise subjective judgment on asset portfolio choice decisions. The subjective investment portfolio choice includes the discretion to purchase some assets that do not meet its normal investment criteria, when they perceive unusual information which incurs event jumps in the asset return. This paper studies on what criterion or criteria should be used when the asset in the investment portfolio is subject to event jumps as well as how the criterion or criteria can be found. We use marginal excess return in the value add return function for indicating the return decreasing under information impact and finding a critical value related to the growth optimum portfolio choice on a risk adjusted basis. We reveal, as a special case, the optimal portfolio is equivalent to the benchmark portfolio, if the investor is myopic of constant relative risk aversion. Managers of the large multinational firms and investment funds usually seek the highest total portfolio return over time that is consistent with emphases on both capital appreciation and investment income/return under a specified risk level.
[...] The corresponding optimal policies obtained there are all constant proportions, or in constant mix, portfolio allocation strategies, whereby the portfolio is continuously rebalanced so as to always keep a constant proportion of wealth in the various asset classes, regardless of the level of instant wealth Our use of marginal excess return in the value add return function for indicating the return decreasing under information impact and finding a critical value related to the growth optimum portfolio choice on a risk adjusted basis. [...]
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[...] The sum of the weights in the benchmark portfolio and the R R M + ce growth optimum is R T rds rds M = 1 + ce which is greater or less than one depending on the sign + R R T of the constant c Criteria for Adjusting Portfolio Choice We now turn to the discussion of the optimal portfolio return over time. Since the optimal weight vector is a linear combination of the growth optimum and the benchmark portfolio as in Equation one might imagine that the optimal portfolio return should be expressible in terms of the returns on the growth optimum and the benchmark portfolio. [...]
[...] 0.0305 - 0.0452 - 0.0789 0.3569 For simplicity without loss of the generality, given γ in the risky assets by = we calculate the benchmark portfolio weights with no jumps 15 0.0068 0.0148 0.0134 μ - r Φ* = = 0.0184 = M 3 γ 0.0134 0.0193 0.025 Thus, the dynamics of the benchmark M portfolio return is 75.1365 - 46.7615 - 6.7523 - 6.9445 - 108.1713 - 2.2607 dM ) = + (Φ M (μ - r 1)]dt + (Φ M = 4.1065 dt + M ) dZ1 dZ 2 dZ 3 [ - 3.8561 - 0.4529 - 0.6326 - 4.7141 - 0.1278 ] dZ 4 dZ dZ 6 dZ For the risk premium, [μ - r 1 λ μ x ] = - 0.0199 0.02 0.0628 0.0195 0.0134 0.0193 0.025 upward jumps, and [ ] t with [μ - r 1 λμ x ] = [ 0.0125 0.0161 0.0134 0.0193 0.025 ] with downward jumps, and t r = By Equation ΦG = - r 1 λμ x ] = [ ] with upward jumps, and t 351.4773 79.6417 ] t with downward jumps. [...]
[...] We focus on the determination of an investment strategy that is optimal relative to the performance of a benchmark portfolio for an investment criterion Benchmark Portfolio Let Φ M = [φ M ,φ Mn be the benchmark portfolio with φM i being the fraction of the benchmark portfolio in the ith security. In solving for the optimal portfolio strategy, we adopt the standard stochastic control approach without any jumps. We solve for the benchmark optimal portfolio strategy the indirect utility function is of the form Φ* without any jumps by first conjecturing that M J , t ) = where 1 W exp( A(t γ A(t ) is a time dependent only function. [...]
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