I have the following problem: an equity portfolio allocated to 3 countries. Each country has an independent indicator (signal) which takes values from -4 to 4. The allocation for each country at neutral is 1/3 (33.33%) and based on the indicator can oscillate -20%/+20%.
the weights are: w1 +w2 +w3 =100% constraint w1,w2,w3 =33.33% (at neutral) w1,w2,w3 e [13.33%;53,33%] constraint the indicators : i1,2,3 e [-4;4]
the allocation can be linear, proportional. How can this be solved for 3 countries? because for 1 is easy: Like -4 represents -20% in a country. 0 represents neutral allocation , keeping 33.33% in that specific country. For 2 I made a compound indicator like the difference between countries indicators. But for 3+ countries I cannot find the solution.