The total number of possibilities for the five stocks is 243.
Work Step by Step
We know that the total number of possibilities can be calculated using the fundamental counting principle. The fundamental counting principle states that the number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur. In our case, every stock has three possibilities. It can go up, go down, or stay unchanged. Thus, the total number of possibilities if a person owns $5$ stocks is: $3\times 3\times 3\times 3\times 3=243$ ways.