Calculate the percentage of the root owned by its parents

In simplified terms, I'm trying to calculate the percentage of the root of a tree owned by its parents, further up the tree. How can I do this in SQL alone?

Here's my (sample) schema. Please note that though the hierarchy itself is quite simple there is an additional holding_id, which means that a single parent can "own" different parts of their child.

create table hierarchy_test ( 
       id number -- "root" ID
     , parent_id number -- Parent of ID
     , holding_id number -- The ID can be split into multiple parts
     , percent_owned number (3, 2)
     , primary key (id, parent_id, holding_id) 
        );

And some sample data:

insert all 
 into hierarchy_test values (1, 2, 1, 1) 
 into hierarchy_test values (2, 3, 1, 0.25)
 into hierarchy_test values (2, 4, 1, 0.25)
 into hierarchy_test values (2, 5, 1, 0.1)
 into hierarchy_test values (2, 4, 2, 0.4)
 into hierarchy_test values (4, 5, 1, 1)
 into hierarchy_test values (5, 6, 1, 0.3)
 into hierarchy_test values (5, 7, 1, 0.2)
 into hierarchy_test values (5, 8, 1, 0.5)
select * from dual;

SQL Fiddle

The following query returns the calculation I would like to make. Due to the nature of SYS_CONNECT_BY_PATH it can't, to my knowledge, perform the calculation itself.

 select a.*, level as lvl
      , '1' || sys_connect_by_path(percent_owned, ' * ') as calc
   from hierarchy_test a
  start with id = 1
connect by nocycle prior parent_id = id

There are cyclical relationships in the data, just not in this example.

At the moment I'm going to use a pretty simple function to turn the string in the calc column into a number

create or replace function some_sum ( P_Sum in varchar2 ) return number is
   l_result number;
begin  
   execute immediate 'select ' || P_Sum || ' from dual'