Here's a solution that exactly matches the phrases specified in AnonyMonk's Re: Using Look-ahead and Look-behind post (which the code of Re^2: Using Look-ahead and Look-behind does not quite do), and also shows how to use the newfangled backtracking control verbs of 5.10 to emulate variable-width negative look-behind. Variable-width positive look-behind is emulated by 5.10's  \K assertion.

Explanation:

• Any 'equity' that is preceded by
  • either a character that is not a comma or whitespace, or
  • by the 'private' phrase
  FAILS and is skipped over (this test has first precedence);
• Otherwise, any 'equity' that is not followed by a comma that is then followed by any non-whitespace SUCCEEDS.

>perl -wMstrict -le
"use Test::More 'no_plan';
 ;;
 for my $ar_vector (
   [ YES => 'equity, private equity', ],
   [ YES => 'equity',                 ],
   [ no  => 'private equity',         ],
   [ YES => 'private equity,equity',  ],
   [ YES => 'private equity, equity', ],
   [ no  => 'equity,private equity',  ],
   [ no  => 'private equity',         ],
   [ no  => 'mutual funds',           ],
   [ no  => 'cds'                     ],
   ) {
   my ($expected, $string) = @$ar_vector;
   is match($string), $expected, qq{'$string'};
   }
 ;;
 sub match {
   my ($string) = @_;
   ;;
   my $char_not_comma_or_space = qr{ [^,\s]      }xms;
   my $private                 = qr{ private \s+ }xms;
   return 'YES' if $string =~
     m{ (?: $char_not_comma_or_space | $private) equity (*SKIP)(*FAIL)
        |
        equity (?! , \S)
      }xms;
   return 'no',
   }
"
ok 1 - 'equity, private equity'
ok 2 - 'equity'
ok 3 - 'private equity'
ok 4 - 'private equity,equity'
ok 5 - 'private equity, equity'
ok 6 - 'equity,private equity'
ok 7 - 'private equity'
ok 8 - 'mutual funds'
ok 9 - 'cds'
1..9
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