Elan,

First a comment about format - when you sorted the returns in ascending order you threw us for a curve. It took me a few minutes to figure out that the numbers in the three columns are not coordinated. Each column has an independent sorting sequence, making it very difficult to follow your calculation. Why sort it at all?

Here's what I did:

       Actual        Downside        Upside
    distribution   distribution   distribution    
      --------       --------       --------
        #1              #1        (Pretend #1)
        #2              #2        (Pretend #2)
        #3              #3        (Pretend #3)
        #4              #4        (Pretend #4)
        #5              #5        (Pretend #5)
        #6              #6        (Pretend #6)
        #7         (Pretend #7)        #7
        #8         (Pretend #8)        #8
        #9         (Pretend #9)        #9
       #10        (Pretend #10)       #10
       #11        (Pretend #11)       #11
       #12        (Pretend #12)       #12

To put it another way, consider this skewed distribution:

                 XXXXX
                XXXXXXXXXX
               XXXXXXXXXXXXXXXXX
              XXXXXXXXXXXXXXXXXXXXXXXXX
             XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

What I've done is break it into two distributions:

             XXX          XX
            XXXX          XXXXXX
           XXXXX          XXXXXXXXXXXX
          XXXXXX          XXXXXXXXXXXXXXXXXXX
         XXXXXXX          XXXXXXXXXXXXXXXXXXXXXXXXXX

and then added in the "missing half" of each one, so that I can calculate the S.D. of each:

             XXXYY
            XXXXYYY
           XXXXXYYYY
          XXXXXXYYYYY
         XXXXXXXYYYYYY

                        YYXX
                     YYYYYXXXXXX
               YYYYYYYYYYYXXXXXXXXXXXX
        YYYYYYYYYYYYYYYYYYXXXXXXXXXXXXXXXXXXX
 YYYYYYYYYYYYYYYYYYYYYYYYYXXXXXXXXXXXXXXXXXXXXXXXXXX

I've no doubt that something like Sortino's approach, using a MAR, is more valid and useful. But there was some talk here today about looking at both sides of the distribution, to measure not just "risk" but to get a better idea of what one can expect in both good years and bad. So, this simple(-minded) approach occurred to me.

Dave Goldman
Portland, OR