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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