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Author: DaveGoldman Three stars, 500 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 253522  
Subject: Re: Naive upside/downside calculation Date: 7/17/1999 1:50 AM
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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
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