A little Statistics

Short note today. I was right about VPHM, went up almost exactly the 5% I predicted. Good day for my portfolio as it went up .86%. At one point I thought I might pass my arch-rival IWV but then I fell back a bit.

Now here is a post I made on the Yahoo Group board:

Chris' comments about MFI stocks made me wonder, what is the distribution of returns like? So I went to my monthly database and listed the returns of all stocks that have been held for at least 6 months (January 2006 - June 2006 databases). I then made a little histogram to see how spread the returns have been (please note that some stocks are duplicated as I typically get the 50 stocks greater than 100m at the start of each month, of course they have differing entry prices):

Here are some statistics:

Count	276
Mean Change	11.9%
Median Change	10.5%
Standard Deviation	32.2%
Percent Change	Count
Over 100%	3
90 to 100%	3
80 to 90%	1
70 to 80%	4
60 to 70%	7
50 to 60%	11
40 to 50%	19
30 to 40%	24
20 to 30%	25
10 to 20%	44
0 to 10%	34
-10 to 0%	36
-20 to -10%	26
-30 to -20%	17
-40 to -30%	11
-50 to -40%	4
-60 to -50%	4
-60% and worse	2

The worst stock is in the subject field: OVTI at -63% (sadly also in my portfolio). The best stock is PNCL at +156% (thankfully also in my portfolio).

Finally, Chris' comment is spot on. 36% of the stocks have declined in price (I do include dividends). I think the volatility amongst specific stocks really highlights the importance of spreading your risk amongst the 25-30 stocks JG discusses. I will try and re-visit after more portfolios have aged an entire year.

For statisticians out there, the 32% standard deviation seems quite high to me. In a normal distribution, you'd expect 64% of your data to be within one SD of the mean. So that would imply 64% would be within 12%-32% and 12%+32% or a range from -20% to 44%. We would expect 90% to be within 2 SD of the mean or -52% to 76%.

That means if you picked a stock at random, I would have 90% confidence that its return would be between -52% and 76%. Yikes, big range. That gets to the book some people have been discussing, I think it is called "Fooled by Randomness". For short periods of time and/or smaller numbers of stocks whether you're doing good or bad, the largest element at play is chance.