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I've been doing a lot of thinking lately on my own approach to this issue.

I actively manage 3 different equity portfolios: a taxable margin account, a smaller non-taxable retirement account (approx. 50% as large), and a very small non-taxable college fund (about 10% as large). Rather than employing equal diversification across all 3 accounts, I maintain equal position sizes. The position size is irrelevant, except inasmuch as it's large enough to keep even Canadian commission costs at a tolerable level, but small enough to take advantage of pricing anomalies when trading gets sloppy on high volume.

When I'm fully invested, I carry about 10 long positions in the margin account, 5 in the retirement account, and only 1 in the college account. There's sometimes overlap between accounts, and I've been carrying lots of cash lately, so the total is usually less than 16 unique positions. Of necessity, I also carry any short or option positions in the margin account, and that might amount to another 4-6 positions. But aside from tax implications, which I do a pretty good [as in poor] job of ignoring, the long equity positions ought to be directly comparable.

My daughter's college account is of course an anecdote of n = 1, but it's not an anecdote of n = 1 lucky stock pick. I'm not averse to trading and I've held 8 different positions over the last 2 years (Linamar, Albertsons, Delphi Automotive, Premdor [now Masonite], Nokia, Aberdeen Asia-Pacific Income Fund, Noranda, and now Japanese I-shares). Every trade has been successful, and the compound average growth rate over 2+ years has been 69%. Two annual contributions of $2,000 apiece early in 2000 and 2001 have grown to $11,160 today. Which is probably more than it cost me to go to university for the first 2 years, but that's another story.

Being 100% focused in this account has forced me to carefully weigh each decision, as has the fact that it's for my daughter, not me. The lack of margin means I can't separate my sell and buy decisions in time. To buy something new, I have to sell what I have, period. Frankly, I think it's made me a better investor, although I'll never take an all-or-nothing approach with my other accounts. Indeed, I've now gotten to the point where I'll probably split this one into 2 separate positions.

I'm exiting the market now in preparation for moving from Canada to the U.S., but when I set up shop again in the U.S., I'm going to try to run a much more concentrated margin portfolio with perhaps 8-10 total positions, both long and short. The amount of capital that could disappear on a bad trade certainly won't be trivial to me, but neither will the amount that I could gain on a good trade. But I'm nevertheless worried about the psychological blow of a bad trade. I weathered 2 enormous losses at the end of last year, but that was after an otherwise good year, and it's easy to do mental discounting under such circumstances. It's not so easy when you start the year off that way.

In 1999, after doing relatively poorly on a reasonably concentrated portfolio of value stocks, I found my confidence badly shaken. And I moved to excessive diversification in about 20-30 different holdings. And they were on average very successful, but the benefit of picking out an annual double when it's only 3% of your port is rather trivial.

I guess I'm trying to say that there can be valid psychological reasons for extreme diversification (including perhaps boredom), but I don't think there are any good mathematical arguments. The mathematical arguments involve avoiding extreme negative results, especially a total wipeout, but if you're any good, 6 or so positions ought to be plenty of diversification to achieve that level of safety. And if you're not any good, you should probably only own one stock—Vipers or Spyders.

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