Fooled by Randomness

If people haven't read this book, I highly advise it:

Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

The book discusses how many people attribute good stock picking to people when they have merely been fortunate.

This ties in well with a discussion raging on the MFI Yahoo Board (magicformulainvesting) on how many stocks you should buy per year. JG recommends 20 to 30 per year. You need to balance transaction costs with stomach for volatility. To test this, I used the 2000 stock years I have in my monthly tracking portfolios I have been running since January 2006. I tried three approaches:

1. Buying one stock per month (so 12 per year)
2. Buying 2 stock per month (24 per year) and
3. Buying 3 stocks per month (36 per year).

I ran 1000 Portfolios (remember, each portfolio is invested started January 2006 to current). assuming $100,000 invested at the start. Here are the results and then I will explain a bit:

Column1	12/Year	12/Year2	24/Year	24/Year2	36/Year	36/Year2
Band	Incemental	Cumulative	Incemental	Cumulative	Incemental	Cumulative
30K-40K	0.1%	0.1%	0.0%	0.0%	0.0%	0.0%
40K-50K	0.9%	1.0%	0.1%	0.1%	0.0%	0.0%
50K-60K	2.4%	3.4%	0.3%	0.4%	0.1%	0.1%
60K-70K	5.5%	8.9%	1.0%	1.4%	0.4%	0.5%
70K-80K	11.3%	20.2%	6.7%	8.1%	3.2%	3.7%
80K-90K	12.9%	33.1%	14.0%	22.1%	10.9%	14.6%
90K-100K	15.3%	48.4%	19.9%	42.0%	22.6%	37.2%
100K-110K	14.1%	62.5%	20.6%	62.6%	25.8%	63.0%
110K-120K	10.6%	73.1%	15.7%	78.3%	21.0%	84.0%
120K-130K	7.9%	81.0%	10.6%	88.9%	10.0%	94.0%
130K-140K	5.3%	86.3%	5.4%	94.3%	3.9%	97.9%
140K-150K	4.7%	91.0%	2.7%	97.0%	1.4%	99.3%
150K-160K	2.9%	93.9%	1.7%	98.7%	0.7%	100.0%
160K-170K	1.8%	95.7%	0.9%	99.6%	0.0%	100.0%
170K-180K	1.4%	97.1%	0.2%	99.8%	0.0%	100.0%
180K-190K	1.1%	98.2%	0.1%	99.9%	0.0%	100.0%
190K-200K	0.4%	98.6%	0.1%	100.0%	0.0%	100.0%
200K-210K	0.6%	99.2%	0.0%	100.0%	0.0%	100.0%
210K-220K	0.2%	99.4%	0.0%	100.0%	0.0%	100.0%
220K-230K	0.3%	99.7%	0.0%	100.0%	0.0%	100.0%
240K-250K	0.1%	99.8%	0.0%	100.0%	0.0%	100.0%
270K+	0.1%	99.9%	0.0%	100.0%	0.0%	100.0%
260K-270K	0.1%	100.0%	0.0%	100.0%	0.0%	100.0%
Average	106,085.63		105,727.07		105,471.22
Std Dev	31,909.57		20,081.63		15,195.86

Here is the same info graphically:

You can see they all have about the same average. That is expected.

The difference is in the "spread" of the graph, which is measured by the standard deviation statistic.

If you buy just one stock a month, and have been at it for pushing five years, you would have a 20% probability of having lost $20,000+ of the original $100k stake.

Conversely, you'd have a 20% chance of being $120k+.

But if you bought 36 stocks per year, the probability of losing 20K+ drops from 20% to under 4%. So the distribution clusters more closely about the mean.

What Does All of This Mean? (Why are you telling me this?)

This shows that even if you picked stocks purely randomly, that after almost five years it is very possible to have substantial variability amongst everyone's results. So you have to be careful, if someone is doing better than you, it doesn't mean they are better stock pickers. It could be "luck" or "randomness.