What if we picked random equal-weight portfolios in January 2007 and held them all for 16 years?

How do you think they would do against the Nifty?

How would their outcomes vary depending on the number of stocks each of those random portfolios held?

Random portfolios mean every stock above 300 Cr in Market cap in Jan 2007 had an equal chance of getting picked in each portfolio. So, the 1,000 portfolios saw each stocks picked equal number of times, give or take. Note that the population included the non-survivors, i.e. stocks that went on to lose 100% of their value.

The chart shows the distribution of annualised returns from holding 1,000 random 10-stock portfolios. The dotted vertical line is what the Nifty did over the same time. Nifty’s performance includes dividends.

The median 10-stock portfolio returned 11.7% from 2007 to 2023, marginally better than the Nifty. Over half of the random portfolios beat the Nifty.

But the range of outcomes goes all the way from -10% to +25% annually. This makes sense if you think about how some random portfolios would’ve been “unlucky” to get several duds while at the other end, some would get several blockbuster stocks.

What if we increased the number of stocks in each portfolio? Would the return distribution change significantly?

The shape of the distribution remains the same with one difference. The tails, the extreme left and right ends of the distribution get shorter i.e. The worst outcomes from holding 10-stock portfolios become less worse and the best outcomes become less good by increasing the number of holdings from 10 to 20.

The median 20-stock portfolio return goes up marginally to 11.9%.

The logical extension would be to increase the number of holdings from 20 to 30.

The tails get even “shorter” on the possible range of outcomes. Only 2 out of 1,000 30-stock portfolios ended with a negative return when held for 16 years. The best possible outcome also reduced from 25% with 10 stocks to 19% with 30 stocks. And yet, the median return didn’t get worse.

Chart shows all the outcomes plotted together.

“But what happens if instead of holding the same portfolio for 16 years, you rebalanced yearly?”

Turns out, not a whole lot changes, except for the peak of the distribution going up significantly, which means the most frequent outcome becomes even more frequent.

Key takeaways from the random portfolio experiment:

- A lot of randomly picked portfolios end up beating the Nifty. And a lot of randomness gets misattributed to manager skill
- The role of luck is higher in concentrated portfolios. Imagine being the manager who picked that portfolio with the right tail return in the first chart. As the number of stocks goes up, some of that impact comes down
- Diversification is not just for the clueless. Eliminating, or at least reducing the extreme left-tail outcomes, at the cost of the extreme right-tail ensures you don’t get wiped out. Hence, portfolios, not individual stocks, matter.

*Have thoughts? Do share. I’m on Twitter @CalmInvestor*