## July 28, 2015

### Correlation between portfolio size and expected retrurns

Excellent article on pros and cons of different portfolio sizes.

By alpha architect

Each month, we select the largest 1,000 U.S. stocks to form our universe. We then randomly form portfolios as follows:

• Portfolio with 15 stocks.
• Portfolio with 50 stocks.
• Portfolio with 100 stocks.
• Portfolio with 300 stocks.
• Portfolio with 500 stocks.
Every month, we create 3,000 portfolios for each of the 5 perturbations listed above. The idea is to randomly select either 15, 50, 100, 300 or 500 stocks from the universe of 1,000 stocks. However, in order to simulate a large number of possibilities, we create 3,000 portfolios (for all 5 selections above) every month!

So on 12/31/1978, we create:

• 3,000 portfolios of 15 stocks
• 3,000 portfolios of 50 stocks
• 3,000 portfolios of 100 stocks
• 3,000 portfolios of 300 stocks
• 3,000 portfolios of 500 stocks

The portfolio returns are equal-weighted. We repeat this process every month. So in total, we have 3,000 draws of the 5 portfolios across time.

Summary results:

• Smaller the portfolio size, the more variance in the portfolio returns (fat tails); the larger the portfolio size, there is less variance in the portfolio returns
• Larger the portfolio, the smaller the chance of high performance
• Smaller portfolios have higher highs (max) and lower lows (min), as well as a higher standard deviation
• Smaller portfolios (15, 50 and 100 stocks) can sometimes beat the market (S&P 500 EW). However, the small portfolios lose more often than they win!

Visit this link for simulation results: http://blog.alphaarchitect.com/2015/07/27/one-way-to-beat-the-market-be-different/?vfmdirect