Before the global financial crisis(GFC) gripped our world of portfolio construction, I was happy to think in terms of a highly concentrated portfolio of eight to 15 blue-chip stocks. It is easier to find a few good stocks than a large number; and the diversification benefits fall off rapidly when increasing the number of stocks. I based my analysis on my 2005 simulation experiment of historical stock returns.
In 2008 I was asked if I had changed my rule. I didn’t have the time during the GFC to do a proper analysis, so I had arbitrarily increased my range to 15 to 20 stocks. Even with supposedly quality stocks, some companies looked likely to fall over – or at least take a massive hit in price – but knowing which ones was tricky. With 15 to 20 stocks there is less dependence on any one stock, should it get suspended – or worse. Now it is time to revisit the number of stocks question using my previous analytic methodology. I took daily price returns data from the ASX 200 stocks for the two financial years 2008/09 and 2009/10 and simulated the volatility of hypothetical equally weighted portfolios from that historical data.
I constructed one million randomly-drawn portfolios for each size of one through fifty stocks and calculated the historical volatility separately for the two financial years. In Chart 1, I show the volatility of the median-volatility portfolio for the two years – and the worst performing portfolio for 2009/10. The black line gives a visual guide for the median volatility of a one-stock portfolio (an average single stock). Unsurprisingly,
the volatility of the median portfolio in 2008/09 is much higher than for 2009/10 no matter how many stocks there are in the portfolio. Indeed, I can see that a worst-case portfolio (allowing for the volatilities and correlations of the component stocks) of five five-stock portfolios in 2009/10 has about the same volatility as an average portfolio of the same size in the previous year.
By following the black line to the right from the one-stock average portfolio in 2009/10, I can see that it crosses the red line at eight stocks. This was my basis (in 2005) for choosing a minimum of eight stocks in a portfolio – somewhat arbitrary – but my minimum requirement is that I want my portfolio to have no more volatility than an average stock. The blue line flattens out quickly by about 15 stocks. In a chart not shown here, a similar analysis on the 2008/09 data produces a minimum number of stocks of 13. The old rules of thumb appear to be back on track! But what happens to these results if the set of stocks is restricted to the ASX 50, ASX 100, or mid caps (stocks 51 to 100)? I show only the median volatility portfolios in Chart 2 for 2008/09. The chart for 2009/10 looks similar, except all volatilities are much, much lower.
The ASX 50 curve is below the ASX 100 everywhere – but more so in a relative sense for a larger portfolio. The difference between mid caps and the ASX 200 is very small. Indeed, the median volatility of a seven-stock (or more) portfolio selected only from the ASX 50 is lower than for any sized portfolio from the ASX 200. Adding
more small cap stocks does little to reduce portfolio volatility.
So what are the rules? The number of stocks should match your risk profile but a few simple rules of thumb flow from this analysis – and a modicum of common sense:
- Eight stocks seems a reasonable minimum in “good times”, and this should be increased in bad times – say to 13 or 15.
- No matter what your choice set, there is little to gain in a volatility sense by holding many more than 20 to 25 stocks from the ASX 200.
- Restricting your choice set to stocks from the ASX 50, or ASX 100, has sizeable diversification benefits that cannot be easily bettered by including a large number of smaller capitalised stocks.
- Using unequal weights has advantages when the weighting is in tune with volatility and correlation.
- Having regard to sector weights helps when those sector returns are less correlated than the returns within a sector.
- The “old rules” seem to still be working and didn’t need too much modification during the GFC.
- Portfolio construction isn’t for amateurs.