Diversification Hypothetical

[shouldaindex]

Which is more diversified a portfolio of stocks?

A: Index Fund @ 50% and 5 stocks @ 10% = 100% of portfolio

B: 15 stocks @ 6.6% = 100% of portfolio

And why?

 

[DeepState]

Which is more diversified a portfolio of stocks?

A: Index Fund @ 50% and 5 stocks @ 10% = 100% of portfolio

B: 15 stocks @ 6.6% = 100% of portfolio

And why?

Insufficient information. Depending on the characteristics of each stock either A or B could be more diversified.

 

[sinner]

Which is more diversified a portfolio of stocks?

A: Index Fund @ 50% and 5 stocks @ 10% = 100% of portfolio

B: 15 stocks @ 6.6% = 100% of portfolio

And why?

Assuming we are talking about diversification against idiosyncratic risk compared to a benchmark equity index (because generally all equities are exposed to systematic and factor/other secondary risks*).

There has been some research on the marginal diversification benefit derived from adding another stock to the portfolio. From recollection I thought the number of stocks was about 30-40 before the marginal benefit begins to diminish.

A quick check through my notes furnished this:
http://blog.alphaarchitect.com/2014...wn-the-costs-and-benefits-of-diversification/

30-50 stocks seems to be a sweet-spot where an investor eliminates portfolio idiosyncratic volatility, as additional diversification beyond this point does not help reduce volatility in any dramatic way. However, by diversifying beyond 30-50 stocks, we also prevent our portfolio from concentrating on stocks we feel are “undervalued.” In other words, we probably want Warren Buffett to hold 30 or so stocks to ensure he doesn’t completely blow up, but we don’t want to force him to hold more than that, because it is unlikely he has more than 30 good ideas. In effect, he would be “diworsifying.”

fair bit of good info contained in the link.

So in answer to your original question, assuming we can modify the parameters of B to be "33 stocks @ 3%" then I would say that probably A will still be more diversified, however the modified B will likely be "sufficiently/efficiently" diversified and therefore more optimal**.

* (investors can diversify against systematic and secondary risks by investing in multiple asset classes - cash/credit, commodities, hedge funds, gold - and geographies)
** (given assumptions of a generalised investable universe of stocks)

 

[DaLong]

A common measures of concentration (the opposite of diversification) is the Herfindahl index.
https://en.wikipedia.org/wiki/Herfindahl_index

Alternatively a measure of idiosyncratic risk is the % of market cap of top x (e.g. 5) stocks.

For both measures your 15 stock portfolio will most likely have a higher level of diversification.

These are simplified measures and don't depend on the correlations in between your investments or individual level of volatility of your securities.

 

[So_Cynical]

15 stocks exposes you to more opportunity, takeovers, capital raisings etc, personally my 27 stock portfolio (mostly micro and small) has coughed up 2 deeply discounted SPP's in the last 5 months, giving away easy money, index and 5 stocks wouldn't do that as much, especially large caps, 14 stocks in my super fund (ASX300) boring as bat ****, nothing happens.