This question has been asked in a number of Blog Posts and we pussy-foot around it because there really is no definitive answer. On the one hand we need enough to give us an adequate level of diversification (whatever that means) to reduce volatility (risk) while keeping our commissions, management costs and fees to a minimum.
We maybe start out by thinking of diversification as “more is better”, progress to thinking of it in terms of different asset classes (Equities, Bonds, REITS, Commodities, Metals,…etc), then, recognizing that even this does not necessarily guarantee that we are diversified, we may look closer at correlations and “clustering”.
Also, we all have different investment styles – Strategic Asset Allocation (SAA) requires us to make discretionary decisions as to which assets to hold and the allocation to be made to each asset – Portfolio Optimization reduces the discretionary limits to a degree and calculates “recommended” allocations to different assets/asset classes – momentum tends to dominate diversification decisions to some extent and leave the discretionary decisions to allocation weightings.
I recently found the following figure in one of Gary Antonacci’s articles on “Key Momentum Factors”.
This shows that portfolio volatility drops rapidly (exponentially) as we increase the number of assets from 1-5, but that adding more assets beyond this level has little impact. On the other side of the equation, returns (based on momentum) tend to drop in a more linear manner – thus there will be an optimal balance in terms of return/risk – this provides a good explanation for the excellent performance of the Feynman Max4 Portfolio.
Let me play Devil’s Advocate and suggest that (from a “scientific” point-of-view) it may not be advantageous to construct portfolios containing more than 4 or 5 assets (remembering that these assets are already “diversified” ETFs).
This should be good for discussion – please don’t “shoot the messenger”, remember I’m playing Devil’s Advocate – disclosure – I don’t (presently) have any portfolios with so few assets.