This isn't true.

I think that most people believe, implicitly or explicitly, that diversified portfolio is balanced with respect to risk. In other words, diversification has a general meaning that most people intuitively grasp ("don't put all your eggs in one basket"),

Without relying too heavily on theory, let's take a look at three charts the represent a stereotypical "balanced" portfolio: 60% stocks (VTSMX) and 40% bonds (VBMFX). Results are a backtest from Portfolio Visualizer from 01/2011 to 05/2018 (link at the end of this post).

- The piechart on the left shows the portfolio in proportion to its dollar VALUE.

- The piechart in the middle shows the portfolio in proportion to the dollar RETURNS over the past five years or so.

- The piechart on the right shows the portfolio in proportion to the RISK each asset contributed.

You can easily and quickly see that, from a risk perspective, the 60/40 portfolio is far from balanced: virtually all the risk is coming from one asset. I can't imagine anyone looking at the risk profile of this two-fund portfolio and concluding that there is no room for improving the diversification of risk.

The Vanguard Total Stock Market Index fund contains almost entirely U.S. large cap stocks. It holds many of them, in many different sectors, in proportion to their market capitalization, but represents only a slice of the variety of investable companies. VTSMX has virtually no exposure to the risk and style factors (small companies, value companies, quality companies, low beta stocks, etc.) that economists have identified as offering excess returns or having relatively low correlations with large cap U.S. stocks.

Likewise, the Vanguard Total Bond Market Index fund represents an impressive portfolio, but it does not have the level of exposure to credit risk and term risk it needs in order to balance the stocks held in VTSMX.

Making some changes aimed at diversification (replacing Total Bond Market Index with a long-term bond ETF and adding two small cap ETFS, one invested in U.S. companies and one in non-U.S. companies) makes a dramatic difference to the concentration of risk in this portfolio.

There is no single quantitative definition of diversification that is equivalent to the Sharpe ratio (which represents the highest risk-adjusted expected return of any combination of risky assets and is presumed to be mean-variance optimized), but there are several measures that offer some utility: diversification ratio, minimum variance, inverse volatility, and effective numbers of bets.

I think, for advanced individual investors, the diversification ratio offers a balance of utility and ease of understanding. It basically measures the average volatility of each asset in the portfolio to the overall volatility of portfolio, and the higher the number the better the assets are working together to offset risk. The lowest possible figure is 1.0, and for portfolios of publicly traded stocks and bonds it would be hard to get the ratio above 2.0 (though higher numbers are theoretically possible).

The two-fund version of the 60/40 portfolio above has a diversification ratio of 1.19 while the four-fund version has a diversification ratio of 1.60, a significant improvement.

The diversification ratio also has the benefit/disadvantage of being agnostic to expected returns: it is constructed based entirely on volatility and correlation measures. It does not incorporate either historical returns or expected returns, which makes it less likely than a mean-variance measure (like the Sharpe ratio) to overweight last year's winners.

Link to Portfolio Visualizer backtest: https://www.portfoliovisualizer.com/bac ... tion8_2=40