How many stocks does it takes to have a well-diversified equity portfolio?
Adding more stocks to a portfolio causes the portfolio's volatility to decline ever closer to that of the market.
By continuing to add stocks at random, we can get the portfolio volatility as close as we want to that of the market and Investors often conclude that, at some point, the portfolio's volatility is "close enough" to that of the market, and the portfolio is therefore well diversified. All that remains is for each investor to decide what "close enough" looks like.
Today, investors can easily own a portfolio that is very close to a well-diversified, well-constructed market index. In other words, a very close approximation of a true "market" portfolio is available to most investors. In fact, it is probably cheaper for many investors to own a broadly diversified market portfolio than a highly concentrated, poorly diversified portfolio. If the diversification benefits of a market-like portfolio are readily available at a reasonable cost, why should anyone own fewer stocks?
Many investors would respond to this question by saying that there are only so many undervalued stocks, and those are the only ones that they want in their portfolios. This leads to concentrated portfolios, but they are willing to incur the resulting higher risk because they see the possibility of higher returns through security selection. The assumption underlying this response is that the investor has the ability to generate enough additional return to more than compensate for the lost diversification benefits.
How good at security selection would an investor have to be in order to accomplish this?
In studies, 10-stock portfolio would require an expected monthly return 28 basis points higher than the market index, and a 50-stock portfolio would need an additional 10 basis points per month. These monthly numbers correspond to annual above-market performance of about 3.4%pa and 1.2%pa, respectively. Since the typical professionally managed equity portfolio lags the market after expenses, these seem to be high hurdles that would be very difficult for most investors to clear. As we add more stocks the hurdle becomes lower. However, since the majority of professionally managed portfolios have trouble clearing an excess return hurdle of zero, achieving even a small positive excess return should not be seen as a trivial task.
These estimated excess returns are probably understated, for two reasons. First, the portfolios of many investors are concentrated in just a few sectors, in addition to containing relatively few stocks. By concentrating in certain sectors, portfolios lose additional diversification benefits. The other reason is related to turnover. The search for undervalued securities tends to increase portfolio turnover, since it is necessary to sell stocks that are no longer seen to be undervalued, replacing them with a new set that the investor believes to currently be undervalued. Since turnover is costly, additional returns must be generated to cover the costs.
Of course it's not necessary to be a good stock picker in order to generate a higher Sharpe ratio than the market. Studies of historical returns tell us that portfolios of value stocks have accomplished this feat on average. While this is true, it is not necessary to give up diversification benefits in order to achieve a value bias. Asset class tilts do not require investors to hold concentrated portfolios.
What about the well documented benefits of international diversification?
For the January 1970-May 2008 sample period, the monthly standard deviations of a Value-Weighted Index of US stocks and the MSCI EAFE Index were 4.49% and 4.71%, respectively. However, the monthly standard deviation of a 50/50 combination of the two was 4.07%. International diversification has the potential to substantially reduce portfolio volatility. Therefore, a well-diversified portfolio should contain stocks from multiple countries. To maximize the potential diversification benefit, holdings should be diversified across continents and industries, and they should include both developed and emerging markets.
There are currently tens of thousands of publicly traded stocks around the world 11,000 represents a good slice of global capitalism but even this many does not really represent the whole "market"
But of course true diversification really means investing in different asset classes.
The post-mortem on the global financial crisis is raising the question in some minds about whether it is time to read the last rites for diversification — the principle that you reduce your investment risk by spreading it around.
Among the would-be mourners are critics who say the diversification principle failed spectacularly for investors just when they needed it the most — during the biggest market meltdown seen in generations.
After all, the idea behind diversification is that no two investments perform in exactly the same way at the same time. By mixing up the asset classes in your portfolio and diversifying within those asset classes, the idea is that you provide yourself with a cushion or shock absorber in the down times.
But then came the financial crisis of 2008 and suddenly there seemed to be no safety net. Just about every asset class — apart from government bonds and cash — got walloped. In the jargon of financial economists, those asset classes appeared to become much more "correlated".
But the appearance of rising correlations does not necessarily mean that diversification does not work. And you can prove that by considering what might have happened if investors had been less diversified than they could have been.
It's a point made by Dartmouth Tuck School of Business finance professor Ken French.
"Diversification still works," French explains, "and investors would have had even more uncertainty about the return on their portfolios if they had been poorly diversified."
French points out that diversification does not eliminate the volatility of the overall market. What it does do is protect against the additional volatility arising from the characteristics of individual firms or asset classes.
"It's that extra volatility that you don't have to have if you diversify well."
On the question of rising correlations in highly volatile markets, French notes that the return on any asset comprises two components — the market return itself and the return attributable to the specifics of the individual asset.
During the extreme volatility of 2008, the market movement became proportionately much more influential so that it appeared that individual stocks and asset classes appeared to be much more lined up with each other.
"What matters when we think about diversification is the firm-specific pieces, not the market piece," French says. "And we know that in these volatile periods, the firm-specific pieces also get bigger. So while it may look like the benefits of diversification have gone down, they have actually gone up."
These differences in the firm-specific variation in returns are what financial economists call "cross-sectional dispersion". And it is well established that just as market volatility tends to spike after periods of negative performance, so do the cross-sectional dispersions.
What this all means for investors is that the need for broad diversification both across and within asset classes becomes even more important at times of high volatility.
Reports of the death of diversification have been greatly exaggerated.