Passively managing individual stocks

In "Common Sense on Mutual Funds,"  Jack Bogle suggests that a reasonable alternative to an index fund for some investors would be to hold a well-diversified portfolio of individual stocks, as long as they are held long-term, with a minimum of trading costs incurred. This article outlines some suggestions for how to build a portfolio of individual stocks to cover at least part of one's overall stock allocation. It will also attempt to summarize the advantages and possible pitfalls of doing so.

Note that the discussion here assumes that one is not trying to beat the market, but rather, by passively managing individual stocks create a "DIY index fund."

Merits
So why might one want to do this?

Costs
An obvious advantage that individual stocks have over an index fund is an expense ratio (ER) of zero. Depending on what class of stocks one is trying to cover, this may or may not be a significant advantage in itself. In the case of single-country or -industry stocks, for example, where index funds often have ERs of 0.5% or more, the savings solely due to ER of using individual stocks would be more substantial than in the case of the broader S&P 500 index.

Taxes
Individual stocks present many more opportunities for tax-loss harvesting than do index funds. The potential advantage has been estimated to be equivalent to about 0.5%/year, depending on tax bracket. ***Expansion and Refs -- Andy?***

In the case of a US taxpayer living outside the US (but still subject to citizenship-based taxation): Given these constraints, such a person may find a portfolio of individual stocks the best way to cover, e.g., the domestic stock market of the country of residence.
 * Locally-domiciled index funds are treated as Passive Foreign Investment Companies (PFICs) by the IRS, which results in extremely unfavorable taxation; and
 * US-domiciled funds may not be available, may face unfavorable or double taxation in the country of residence, and/or may have high expense ratios (for example, single-country funds covering the country of residence).

Demerits
Why might one not want to do this?

Skewness
Individual stocks are generally observed to exhibit positive skewness, meaning that most stocks will have a somewhat lower return than the market average, with a few having much higher return.

Psychology
Owning individual stocks instead of an index fund is kind of like seeing how the proverbial sausage is made. Some of your stocks will rocket up, some will go out of business, and, due to the skewness mentioned above, the majority will underperform the market as a whole. The same things happen inside an index fund, of course, but hidden from view. While these gyrations can provide tax-savings opportunities, they also take some getting used to. Not everyone is of a mindset to watch the sausage production process in their portfolio with equanimity. Know thyself.

How many stocks?
There are several different ways to estimate how many stocks one should aim to hold at minimum.

Statman formula
Statman provides the following formula for the benefit $$B_{nm}$$ in terms of risk-adjusted return gained by moving from $$n$$ stocks to $$m$$ stocks:

B_{nm} = \left(\sqrt{\frac{\frac{1}{n}+\frac{n-1}{n}\rho}{\frac{1}{m}+\frac{m-1}{m}\rho}}-1\right)EP $$ where $$\rho$$ is the expected correlation between any pair of stocks, and $$EP$$ is the expected equity premium. (In his paper, he uses $$\rho$$ = 0.08, and $$EP$$ = 8.79%/year. ***Track down sources for these numbers -- Statman's paper seem to have a misattribution here***)

This formula assumes simple Gaussian return distributions with zero skewness (which is known not to be correct, as noted above), and requires the use of some assumptions about correlation and equity premium, but with those caveats in mind, it is useful to get a ballpark idea of the minimum number of stocks to aim for.

Let's take as an example an investor in Canada who is a US taxpayer, for whom the best non-PFIC alternative for covering Canadian stocks might be the iShares MSCI Canada ETF (EWC). EWC has $$m$$ = 97 stocks, and an ER of 0.49%. If the investor holds $$\ge n$$ individual Canadian stocks such that $$B_{nm} < 0.49%$$, that investor will come out ahead by holding individual stocks as compared to holding the ETF. Using the somewhat bold assumption that $$\rho$$ and $$EP$$ for the Canadian market are similar to the values Statman uses above for the US market, the investor expectantly comes out ahead over EWC after about 50 stocks.

For another example, a US taxpayer in Japan might consider iShares MSCI Japan ETF (EWJ) for Japanese equities, which has 317 holdings and 0.49% expense ratio. That investor would expect to come out ahead of EWJ after about 75 individual Japanese stocks.

For the above two investors, the minimum required number of stocks would go down if possible savings due to tax-loss harvesting are taken into account. However, since they both have to pay taxes to two different governments, and based on gains and losses calculated in two different currencies that float relative to each other, the tax-loss harvesting opportunities would likely be considerably reduced as compared to a taxpayer subject only to one country's tax code.

A US-based investor, on the other hand, might instead expect for tax-loss harvesting to provide a bigger benefit than ER savings. In comparison to an S&P 500 index fund such as the Vanguard S&P 500 ETF (VOO) with ER of 0.05%, if the expected tax savings from tax loss harvesting are 0.5%/year, that investor would expect to come out ahead of VOO after about 75 stocks. If the expected tax savings are 1%/year, that number falls to about 40 stocks. Similar considerations would apply to any investor based outside the US who is not also a US taxpayer.

Note that the minimum number of stocks according to this formula goes down for lower values of $$EP$$, and higher values of $$\rho$$.