Passively managing individual stocks

From Bogleheads

Bogleheads generally accept that the best portfolios use passive management, low costs, wide diversification and aim for tax efficiency. The simplest way to achieve these is to use a low-cost passive index fund. However, you may find that constructing your own portfolio of individual stocks offers some cost or tax advantages, and these advantages may be enough to overcome any potential disadvantages from a less diversified portfolio.

In Common Sense on Mutual Funds,[1] John 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, and minimizing trading costs. This article outlines some suggestions for how to build a portfolio of individual stocks to cover at least part of your overall stock allocation. It also aims to summarize the advantages and possible pitfalls of doing this.

The discussion here assumes that you are not trying to beat the market, but instead passively managing individual stocks to create your own "DIY index fund."

Advantages

Holding a well-diversified portfolio of passively managed individual stocks instead of index funds may give you some cost advantages, and more opportunities for tax-loss harvesting and for donating appreciated assets.

US citizens living abroad can have special difficulties using index funds, and these may also make holding individual stocks a suitable option.

Costs

One obvious advantage that individual stocks have over an index fund is an expense ratio (ER) of zero. Depending on what class of stocks you are trying to cover, this may or may not be a significant advantage in itself. For example, index funds for single-country or single-industry stocks often have expense ratios of 0.5% or more, and here the saving from using individual stocks would be more substantial than for the broader S&P 500 index.

A hidden cost in mutual funds is the impact of turnover, because those costs are not reflected in the expense ratio. If you have a lower turnover than a comparable index fund, you will probably have lower turnover costs. And an index fund may be forced to trade, to track companies removed from or added to the index, while someone with a limited portfolio is not forced to make as many changes.

Taxes

Individual stocks offer many more opportunities for tax-loss harvesting than index funds. Estimates put the potential advantage at about 0.5%/year, depending on your tax bracket.[2][3]

If you have individual stocks you can find additional tax management benefits through donations, gifting and dividend yield management. The tax management section below discusses these in more depth.

US taxpayers abroad

In particular, if you are a US taxpayer living outside the US (but still subject to citizenship-based taxation):

  • US tax law treats almost all locally-domiciled and non-US domiciled index funds as a passive foreign investment company (PFIC), and this creates extremely unfavorable taxation; and
  • US-domiciled funds may not be available to you, or they may have unfavorable or double taxation in your country of residence, or they may have high expense ratios (for example, single-country funds covering your country of residence).

Given these constraints, US taxpayers living outside the US may find that a portfolio of individual stocks is the best way to invest.

Disadvantages

Although creating a portfolio of individual stocks has some advantages, keep the following in mind. An individual stock portfolio will be less diversified than the market portfolio, and will be exposed to the problem of market skewness. Also, a portfolio of individual stocks is likely to need more bookkeeping than investing in a total market index fund. Finally, empirical studies have shown that investors are susceptible to behavioral pitfalls that result in poor performance.

Diversification

By definition, any subset of stocks is less diversified than the whole market, and so exposes you to greater unsystematic risk.

Skewness

Individual stocks generally exhibit positive skewness, meaning that most stocks will have a somewhat lower return than the market average, with a few having much higher return. As noted by Bernstein[4] and many others, any subset of stocks is likely have a lower return than the whole market, due to failing to include some of the highest performers; that is, the median return is lower than the mean return.

Skewness is more pronounced in smaller stocks, so that a strategy of investing only in Large Capital individual stocks (and using mutual funds for diversification in other areas) tends to be less exposed to this issue.

Documentation

You will have to track more cost bases (see below) for a collection of individual stocks than for a single index fund, depending on how you made the purchases (for example, single lump-sum into the index instead of monthly purchases). In addition, individual stocks sometimes create taxable or other paperwork-generating events such as going private, getting bought out, going bankrupt and splitting. This is particularly the case with smaller cap stocks.

Behavioral effects

Owning individual stocks instead of an index fund is like seeing how the proverbial sausage is made.[note 1] Some of your stocks will rocket up, some will go out of business, and, because of the skewness mentioned above, the majority will underperform the market as a whole. Of course, the same things happen inside an index fund, but hidden from view. While these gyrations can give you opportunities to save tax, they also take some getting used to. Not everyone wants to watch the sausage production process in their portfolio with equanimity. Know yourself.

These difficulties are evident in empirical studies of the stock trading behavior of individual stock market investors. Odean and Barber have studied individual performance (beginning in 1991)[5] and stated of overconfident individual investors:[6]

[They] (1) underperform standard benchmarks (for example, a low cost index fund), (2) sell winning investments while holding losing investments (the "disposition effect"),[7] (3) are heavily influenced by limited attention and past return performance in their purchase decisions, (4) engage in naïve reinforcement learning by repeating past behaviors that coincided with pleasure while avoiding past behaviors that generated pain, and (5) tend to hold undiversified stock portfolios. These behaviors deleteriously affect the financial well being of individual investors.

— Odean and Barber[8]

How many stocks?

There are several different ways to estimate the minimum number of stocks you should aim to hold. A few approaches found in the academic literature are discussed here. While none of the papers discussed below provide a definitive answer to that question, they may help to give you some ideas.

Meir Statman

Meir Statman[9] provides the following formula for the benefit in terms of risk-adjusted return gained by moving from stocks to stocks:

where is the expected correlation between any pair of stocks, and is the expected equity premium. (In his paper, he uses = 0.08,[note 2] and = 8.79%/year.[note 3])

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.

Taking 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 = 97 stocks, and an ER of 0.49%/year. If the investor holds at least individual Canadian stocks such that < 0.49%/year, that investor will have a higher expected risk-adjusted return by holding those individual stocks than by holding the ETF.[note 4] Using the somewhat bold assumption that and 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%/year expense ratio. That investor would have a higher expected risk-adjusted return than 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, 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%/year, if the expected tax savings from tax loss harvesting are 0.5%/year, that investor would expect to come out ahead of VOO on a risk-adjusted basis 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 5]

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

Meir Statman's formula implicitly assumes portfolios of equally-weighted stocks. For a capitalization-weighted index, the effective number of stocks would be less than the actual number, because the fluctuations of the largest capitalization stocks contribute much more to the overall portfolio volatility than to those of the smallest capitalization stocks (though this would be partially counterbalanced by the higher individual volatilities of smaller-capitalization stocks). If you are comparing a roughly equal-weighted portfolio to a capitalization-weighted index fund, substituting the effective number of stocks in the index for the actual number would produce a somewhat lower suggested minimum number of individual stocks to hold. On the other hand, accounting for skewness should lead to an increase in the suggested minimum number of stocks to hold.

Ronald Surz and Mitchell Price

Ronald Surz and Mitchell Price (2000)[10] examine diversification measures such as R-squared and tracking error for US individual stock selections over the January 1986 - June 1999 period.

Over this period the overall market experienced a standard deviation of 14.5%. A single stock portfolio provided an average standard deviation of 45.0%; a fifteen stock portfolio averaged 16.5% (range 14.3% - 19.2%); a thirty stock portfolio averaged 15.4% (range 13.9% - 17.5%); a sixty stock portfolio averaged 15.2% (range 13.6% - 17.2%).

While one individual stock has a standard deviation of 45% and the entire market has 14.5%, portfolios of 30 stocks are shown to eliminate 97% of the excess (diversifiable) standard deviation. A 60 stock portfolio eliminates 98% of excess standard deviation.

Ronald Surz and Mitchell Price found that increasing the number of stocks in a portfolio increased the portfolio's R-squared and reduced portfolio tracking error.[note 6] The authors suggest two methods for reducing tracking error over random stock selection:

  1. Professional money managers can use portfolio optimization.
  2. A less sophisticated approach can invest in the largest capitalization stocks.

David Ikenberry, Richard Shockley and Kent Womack

David Ikenberry, Richard Shockley and Kent Womack[11] use historical backtesting over the 34-year period from 1962 through 1995 to examine the impact of skewness, which they measure as the difference between the mean and median yearly average return for an n-stock portfolio, for several values of n from 15 to 150. They found that for 35-stock portfolios, where the stocks are randomly chosen from the S&P 500 index and equally weighted, the average yearly median portfolio return lags the mean by 0.22%. This number goes down to 0.14% for 50-stock portfolios, 0.09% for 75-stock portfolios, 0.06% for 100-stock portfolios, and 0.03% for 150-stock portfolios. The skewness cost is somewhat lower for capitalization-weighted portfolios, and for equal-weighted portfolios where the probability of selecting a stock is proportional to its market capitalization. For more details, see Table V and Figure 2 of their paper.

They do not find evidence of any systematic return penalty for sub-sampling the S&P 500 index. (However, they are not comparing risk-adjusted returns, just straight returns, so their results cannot be directly compared with, for example, Meir Statman's formula.) They find that for the portfolios where the holdings are capitalization weighted, or equally weighted but selected with a probability proportional to capitalization, the yearly mean and median returns slightly exceed the return of the S&P 500 index itself, though not by statistically significant amounts (about 1-sigma in standard deviation of the mean, if calculated using the yearly numbers in their Table II). They also find that equal-probability, equal-weighted portfolios show about a 2.5% boost in mean and median returns compared to the capitalization-weighted portfolios, and slightly more compared to the S&P 500 index itself. This is only a little over a 2-sigma effect (again, calculating from their yearly numbers in Table II), but suggests the presence of a measurable small-cap premium even within the confines of the S&P 500 universe.

Dale Domian, David Louton and Marie Racine

Dale Domian, David Louton and Marie Racine[12] use historical backtesting over the 20-year period from Jan 1985 to Dec 2004 to study the effect of the number of stocks in a portfolio on shortfall risk. They created equal-weighted portfolios from a universe of 1000 stocks, consisting of the 100 largest companies in each of 10 industries, covering 82% of the capitalization of the total market. They calculate ending wealth distributions for random buy-and-hold portfolios of varying numbers of stocks. Using a 1% chance of underperforming US Treasuries over that time period as criterion, they state that at least 164 stocks are needed.

In the context of the present discussion, a more apt comparison might be with the return of a cap-weighted index fund covering that universe. For nearest comparison purposes, the 20-year cumulative return of the MSCI US Large and Mid cap index[13] turned one dollar invested over that same period into $11.96, for an annualized return of 13.2%. Looking at Figure 3 of their paper (Wealth per dollar of initial investment), it can be seen that a 30-stock portfolio had just over a 50% chance of beating the index, a 50-stock portfolio over 55%, and a 100-stock portfolio about a 65% chance. These results presumably reflect the effect of a small-cap premium within the 1000-stock universe.

These results do not consider costs. If a cost advantage of 0.5%/year is expected from individual stocks over an index fund tracking the index, the ending value of one dollar in the index with an annualized return of 12.7% (= 13.2%-0.5%) becomes $10.94, at which point a 20-stock portfolio has a greater than 50% chance of beating the index fund. A 30-stock portfolio then has close to a 60% chance of coming out ahead, a 50-stock portfolio better than 65%, and a 100-stock portfolio has better than 75% chance of outperforming the index fund.

Of course, the magnitude of possible shortfalls should also be taken into consideration. Figure 3 shows how that magnitude grows with decreasing numbers of stocks.

Summary

In general, the answer to "how many stocks are recommended?" is, of course, as many as practically possible. Holding fewer stocks increases unsystematic risk and the effect of skewness on final portfolio value. Holding stocks in equal weights can pick up some small-cap premium, but remember that this also increases volatility. There is no free lunch.

As a rule, reducing the number of stocks held is always a negative when it comes to risk/reward ratio. Lower costs, from reduced expense ratios and increased tax savings, are the only guaranteed benefit. The trick is to figure out where the benefit balances out the increased risk. This is a personal decision.

Portfolio construction

How to choose stocks?

Some potentially useful factors to consider in choosing stocks are:

  • Size (capitalization)
  • Value (book-to-market ratio)
  • Industry (at least early on)
  • Liquidity (for smaller stocks)
  • Dividend rate (for tax management purposes)

Size and value loadings and industry classification are of interest if you are trying to match or tilt away from market weights. Size and value are established Fama-French risk factors, which some investors like to tilt towards or away from. Dale Domian, David Louton and Marie Racine (see above) found that diversification across industries helped reduce dispersion of returns for small portfolio sizes, though it becomes less important for larger numbers of stocks held. Industry classification may also be of interest if you already have too much exposure to the risk of a certain industry through work, and want to reduce your portfolio's exposure to that industry. Low liquidity can be a problem in very small-cap stocks, leading to larger bid-ask spreads. Dividend yield may be of interest if you want to minimize your current taxable income.

Some other factors which have support in the academic literature are momentum, profitability, and low-beta. If you are interested in pursuing these tilts you may find individual stocks can do this, in the absence of easily-available index funds that incorporate those tilts.

If the Efficient Market Hypothesis holds, then reading balance sheets, shareholder reports and analyst recommendations is unnecessary and a complete waste of time. The strategy you use for deciding which exact stocks to hold should not matter -- you can neither help nor hurt yourself through choice of strategy. Random selection is a perfectly valid strategy, although it is not much trouble to select stocks from different industries so that you have a reasonable diversification across sectors and industries.

Weighting

The easiest way for you to buy stocks is in roughly equal weights -- for example, by buying equal-sized amounts of new stocks every month with new money. This will typically lead to a significant small-cap tilt in the portfolio if you choose stocks more or less at random. If you do not want exposure to the size factor, then David Ikenberry, Richard Shockley and Kent Womack found that weighting your stocks by relative market capitalization to yield median returns very close to the overall (capitalization-weighted) index (see above). As a practical matter, this leads to huge disparities in stock holding sizes for an individual investor, and is difficult to maintain as new money is added to the portfolio. An alternative is to buy equal dollar amounts of each stock, but weight the probability of buying a stock in proportion to its market capitalization; David Ikenberry, Richard Shockley and Kent Womack found that this generates results that are statistically indistinguishable from weighting individual holdings in proportion to market cap.

Tracking error

With smaller portfolios, you will experience "tracking error". This is the effect in which your returns in any one period differ from the entire market. While your long-term returns should be similar to the market, in any individual period you will see differences. The best example of this is when comparing US stock returns to international stock returns. Both may have the same long-term returns, but in any one year the returns will certainly differ.

If you compare international returns to a US benchmark index, you will see a difference each year and that would be tracking error. If you build a portfolio of US large cap stocks and compares the yearly results to the S&P 500, you will see a difference each year. Over the long-term the cumulative results should be similar, but in any given year there will be a difference. Ronald Surz and Mitchell Price address tracking error and they indicate that random portfolios of 15 stocks should expect a tracking error of 8.1%, which reduces to 6.2% for a 30-stock portfolio and 5.3% for a 60 stock portfolio. They also indicate that by constructing the portfolio with a focus on balance among industries will reduce the tracking error to 5.4% (15 stocks), 4.2% (30 stocks) and 3.5% (60 stocks).

Tracking error is harmless to the disciplined long-term investor. Over time, you will generate the same cumulative returns as your benchmark index since your portfolio has the same risk characteristics.[14] However, some investors may be alarmed to see tracking error, especially in years when their small portfolio underperforms the benchmark index.

Transaction costs

To minimize transaction costs (commissions and bid-ask spreads), it is best to avoid turnover as much as possible. For example, if you are considering tax loss harvesting then you should only do this if your tax benefit significantly outweighs your transaction costs.

One of the results that Dale Domian, David Louton and Marie Racine (above) found was that rebalanced portfolios have lower terminal wealth dispersions. However, besides incurring extra transaction costs, rebalancing systematically would create immediate taxable gains, so it is probably best avoided outside of a commission-free and tax-free situation. An exception might be if a single stock grows to become a significant fraction of the size of the portfolio all by itself; in this case, selling off some losing positions along with paring down the excess position can help minimize the tax impact.

Tax management

If you have individual stocks, you can cherry-pick the big winners and the big losers for tax management, while the index fund investor can only choose to buy, sell or donate the fund at today's net asset value (NAV) (which reflects the net of winners and losers). The individual stock investor will cherry-pick out the largest gainers and use those for more tax-efficient donations.

For example, if you plan to donate $2,000 to a charity, you can donate shares worth $2,000 (with a cost basis of $500) and pay no capital gains tax on that appreciation. The alternative is to sell the shares, realize a capital gain of $1,500 and pay $225 in income tax, leaving less money for charity or other purposes.

Another alternative is to gift highly appreciated shares to children. The child can often sell the shares and pay no capital gains tax, or pay tax at a lower rate than the parent. Donating or gifting the biggest gainers helps to rebalance the portfolio, so that the largest holdings do not further impair diversification.[note 7]

When death is imminent or foreseen, holding appreciated stocks may be useful, because appreciated assets qualify for a step-up in basis to market value, which greatly reduces, or even eliminates, the beneficiary's tax liability upon sale.

If you hold taxable accounts, you may want to minimize the dividend yield for tax efficiency, as realizing appreciation through capital gains is often more tax efficient than realizing the stock returns through dividends.[note 8] An index investor must accept the dividend from the portfolio held by the index fund, while an individual stocks investor might prefer low-dividend or no-dividend stocks for their portfolio (as a general proposition, value stocks pay higher dividends than growth stocks).[note 9] A note of caution - it is not realistic to construct a portfolio with a 0.0% dividend yield, since there are not enough no-dividend companies in diverse industries and sectors to build a reasonably diversified portfolio.

As noted above, the most powerful tax management tool is tax loss harvesting, and if you hold individual stocks you can cherry-pick the losers from your portfolio and sell them for tax losses. You can use tax losses to offset capital gains, or (preferably) as a deduction against ordinary income of up to $3,000 per year. If your tax losses are greater than $3,000, you can carry over the remainder to be used in the following years. Unused carryover tax losses only expire after the death of the stockholder.[note 10]

Controlling - meaning avoiding or minimizing - capital gains is also a tax management strategy. Tax losses are most valuable when you use them to reduce your ordinary income. These tax loss benefits typically accrue at higher tax rates, up to the maximum tax rate. When and if you generate any capital gains, these gains cancel out your banked tax losses, and this benefit is only at the capital gains rate (typically only 15%).

You can minimize capital gains using several tactics. An index mutual fund must sell shares when the company is removed from the benchmark index, but an individual investor is not forced to sell for that reason. As a result, an individual stock investor can realize a lower turnover and lower capital gains. If you use charitable donations to help rebalance, this also serves to minimize realized capital gains. Using new money to help rebalance is another strategy to minimize realizing capital gains.

Although it is possible to manage realizing gains, it is probably not practical to assume the individual stock investor will never have capital gains, as companies are periodically taken over in cash transactions. In addition, it may be worth realizing capital gains if rebalancing is truly necessary and there are no other viable alternatives (such as using new money or charitable donations).

After many years of tax management, you might end up with a portfolio with some shares that have little appreciation and some with greater appreciation. Those with little appreciation are perfect candidates to use in situations where you have a cash flow need, but want to avoid moving into a higher tax bracket. You can sell shares with little or no gain for cash flow without any impact on income taxes. In that sense, selling those stocks is identical to withdrawing funds from a Roth IRA.

Record keeping

The minimum records that you need to keep are the same as those for index funds: cost basis and date of each purchased lot, for eventual tax reporting purposes. For tax management purposes, it is also helpful to track your current unrealized gain or loss. The records your brokerage maintains may be enough.

If you want to track your performance against an index fund, it is straightforward to add an automatic lookup for the current price of that fund, and have the spreadsheet calculate how much a particular lot is worth as compared to what the same amount of money invested in the index fund would have been worth.

What is not so straightforward is accounting for dividends. If your dividend yield is similar to that of the fund, then comparing prices only may be sufficient. Otherwise, differences in dividend yield between the portfolio and the index fund will contribute to (apparent) tracking error. If this is a concern, you may need to manually account for dividends.

US taxpayers abroad

A US taxpayer abroad will need to keep this information in two different currencies. A convenient way to do this is to set up a spreadsheet with a line for each lot, with columns for purchase date and cost in the currency used for purchase, number of shares, exchange rate, and a calculated column for the purchase price in the other currency. Current prices and exchange rates can generally be automatically updated from the internet, and current gain or loss for each position automatically calculated in both currencies.

A little knowledge of spreadsheet programming is required, but once set up, the majority of the ongoing maintenance is just to add a new line whenever a new purchase is made. When a stock is sold or is delisted, the "current price" can be frozen to the sale or final price, and the line moved to a different area of the spreadsheet for historical tracking purposes. If a stock splits, you will need to update the number of shares.

Notes

  1. This is an idiomatic phrase, meaning that knowledge of the underlying process may be unpleasant.
  2. Estimate for 1997 from p. 23 of John Y. Campbell, Martin Lettau, Burton G. Malkiel, and Yexiao Xu, Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk(2001).
  3. The "mean realized equity premium during 1926-2001." But, he also notes, "today there is little agreement that it is a fair estimate of the expected equity premium. Fama and French (2001) estimated the expected equity premium based on P/E ratios and dividend yield. The average of the two is 3.44%." See Fama, Eugene F. and French, Kenneth R., The Equity Premium (April 2001). EFMA 2001 Lugano Meetings; CRSP Working Paper No. 522. Available at SSRN.
  4. This considers only the difference in ER, and ignores any difference in commissions between buying individual stocks and buying EWC, currency exchange costs incurred to buy EWC (which itself incurs hidden exchange costs internally), any unfavorable tax implications there may be on the Canadian side due to holding an offshore-domiciled ETF, weighting differences, skewness effects, tax loss harvesting, etc.
  5. Or, perhaps, an Eritrean taxpayer, Eritrea being the other country, besides the US, that taxes its non-resident citizens.
  6. Ronald Surz and Mitchell Price find that for random 15-stock portfolios R-squared averaged 0.76 (range 0.63 - 0.86); for 30-stock portfolios the average was 0.86 (range 0.76 -0.91); for 60-stock portfolios, an average of 0.88 (range 0.79 - 0.94).
    Tracking errors for random portfolios: 8.1% for 15-stock portfolios; 6.2% for 30-stock portfolios; 5.3% for 60-stock portfolios.
    Tracking errors for optimized portfolios: 5.4% for 15-stock portfolios; 4.2% for 30-stock portfolios; 3.5% for 60-stock portfolios.
    Tracking errors for portfolios selecting the largest stocks: 7.5% for 15-stock portfolios; 5.2% for 30-stock portfolios; 4.1% for 60-stock portfolios.
  7. US investors with charitable desires have a number of additional options for bequests outside of direct gifting. These can include establishing s donor advised fund for deferred gifting, or if an income from the contributed asset is still desired, from a split-interest gift, which could include the following:
  8. For US passive investors in the lower tax brackets, like capital gains, annual streams of qualified dividends are taxed at zero percent. However, these dividends are still subject to state income tax. Capital gains can be deferred until the stock is sold.
  9. Vanguard value and growth index funds show the basic tendency of value stocks to provide higher dividends than growth stocks. See Principles of tax-efficient fund placement for data.
  10. Capital losses and carry over losses (the $3,000 annual limit) must be deducted on a decedent's final tax return and remaining carryover losses cannot be carried over in the following years. See Publication 544, Sales and Other Dispositions of Assets, IRS

References

  1. John Bogle. Common Sense on Mutual Funds. pp. 373–401. ISBN 978-0-470-13813-7.
  2. Robert D. Arnott; Andrew L. Berkin Ph.D; Jia Ye Ph.D (2000). "Tax Management and Mismanagement of Taxable Assets" (PDF). First Quadrant. Archived from the original (PDF) on October 18, 2006.
  3. Robert D. Arnott; Andrew L. Berkin Ph.D; Jia Ye Ph.D (2003). "Tax Management, Loss Harvesting, and HIFO Accounting" (PDF). First Quadrant. Archived from the original (PDF) on October 18, 2006.
  4. William Bernstein (2000). "The 15-Stock Diversification Myth". Efficient Frontier. Retrieved November 13, 2023.
  5. Brad M. Barber; Terrance Odean (May 1998). "The Common Stock Investment Performance of Individual Investors". Retrieved November 13, 2023. Available at SSRN.
  6. Brad M. Barber; Terrance Odean. "The Courage of Misguided Convictions: The Trading Behavior of Individual Investors". Retrieved November 13, 2023. Available at SSRN.
  7. Terrance Odean (December 1997). "Are Investors Reluctant to Realize Their Losses?". Retrieved November 13, 2023. Available at SSRN.
  8. Brad M. Barber; Terrance Odean (September 7, 2011). "The Behavior of Individual Investors". Retrieved November 13, 2023. Available at SSRN.
  9. Meir Statman (October 2002). "How Much Diversification is Enough?". Retrieved November 13, 2023. Available at SSRN.
  10. Ronald J. Surz; Mitchell Price (2000). "The Truth About Diversification By Numbers" (PDF). Journal of Investing. Archived from the original (PDF) on December 1, 2023.
  11. David L. Ikenberry; Richard L. Shockley; Kent L. Womack. "Why active fund managers often underperform the S&P 500 index: The impact of size and skewness" (PDF).[dead link]
  12. Dale L. Domian; David A. Louton; Marie D. Racine (April 2006). "Diversification in Portfolios of Individual Stocks: 100 Stocks are Not Enough". Retrieved November 13, 2023. Available at SSRN.
  13. "Index Performance". MSCI.
  14. Craig Israelsen (October 2012). "Looking at how different indexes affect performance". JOI. Archived from the original on January 17, 2019.

External links

Bibliography