Diversification: Costs Can Outweigh Benefits

Pros and Cons of a Broadly Diversified Portfolio
Pros and Cons of a Focused Portfolio
An Illustrative Analysis
Portfolios of the Best-Performing Stocks
Portfolios of the Worst-Performing Stocks
The Upper and Lower Curves Converge
Opportunity Costs of Diversification
Opportunity Cost Summary
Benefits of Diversifying
Summary of Benefits
Conclusions and Recommendations

Much is said in the popular investing media about the benefits of diversifying a stock portfolio. Fund managers routinely extol the virtues of diversification to protect the investor's portfolio from volatility and paper and realized losses. Modern portfolio theory urges investors to diversify according to their level of risk. On the other hand, Warren Buffett tells investors to concentrate on stocks they know well. His "focus investing" approach leads investors to place bets on a few stocks with the expectation and hope of picking big winners. We urge the committed investor to achieve a blend of focus and diversity, and not accept either pure mode as appropriate to your situation and goals.

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Pros and Cons of a Broadly Diversified Portfolio

A broadly diversified portfolio has enough stocks in it so that its performance is highly correlated with the broad market or a selected sector index. For example, a very broadly diversified portfolio is one with all or most of the S&P 500 stocks. A broadly diversified sector portfolio is one that includes, for example, all the semiconductors stocks in the Philadelphia Semiconductor Index (SOX).

The advantages of a very broadly diversified portfolio are:

• One or a few poorly performing stocks do not significantly reduce the overall portfolio performance.

• It requires less active management, with fewer buy and sell decisions, and attendant lower costs.

• Performance is highly correlated with broad indices, either market or sector, and thus does well in a general up market.

• Performance will be no worse than the broad market or index.

The disadvantages of a broadly diversified portfolio are:

• An excellently performing stock does not significantly improve the performance of the portfolio, and thus large potential gains are missed.

• Performance is highly correlated with the broad market or sector, and thus does poorly in a down market.

• Performance will not be better than the broad market or index.

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Pros and Cons of a Focused Portfolio

A focused portfolio includes fewer stocks than a broadly diversified portfolio. Usually the focused portfolio includes 20 or fewer stocks. Of course, the number of stocks upon which you can focus is limited by your time and other resources. If you can focus on 20 or more stocks, you can have some of the benefits of diversity and focus combined.

The advantages of a focused portfolio are:

• An excellently performing stock significantly improves the performance of the portfolio.

• It may not be highly correlated with broad market or sector and therefore may do well in a down market.

• Performance may be considerably better than broad market or index.

The disadvantages of a focused portfolio are:

• A poorly performing stock significantly reduces the performance of the portfolio.

• It requires active management and may require frequent buy and sell decisions and costs.

• It may not be highly correlated with broad market or sector. It may not do well in an up market.

• Its performance may be worse than broad market or index.

Common sense suggests that if you consistently pick winning stocks, you don't need to own many stocks to achieve high returns. In fact, diversification can reduce your returns if you combine lower-performing stocks with your winners. However, if you have difficulty picking winners, you should add more stocks to your portfolio with the expectation that some of the additional stocks will improve the performance of your portfolio.

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An Illustrative Example

So the key questions you need to ask are:

• How many stocks should I own?

• What is the cost of adding stocks to my portfolio?

• What is the benefit of adding stocks to my portfolio?

• How much money can I spend to identify winning stocks?

The following examples help us answer these questions. We used stocks in the widely held DJIA as the database. The sample period was April 1991 to April 2001 and includes the monthly closing prices for each stock for the two dates. The price data were taken from BigCharts.com. Our method ranked the 30 DJIA stocks according to their 10-year percent gain, created different stock portfolios, computed their dollar values and then analyzed the best and worst performing portfolios.

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Portfolios of the Best-Performing Stocks

We ranked the 30 DJIA stocks in descending (highest to lowest) order according to their 10-year performance, and then computed the percent gain from April 1991 to 2001 for each DJIA stock as:

% Gain = (April 2001 stock price - April 1991 stock price)/April 1991 stock price

The next table shows the percent gains ranked from best to worst for the 30 stocks

Next, we created the best performing one-stock, two-stock, three-stock, and up to 30-stock portfolios. For example, the best one-stock portfolio included MSFT, the best-performing stock for the 10-year period. The best two-stock portfolio included MSFT and C, the two best-performing stocks. The third best-performing portfolio included MSFT, C and INTC. Finally, the last portfolio contained all 30 DJIA stocks.

Then, we computed the dollar value of each portfolio. For each portfolio, we "invested" $1,000 in April 1991 and then calculated the portfolio values for April 2001.

The next table shows the dollar value of each portfolio from best to worst. The Opportunity Cost column is discussed in Opportunity Costs of Diversification.

The value of the MSFT portfolio was $18,471. Because MSFT was the best performer for the 10-year period, no other portfolio of one stock had a greater value. In fact no other portfolio of any size had, or could have had, a greater value. Obviously, with perfect hindsight, diversity was a financial mistake.

The curve in the next chart shows the total value of each portfolio starting with the best-performing portfolio and ending with the portfolio containing all 30 DJIA stocks.

The first data point in the upper left-hand corner represents the highest value portfolio (MSFT). The next data point is for MSFT and C. Because these values are arranged in descending order, the upper curve shows decreasing dollar values when stocks are added to a portfolio.

This curve presents the highest possible value for each portfolio of a specific number of DJIA stocks. No other combination of DJIA stocks could have produced a larger value. This curve shows the stock selections of the very best stock pickers.

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Portfolios of the Worst-Performing Stocks

This section describes the performance of the worst-performing DJIA stocks. The procedures used in the section are the same as we used for the best-performing stocks. First, the 30 stocks were ranked in ascending order (lowest to highest) based on their 10-year percent gain. T was the worst performing stock followed by EK and IP. The next table shows the percent gains ranked from worst to best for the 30 stocks.

We then ranked the portfolios according to their total dollar values for April 2001. The first portfolio, the one-stock portfolio, included only the worst performing stock T. Next, the two-stock portfolio included the worst two performers, T and EK. The three-stock portfolio included the three worst performers T, EK and IP. The last portfolio included all 30 DJIA stocks.

The next table shows the dollar values of each portfolio from worst to best. The Benefit column is discussed in Benefits of Diversifying.

The curve of this chart shows the total value of each portfolio starting with the worst-performing portfolio and ending with the portfolio containing all 30 DJIA stocks.

The first data point in the lower left-hand corner represents the lowest value portfolio, which was T. The second data point is for the two-stock portfolio that included T and EK. Because the data for the chart were arranged in ascending order, the chart shows increasing values as stocks were added, one at a time, to a portfolio. This curve presents the lowest possible values for portfolios of differing number of stocks and is the lower limit of performance for all possible combinations of DJIA stock portfolios.

So the lower curve represents the minimum possible value of a portfolio for a given number of DJIA stocks. No other combination of DJIA stocks could have produced a smaller value. This curve includes the stock selections of the worst stock pickers.

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The Best and Worst Curves Converge

Notice the two curves in this chart converge toward the value of the 30-stock portfolio.

Because there are 30 stocks in DJIA, there is only one possible 30-stock portfolio. Recall the upper curve represents the maximum dollar value of each portfolio and the lower curve the minimum dollar values. Therefore, the value of every other combination of stocks for a given number of stocks must fall between the two curves. For example, the value of all 20-stock portfolios must fall between $6,929 and $2,951, the maximum and minimum dollar values for 20-stock portfolios. Most investors will have portfolios in this region. Only a few investors will own portfolios at the upper and lower boundaries.

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Opportunity Costs of Diversification

You sacrifice potential gain when you add poorer-performing stocks to a portfolio. The dollar amount you give up is called the opportunity cost and is a measure of the cost of diversifying a portfolio. It represents a dollar amount you had an opportunity to receive but chose not to. For example, if you selected MSFT, C, and INTC rather than only MSFT your opportunity cost is the value of the MSFT only portfolio minus the value of the MSFT, C, and INTC portfolio.

To compute the opportunity cost for different portfolios you subtract the value of the portfolio you chose from the value of the MSFT-only portfolio. Four examples of opportunity costs follow. The one-stock portfolio does not have an opportunity cost because is has only one stock. The two-stock portfolio includes MSFT and C. The addition of C to MSFT decreases the overall performance of the second portfolio by $1,108, which is the amount you gave up to diversify. The three-stock portfolio includes the top three performers, MSFT, C and INTC. The portfolio value on April 1, 2001 is $18,232. Therefore, the cost of diversifying was $1,794, or the value of the one-stock portfolio minus the value of the three-stock portfolio.

The opportunity cost of the most diverse portfolio is $13,213, the difference between the one-stock portfolio and the 30-stock portfolio. By choosing maximum diversification you gave up $13,213.

The next chart show the opportunity costs for each of the 30 portfolios.

Because the portfolios are arranged in descending order, the opportunity cost increases as you add lower performing stocks to the portfolio. This pattern indicates the obvious: if you add a new stock whose performance is worse than the worst performer in the existing portfolio, the overall performance of the portfolio decreases. Therefore, you should only add a stock to your portfolio if the stock increases the overall value of the portfolio. In other words the new stock must at least outperform the worst performing one stock in the existing portfolio. This also suggests that if you can pick winners, you need not include many stocks in a portfolio. In fact, adding low-performing stocks can significantly reduce you total gain.

The opportunity cost represents money you give up, and not money you actually lose. Therefore, you can use the amount of the opportunity cost as a measure how much money you can spend to find winners. For example, the opportunity cost for the three-stock portfolio was $1,794. Therefore, you could have spent that amount or less to educate yourself about the stocks you are considering. The opportunity cost for the 30-stock portfolio compared to the best performing one-stock portfolio was $13,213. Therefore, you could have spent up to that amount of money to find the best-performing stock.

Back to Opportunity Cost Table

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Opportunity Cost Summary

When the opportunity cost is large enough, you may decide to purchase information about stocks, visit companies, or hire a professional manager to increase your chance of identifying winners and realizing very large gains. The point is not that anyone can always pick the best performing stocks. But rather that concentrating your effort on picking good stocks can pay handsomely.

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Benefits of Diversification

This section describes how to calculate the benefits of diversifying a portfolio. These procedures use the worst-performing portfolios starting with the one-stock portfolio that includes T, the worst-performing stock. The benefit is the dollar gain you receive when you add a better-performing stock to a portfolio.

This chart shows the benefits of diversification.

The addition of EK to T increased the value of the two-stock portfolio by $23, which is the gain from diversifying. The three-stock portfolio included the three worst performers, T, EK and IP. The portfolio value was $1,001. Therefore, the gain from diversifying was $100, the value of the three-stock portfolio minus the one-stock portfolio.

Even diversifying doesn't help much if you keep picking losers. The 10- and 20-stock portfolios added gains over the worst one-stock portfolio were $1,015 and $2,050 respectively. The added gain of 30-stock portfolio was $4,357, the difference between the 30-stock portfolio and the one-stock portfolio. This gain was the largest of all the 30 portfolios.

If you want to be passive and spend little or no time searching for winners, then choose a diversified portfolio and accept smaller gains.

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Summary of Benefits

As you add better-performing stocks, the value of the portfolio increases. But in many instances the gain is small. The largest gain comes with the most diversified portfolio. Even if you add more stocks to your portfolio but consistently pick poor performers, you gain little from diversifying. Therefore, if you are not a good stock picker, diversify widely to increase the chance you include winners in your portfolio.

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