Articles for Financial Advisors

Risk-Return Characteristics of a 100 Stock Portfolio

Risk-Return Characteristics of a 100 Stock Portfolio

A 2004 AAII Journal article by Daniel Burnside, How Many Stocks Do You Need to be Diversified, points out even a 100-stock portfolio will have a high level of return deviation: “a single security selected at random would have an average tracking error in its monthly return of 5.5% from a cap-weighted index…even a portfolio of 100 stocks will deviate from its target index by an average of 0.60% per month for the value-weighted approach...corresponds to an annualized deviation of ~ 2.1%.”

 

Table 2 shows the period of time analyzed can greatly alter monthly tracking error (standard deviation) of a stock portfolio. For example, a 100-stock portfolio had an average monthly tracking error of 0.4% from 1960-1966 vs. 0.9% from 1995-2001. Table 2 shows diversifiable risk increased over the 42-year period (1960-2001).

 

Table 2

Monthly Tracking Error for Cap-Weighted Stock Indexa

 

Stocks in portfolio

Each Period is 84 Months

1960-66

1967-73

1974-80

1981-87

1988-94

1995-01

1

3.9%

5.0%

5.5%

5.8%

5.1%

7.7%

5

1.9

2.4

2.6

2.7

2.5

3.6

10

1.3

1.7

1.9

2.0

1.8

2.6

20

0.9

1.2

1.3

1.4

1.3

1.9

65

0.5

0.7

0.8

0.8

1.7

1.1

100

0.4

0.6

0.6

0.6

0.6

0.9

aAll data in the table comes from the Burnside July 2004 article.

 

According to Burnside (2004): “…investors may view volatility as the typical amount by which a portfolio’s return will deviate from long-term averages. A single-stock investor will experience annual returns averaging a whopping 35% above or below the market—with some years closer to the market and some years further from the market. As a rule of thumb, diversifiable risk will be reduced by the following:

 

  • Holding 25 stocks reduces diversifiable risk by ~ 80%,
  • Holding 100 stocks reduces diversifiable risk by ~ 90%, and
  • Holding 400 stocks reduces diversifiable risk by ~ 95%.

 

All of these reductions are compared to the risk of holding one stock. A single stock’s tracking error of ~ 40% would be reduced to ~ 8% if you hold 25 stocks, 4% if you hold 100 stocks and 2% if you hold 400 stocks.”

 

Burnside does not recommend portfolio diversification using a stock index if each stock has the same weighting, referred to as an equal-weight index: “an equal-weighted portfolio of every U.S. stock will behave primarily like a small-cap fund, since ~ 3% of the holdings would be large cap, ~ 12% would be mid cap and ~ 85% would be small cap (and small cap would be dominated by micro caps).” Moreover, if an equally weighted stock portfolio was used, tracking error would be ~ 50% > the tracking error shown in Table xx. For example, from 1960-1969, monthly tracking error for a 100-stock portfolio was 0.4% using a cap-weighted index but 0.7% for a 100-stock portfolio based on an equally-weighted stock index (not shown in a table); 0.9% for the period 1995-2001 (cap weighted) vs. 1.5% (equal weighted).

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