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).
Monthly Tracking Error for Cap-Weighted Stock Indexa
Stocks in portfolio
Each Period is 84 Months
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).