Table 27 shows several summary statistics for the annual and monthly returns on the S&P 500. Earlier we discussed the arithmetic mean return and standard deviation of return, and we shall shortly discuss kurtosis.
Table 27. S&P 500 Annual and Monthly Total Returns, 1926–2012: Summary Statistics| Return Series | Number of Periods | Arithmetic Mean (%) | Standard Deviation (%) | Skewness | Excess Kurtosis |
|---|---|---|---|---|---|
| S&P 500 (Annual) | 87 | 11.82 | 20.18 | −0.3768 | 0.0100 |
| S&P 500 (Monthly) | 1,044 | 0.94 | 5.50 | 0.3456 | 9.4288 |
Source: Ibbotson Associates.
Table 27 reveals that S&P 500 annual returns during this period were negatively skewed while monthly returns were positively skewed, and the magnitude of skewness was greater for the annual series. We would find for other market series that the shape of the distribution of returns often depends on the holding period examined.
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