Saturday, February 2, 2019

Some statistics about the S&P 100's 2018 return

The following figure shows the 2018 returns for stocks in the S&P 100:

Some comments:
  • The mean (average) return is 5.5 percent.
  • The median return is 6.6 percent. So half the stocks in the index returned less than this and half returned more (roughly).
  • Skewness is 0.18, meaning the returns are skewed to the right.
  • Kurtosis is -0.02, meaning the graph is flattish, not peaked (relative to a certain standard distribution).
  • 35 percent of the stocks in the index earned a positive return.
  • The 10th percentile return is -31 percent -- for these stocks, 2018 was a very bad year.
  • The 90th percentile return is +18 percent -- in other words, despite a pretty bad year for the market, a reasonable number of stocks did quite well.

The following figure takes the above returns and converts them to their continuously compounded equivalents:

The continuously compounded return is related to the annual return by the following relation:

CtsCompReturn=ln(1 + AnnualReturn)

It is interesting to compare this graph with the first. The mean return here is lower than that obtained by applying the above formula to the mean return of the first graph. On the other hand, and as expected, the percentiles here are just direct translations using the above formula. Unlike the first graph, which is positively skewed, this graph is negatively skewed. This graph is also much more peaked.

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