In SP500, the capitalization of each company is used to compute the weight for that company in the “SP500 portfolio”: \(w_i = \frac{cap_i}{\sum\limits_j cap_j}\)
The volativity of SP500 is also called market volatility.
Descriptive statistics = data summaries (we try to compute some features from the data).
5.2 - Histograms
We can build blockly histograms or smoothed histograms.
We can infer the mean, deviation, skewness and kurtosis from the histograms.
5.3 - Sample Statistics
Percentiles
Sample quantile is often called empirical quantile or percentile.
Quartiles
q.25 is the first quartile
q.50 is the second quartile (or median)
q.75 is the third quartile
q.75 - q.25 is the interquartile range (IQR)
Historical value-at-risk
eg. value at risk computed from the data (eg. from empirical quantiles).
Sample Statistics
We can compute Sample mean, variance, std deviation, skewness, kurtosis and excess kurtosis.