A closer look at daily returns

 

 

 

 

 

 Histogram of daily returns

 

gaussian => kurtosis = 0

 

 

 

 How to plot a histogram

 

 

 

 

 Computing histogram statistics

 

 

 

 

 

 

 

 

 

 

Select the option that best describes the relationship between XYZ and SPY.

Note:

• These are histograms of daily return values, i.e. X-axis is +/- change (%), and Y-axis is the number of occurrences.
• We are considering two general properties indicated by the histogram for each stock: return and volatility (or risk).

 

 

 

 Plot two histograms together

 

 

 

 

 Scatterplots

 

 

 

 

 

Fitting a line to data points 

 

 

 

 

 Slope does not equal correlation

 

 

 

 

 Correlation vs slope

 

 

 

 Scatterplots in python

 

 

 

 

 

Real world use of kurtosis

In early 2000s investment banks built bonds based on mortgages（ morgage: 抵押） => assume these mortgages was normally distributed

=> on that basis, they were able to show that these bonds had low probability of fault => 2 mistakes

=> (1) return of each mortagage was independent 

=> (2) using gassian distrubution discribing the return

(1) and (2) were proved to be wrong => precipitated the great recession of 2008