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
Daily portfolio values
Portfolio statistics
Which portfolio is better?
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Both stocks have similar volatility, so ABC is better due greater returns.
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Here both stocks have similar returns, but XYZ has lower volatility (risk).
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In this case, we actually do not have a clear picture of which stock is better!
Sharpe ratio => matrix return the risk
risk free return => bank interest
Form of the Sharpe ratio
Computing Sharpe ratio
But wait, there's more!
Putting it all together