First, let's calculate simple returns. NumPy has the diff() function that returns an array that is built up of the difference between two consecutive array elements. This is sort of like differentiation in calculus (the derivative of price with respect to time). To get the returns, we also have to divide by the value of the previous day. We must be careful though. The array returned by diff() is one element shorter than the close prices array. After careful deliberation, we get the following code:

returns = np.diff( arr ) / arr[ : -1]

Notice that we don't use the last value in the divisor. The standard deviation is equal to the square root of variance. Compute the standard deviation using the std() function:

print("Standard deviation =", np.std(returns))

This results in the following output:

Standard deviation = 0.0129221344368

The log return or logarithmic return is even easier to calculate. Use the...