Financial Analysis - Build a ChatGPT Pairs Trading Bot - More about Log Returns (Optional)

The video tutorial explains the concept of returns and log returns, highlighting why log returns are approximately equal to simple returns. It uses the first-order Taylor expansion to demonstrate this approximation. The tutorial also covers the calculation of log returns in code, explaining the process of shifting asset prices and computing element-wise log returns.

Why is summing returns to get the return at time T considered approximately correct?

• Because returns are always linear.

• Because log returns are exactly equal to simple returns.

• Because returns do not change over time.

• Because log returns are approximately equal to simple returns.

What mathematical tool is used to explain the approximation of log returns to simple returns?

• Fourier Series

• Taylor Expansion

• Laplace Transform

• Euler's Formula

In the Taylor expansion, around which value is X centered?

• 0

• Negative Infinity

• 1

• Infinity

What is the result of the first-order Taylor expansion for log(1 + X) when X is small?

• X^2

• 1/X

• log(X)

• X

What operation is performed on asset prices to calculate log returns in code?

• Addition

• Division

• Subtraction

• Multiplication

Why is asset shifting used in the calculation of log returns?

• To align prices for division

• To avoid negative values

• To increase computation speed

• To reduce data size

What does the log return at time 3 represent in the context of asset prices?

• log(P3/P2)

• log(P5/P4)

• log(P2/P1)

• log(P4/P3)