import matplotlib.pyplot as plt
import numpy as np
import pandas as pdHerron Topic 5 - Practice Blank
FINA 6333 for Spring 2024
1 Announcements
2 Practice
%precision 2
pd.options.display.float_format = '{:.2f}'.format
%config InlineBackend.figure_format = 'retina'import yfinance as yf
import pandas_datareader as pdr2.1 Estimate \(\pi\) by simulating darts thrown at a dart board
Hints: Select random \(x\)s and \(y\)s such that \(-r \leq x \leq +r\) and \(-r \leq x \leq +r\). Darts are on the board if \(x^2 + y^2 \leq r^2\). The area of the circlular board is \(\pi r^2\), and the area of square around the board is \((2r)^2 = 4r^2\). The fraction \(f\) of darts on the board is the same as the ratio of circle area to square area, so \(f = \frac{\pi r^2}{4 r^2}\).
2.2 Simulate your wealth \(W_T\) by randomly sampling market returns
Use monthly market returns from the French Data Library. Only invest one cash flow \(W_0\), and plot the distribution of \(W_T\).