decreasing variance of increments

import pandas as pd
import numpy as np
import requests
from scipy.stats import norm
from scipy.stats import spearmanr
from tqdm.notebook import tqdm
import matplotlib.pyplot as plt

prediction_corr = 0.02
N = 5000
rounds = 20
iterations = 1000


corr_paths = []
for _ in tqdm(range(iterations)):
  # Generate random walk
  random_walk = norm.rvs(0,1, (rounds, N))
  # Generate final
  final = random_walk.sum(axis=0)
  # Generate noise of same distribution
  noise =  norm.rvs(0,1, (rounds, N)).sum(axis=0)
  # Generate predictions
  predictions = final * prediction_corr + (1-prediction_corr**2)*noise
  # Generate round path
  corr_path = []
  for i in range(rounds):
    # Preliminary score is the corr vs current standings of random walk
    corr_path.append(spearmanr(predictions, random_walk[:i+1].sum(axis=0))[0])
  corr_paths.append(corr_path)

# Differentiate to get corr increments and take standard deviation per day
plt.plot(np.diff(np.array(corr_paths).T,axis=0).std(axis=1))
plt.show()