So, I wrote some code to analyze the odds. I used two methods:<\/p>\n\n\n\n
- \n
- Probability Based on Distribution<\/strong><\/li>\n\n\n\n
- Probability Based on Exceedance Rate of Returns Over an X-Month Timeframe<\/strong><\/li>\n<\/ul>\n\n\n\n
The Basics of Polymarket Betting<\/h2>\n\n\n\n
Polymarket allows users to place bets on the likelihood of various events, ranging from election outcomes to company performance. These bets are binary\u2014either \u201cYes\u201d or \u201cNo.\u201d The value of these bets fluctuates based on market sentiment, much like options in the stock market. The key to making informed decisions on such platforms lies in understanding the underlying data and probabilities. If you\u2019re right, you get $1 per share, and if you\u2019re wrong, you lose your stake.<\/p>\n\n\n\n
Betting on Apple: An Investment Analysis<\/h2>\n\n\n\n
The current market sentiment suggests an 83% chance that Apple will retain its position as the largest company by September 30th. This probability is derived from the cost of betting \u201cYes\u201d on Polymarket, which is currently priced at 84 cents on the dollar. If you\u2019re right, you stand to make 16 cents per dollar invested.<\/p>\n\n\n\n
But is the market sentiment accurate? Let\u2019s delve into the historical data, statistical distributions, and probability models to assess whether this bet offers good value. This process involves analyzing how often other major companies like Microsoft (MSFT) or Nvidia (NVDA) have exceeded Apple\u2019s growth rate in the past and whether such exceedances are likely within the given timeframe.<\/p>\n\n\n\n
Frequency-Based Analysis vs. Distribution-Based Analysis<\/h2>\n\n\n\n
We examined two approaches:<\/p>\n\n\n\n
- \n
- Frequency-Based Analysis<\/strong>: This method examines historical data to determine how often, on average, another company has surpassed Apple in growth rate during any given month. By calculating the \u201cexceedance rate,\u201d we can estimate how likely it is that Apple will be dethroned within the specified period. If this probability is high, betting \u201cYes\u201d on Apple may not be favorable.<\/li>\n\n\n\n
- Distribution-Based Analysis<\/strong>: This approach dives deeper into the statistical distribution of monthly returns, considering variance and volatility. If the data shows that other companies have frequently come close to Apple\u2019s growth rates, the odds of an upset increase.<\/li>\n<\/ol>\n\n\n\n
Determining Probability<\/h2>\n\n\n\n
The first step in determining the probability is to get the market cap of the top 10 companies.<\/p>\n\n\n\n
<\/p>\n\n\n\n
import yfinance as yf\nimport pandas as pd\n\n# List of top 10 companies by ticker\ntickers = [\"AAPL\", \"MSFT\", \"NVDA\", \"GOOG\", \"AMZN\", \"2222.SR\", \"META\", \"BRK-B\", \"TSM\", \"LLY\"]\n\n# Manual conversion rates (as of recent rates)\nconversion_rates = {\n 'SAR': 0.27, # 1 SAR \u2248 0.27 USD\n 'TWD': 0.032 # 1 TWD \u2248 0.032 USD\n}\n\n# Fetch the current market cap for each company\nmarket_caps = {}\nfor ticker in tickers:\n stock = yf.Ticker(ticker)\n info = stock.info\n if 'marketCap' in info:\n market_cap = info['marketCap']\n currency = info.get('financialCurrency', 'USD')\n # Convert market cap to USD if it's not already in USD\n if currency != 'USD':\n if currency in conversion_rates:\n market_cap = market_cap * conversion_rates[currency]\n else:\n print(f\"Conversion rate for {currency} not found, skipping conversion.\")\n market_caps[ticker] = market_cap\n else:\n print(f\"Market cap for {ticker} not found.\")\n\n# Create a DataFrame to store the data\ndf = pd.DataFrame(list(market_caps.items()), columns=['Ticker', 'Market Cap'])\ndf.sort_values(by='Market Cap', ascending=False, inplace=True)\ndf.reset_index(drop=True, inplace=True)\n\n# Find the largest company\ntop_company = df.iloc[0]\n\n# Calculate the percentage increase needed for each of the smaller companies to overtake the top one\ndf['Percentage Increase Needed'] = ((top_company['Market Cap'] - df['Market Cap']) \/ df['Market Cap']) * 100\n\n# Output the results\nprint(f\"Top Company: {top_company['Ticker']} with a Market Cap of ${top_company['Market Cap']:,}\")\nprint(df[['Ticker', 'Market Cap', 'Percentage Increase Needed']])\n<\/pre>\n\n\n\nMarket Capitalization and threshold<\/h2>\n\n\n\n
Once we have the market cap, we can calculate the percentage increase required for each company to exceed AAPL. Below is the output from the code above.<\/p>\n\n\n\n
<\/p>\n\n\n\n
Top Company: AAPL with a Market Cap of $3,481,738,936,320.0\n Ticker Market Cap Percentage Increase Needed\n0 AAPL 3.481739e+12 0.000000\n1 MSFT 3.100618e+12 12.291764\n2 NVDA 2.928146e+12 18.905915\n3 GOOG 2.020401e+12 72.329063\n4 AMZN 1.873465e+12 85.844935\n5 2222.SR 1.818538e+12 91.458086\n6 META 1.318820e+12 164.004029\n7 BRK-B 1.026412e+12 239.214585\n8 LLY 8.644270e+11 302.779992\n9 TSM 2.849440e+10 12119.030326<\/code><\/pre>\n\n\n\nNow that we know the percentage increases required, we can download all historical returns and see which companies have actually achieved this in a previous month.<\/p>\n\n\n\n
import yfinance as yf\nimport pandas as pd\nimport plotly.graph_objects as go\n\n# Assuming 'df' from the previous code cell contains the market cap data\n\n# Download historical monthly data for each ticker\nhistorical_data = {}\nfor ticker in df['Ticker']:\n stock_data = yf.download(ticker, start=\"1900-01-01\", interval=\"1mo\", auto_adjust=True)\n stock_data['Date'] = pd.to_datetime(stock_data.index)\n stock_data.set_index('Date', inplace=True)\n stock_data['Pct Change'] = stock_data['Close'].pct_change() * 100 # Convert to percentage change\n historical_data[ticker] = stock_data\n\n# Identify the top company by ticker\ntop_ticker = df.iloc[0]['Ticker']\n\n# Plotting the data with dynamic variables, but skipping the top company\nfor index, row in df.iterrows():\n ticker = row['Ticker']\n \n if ticker == top_ticker:\n continue # Skip plotting for the top company\n \n threshold = row['Percentage Increase Needed']\n \n # Prepare the data for plotting\n stock_data = historical_data[ticker]\n \n # Create a bar chart with conditional coloring\n colors = ['green' if pct > threshold else 'red' for pct in stock_data['Pct Change']]\n \n fig = go.Figure(data=[go.Bar(\n x=stock_data.index,\n y=stock_data['Pct Change'],\n marker_color=colors\n )])\n \n # Add a red horizontal line at the threshold\n fig.add_hline(y=threshold, line_dash=\"dash\", line_color=\"red\", \n annotation_text=f\"Threshold: {threshold:.2f}%\", \n annotation_position=\"top right\")\n \n # Customize layout\n fig.update_layout(\n title=f'Monthly Percentage Change for {ticker} with Threshold',\n xaxis_title='Date',\n yaxis_title='Percentage Change (%)',\n template='plotly_white'\n )\n \n # Show the plot\n fig.show()\n<\/pre>\n\n\n\nThis code outputs multiple graphs. However, only two companies\u2014MSFT and NVDA\u2014realistically have a chance to exceed AAPL\u2019s market cap in the next month.<\/p>\n\n\n\n
![\"\"](\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\")
<\/figure>\n\n\n\n<\/figure>\n\n\n\nRelative Return<\/h2>\n\n\n\n
Instead of looking at NVDA\u2019s return individually, I’ll examine the correlation between NVDA and AAPL by subtracting NVDA\u2019s return from AAPL\u2019s return for every month.<\/p>\n\n\n\n
<\/p>\n\n\n\n
import plotly.graph_objects as go\n\n# Assuming 'df' and 'historical_data' from the previous cells are still available\n\n# Identify the top company by ticker\ntop_ticker = df.iloc[0]['Ticker']\ntop_stock_data = historical_data[top_ticker]\n\n# Plotting the relative returns for each ticker compared to the top ticker, with threshold lines\nfor index, row in df.iterrows():\n ticker = row['Ticker']\n \n if ticker == top_ticker:\n continue # Skip plotting for the top company\n \n threshold = row['Percentage Increase Needed']\n \n # Fetch the stock data for the current ticker\n stock_data = historical_data[ticker]\n \n # Align and truncate data to the earliest common date\n combined_data = pd.concat([top_stock_data['Pct Change'], stock_data['Pct Change']], axis=1, keys=[top_ticker, ticker]).dropna()\n \n # Subtract top stock's performance from the current stock's performance\n combined_data['Relative Return'] = combined_data[ticker] - combined_data[top_ticker]\n \n # Create a bar chart with conditional coloring\n colors = ['green' if pct > 0 else 'red' for pct in combined_data['Relative Return']]\n \n fig = go.Figure(data=[go.Bar(\n x=combined_data.index,\n y=combined_data['Relative Return'],\n marker_color=colors\n )])\n \n # Add a red horizontal line at the required threshold\n fig.add_hline(y=threshold, line_dash=\"dash\", line_color=\"red\", \n annotation_text=f\"Threshold: {threshold:.2f}%\", \n annotation_position=\"top right\")\n \n # Customize layout\n fig.update_layout(\n title=f'Relative Monthly Returns for {ticker} vs {top_ticker} with Threshold',\n xaxis_title='Date',\n yaxis_title='Relative Return (%)',\n template='plotly_white'\n )\n \n # Show the plot\n fig.show()\n<\/pre>\n\n\n\nNow, we can see the relative returns as well as the threshold of times they exceeded the required amount to surpass AAPL.<\/p>\n\n\n\n
<\/figure>\n\n\n\n<\/figure>\n\n\n\nDistribution of Relative Returns<\/h2>\n\n\n\n
To view this data differently, we can now look at the distribution of this data. The code will loop through the last 10 years, but here is an example for one year:<\/p>\n\n\n\n
<\/p>\n\n\n\n
### Analysis for the Last 1 Year(s) ###\nNVDA exceeded the threshold 3 times.\nNVDA Mean Relative Change: 7.4181%\nNVDA Std Dev of Relative Change: 13.8239%\nNVDA Z-score for threshold 18.91%: 0.8310\nProbability of exceeding threshold based on distribution: 20.2984%<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\nWhat is the expected value?<\/h2>\n\n\n\n
Now that we know the distribution and odds, we can introduce Polymarket’s implied odds\u201483% with a cost of 84 cents per share and a payout of 16 cents per share. Based on these inputs, we can convert this to Expected Value (EV).<\/p>\n\n\n\n
<\/p>\n\n\n\n
Polymarket 'Yes' Probability: 83.00%\nPolymarket 'Yes' Bet Cost: $0.84 per share\nPolymarket 'Yes' Payout: $0.16 per share\n\n### Summary for the Last 1 Year(s) ###\nMonths Analyzed: 12 months\nProbability of Apple remaining the largest (based on exceedance rate): 75.00%\nProbability of Apple remaining the largest (based on distribution): 79.7016%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1200 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.1275 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1200.\nBased on the distribution, for every $1 bet, you should expect to make $0.1275.\n\n\n<\/code><\/pre>\n\n\n\nimport pandas as pd\nfrom datetime import datetime\nfrom scipy.stats import norm\n\n# Given Polymarket values\npolymarket_prob_yes = 0.83 # 83% chance of Apple remaining the largest\npolymarket_price_yes = 0.84 # 84\u00a2 to bet \"Yes\"\npolymarket_payout_yes = 1 - polymarket_price_yes # Payout for \"Yes\" bet\n\nprint(f\"Polymarket 'Yes' Probability: {polymarket_prob_yes * 100:.2f}%\")\nprint(f\"Polymarket 'Yes' Bet Cost: ${polymarket_price_yes:.2f} per share\")\nprint(f\"Polymarket 'Yes' Payout: ${polymarket_payout_yes:.2f} per share\")\n\n# Assuming 'df', 'historical_data', and the correct top_ticker (Apple in this case) are available from previous code cells\n\n# Loop over 1 to 10 years\nfor year in range(1, 11):\n print(f\"\\n### Summary for the Last {year} Year(s) ###\")\n \n # Calculate the cutoff date for the current loop iteration\n cutoff_date = datetime.now() - pd.DateOffset(years=year)\n \n # Calculate the number of months in the specified period\n months_in_period = year * 12\n \n # Initialize a cumulative counter for exceedances and probabilities\n cumulative_exceedances = 0\n cumulative_prob_not_exceeding = 1 # Start with 1 (100% chance of no exceedance)\n \n # Iterate through the tickers in the df to calculate exceedances and probabilities\n for index, row in df.iterrows():\n ticker = row['Ticker']\n if ticker == top_ticker:\n continue # Skip the top company itself\n \n # Fetch the stock data for the current ticker and truncate to the last N years\n stock_data = historical_data[ticker]\n stock_data_truncated = stock_data[stock_data.index >= cutoff_date]\n \n # Align and truncate data to the earliest common date\n combined_data = pd.concat([historical_data[top_ticker]['Pct Change'], stock_data_truncated['Pct Change']], axis=1, keys=[top_ticker, ticker]).dropna()\n \n # Subtract top stock's performance from the current stock's performance\n combined_data['Relative Change'] = combined_data[ticker] - combined_data[top_ticker]\n \n # Calculate how many times this stock exceeded the threshold (Frequency-Based Approach)\n exceedance_count = (combined_data['Relative Change'] >= row['Percentage Increase Needed']).sum()\n \n # If no exceedances, skip this ticker\n if exceedance_count == 0:\n continue\n \n # Add to the cumulative counter\n cumulative_exceedances += exceedance_count\n \n # Distribution and Standard Deviation Approach\n mean_relative_change = combined_data['Relative Change'].mean()\n std_relative_change = combined_data['Relative Change'].std()\n \n # Calculate the Z-score for the threshold\n z_score = (row['Percentage Increase Needed'] - mean_relative_change) \/ std_relative_change\n \n # Calculate the probability of exceeding the threshold using the CDF of the normal distribution\n prob_exceeding_threshold = 1 - norm.cdf(z_score)\n \n # Multiply with the cumulative probability of not exceeding the threshold (for all stocks)\n cumulative_prob_not_exceeding *= (1 - prob_exceeding_threshold)\n \n # Calculate the rate of exceedances per month (Frequency-Based Approach)\n exceedance_rate_per_month = cumulative_exceedances \/ months_in_period\n \n # Calculate the probability that Apple will remain the largest company based on the exceedance rate\n months_until_sept_30 = 1 # Assuming 1 month left until September 30\n prob_remain_largest_based_on_exceedance = 1 - (exceedance_rate_per_month * months_until_sept_30)\n \n # Calculate the cumulative probability that Apple will remain the largest based on the distribution\n prob_remain_largest_based_on_distribution = cumulative_prob_not_exceeding\n\n # EV calculation for the Polymarket bet (using exceedance rate)\n ev_polymarket_yes_exceedance_rate = prob_remain_largest_based_on_exceedance * polymarket_payout_yes\n \n # EV calculation for the Polymarket bet (using distribution-based probability)\n ev_polymarket_yes_distribution = prob_remain_largest_based_on_distribution * polymarket_payout_yes\n\n # Output the results for the current year\n print(f\"Months Analyzed: {months_in_period} months\")\n print(f\"Probability of Apple remaining the largest (based on exceedance rate): {prob_remain_largest_based_on_exceedance:.2%}\")\n print(f\"Probability of Apple remaining the largest (based on distribution): {prob_remain_largest_based_on_distribution:.4%}\")\n print(f\"Expected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): ${ev_polymarket_yes_exceedance_rate:.4f} per $1 bet\")\n print(f\"Expected Value (EV) of betting 'Yes' on Polymarket (based on distribution): ${ev_polymarket_yes_distribution:.4f} per $1 bet\")\n\n # Summary of recommendation\n if ev_polymarket_yes_exceedance_rate > 0:\n print(f\"Based on the exceedance rate, for every $1 bet, you should expect to make ${ev_polymarket_yes_exceedance_rate:.4f}.\")\n else:\n print(f\"Based on the exceedance rate, this bet may not be favorable, as you would expect to lose ${abs(ev_polymarket_yes_exceedance_rate):.4f} per $1 bet.\")\n \n if ev_polymarket_yes_distribution > 0:\n print(f\"Based on the distribution, for every $1 bet, you should expect to make ${ev_polymarket_yes_distribution:.4f}.\")\n else:\n print(f\"Based on the distribution, this bet may not be favorable, as you would expect to lose ${abs(ev_polymarket_yes_distribution):.4f} per $1 bet.\")\n<\/code><\/pre>\n\n\n\nShould You Bet “Yes”?<\/h2>\n\n\n\n
Essentially, we can analyze various years of data to determine how likely it is that NVDA will dethrone AAPL. Based on the output below, which analyzes data from 1 to 10 years, it turns out that betting \u201cYes\u201d on AAPL retaining the largest market cap into October 2024 could be favorable. However, the EV isn’t significant, so I wouldn\u2019t wager a large sum of money on this bet.<\/p>\n\n\n\n
<\/p>\n\n\n\n
Polymarket 'Yes' Probability: 83.00%\nPolymarket 'Yes' Bet Cost: $0.84 per share\nPolymarket 'Yes' Payout: $0.16 per share\n\n### Summary for the Last 1 Year(s) ###\nMonths Analyzed: 12 months\nExceedance Rate: 0.25 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 75.00%\nProbability of at least one stock exceeding the threshold (distribution-based): 20.2984%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1200 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0325 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1200.\nBased on the distribution, for every $1 bet, you should expect to make $0.0325.\n\n### Summary for the Last 2 Year(s) ###\nMonths Analyzed: 24 months\nExceedance Rate: 0.29 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 70.83%\nProbability of at least one stock exceeding the threshold (distribution-based): 24.5599%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1133 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0393 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1133.\nBased on the distribution, for every $1 bet, you should expect to make $0.0393.\n\n### Summary for the Last 3 Year(s) ###\nMonths Analyzed: 36 months\nExceedance Rate: 0.19 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 80.56%\nProbability of at least one stock exceeding the threshold (distribution-based): 18.1044%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1289 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0290 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1289.\nBased on the distribution, for every $1 bet, you should expect to make $0.0290.\n\n### Summary for the Last 4 Year(s) ###\nMonths Analyzed: 48 months\nExceedance Rate: 0.15 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 85.42%\nProbability of at least one stock exceeding the threshold (distribution-based): 14.3875%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1367 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0230 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1367.\nBased on the distribution, for every $1 bet, you should expect to make $0.0230.\n\n### Summary for the Last 5 Year(s) ###\nMonths Analyzed: 60 months\nExceedance Rate: 0.13 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 86.67%\nProbability of at least one stock exceeding the threshold (distribution-based): 12.8382%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1387 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0205 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1387.\nBased on the distribution, for every $1 bet, you should expect to make $0.0205.\n\n### Summary for the Last 6 Year(s) ###\nMonths Analyzed: 72 months\nExceedance Rate: 0.12 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 87.50%\nProbability of at least one stock exceeding the threshold (distribution-based): 11.3315%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1400 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0181 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1400.\nBased on the distribution, for every $1 bet, you should expect to make $0.0181.\n\n### Summary for the Last 7 Year(s) ###\nMonths Analyzed: 84 months\nExceedance Rate: 0.12 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 88.10%\nProbability of at least one stock exceeding the threshold (distribution-based): 10.4131%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1410 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0167 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1410.\nBased on the distribution, for every $1 bet, you should expect to make $0.0167.\n\n### Summary for the Last 8 Year(s) ###\nMonths Analyzed: 96 months\nExceedance Rate: 0.12 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 87.50%\nProbability of at least one stock exceeding the threshold (distribution-based): 11.5422%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1400 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0185 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1400.\nBased on the distribution, for every $1 bet, you should expect to make $0.0185.\n\n### Summary for the Last 9 Year(s) ###\nMonths Analyzed: 108 months\nExceedance Rate: 0.13 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 87.04%\nProbability of at least one stock exceeding the threshold (distribution-based): 12.1167%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1393 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0194 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1393.\nBased on the distribution, for every $1 bet, you should expect to make $0.0194.\n\n### Summary for the Last 10 Year(s) ###\nMonths Analyzed: 120 months\nExceedance Rate: 0.13 exceedances per month\nProbability of Apple remaining the largest (based on exceedance rate): 86.67%\nProbability of at least one stock exceeding the threshold (distribution-based): 11.7986%\nExpected Value (EV) of betting 'Yes' on Polymarket (based on exceedance rate): $0.1387 per $1 bet\nExpected Value (EV) of betting 'Yes' on Polymarket (based on distribution): $0.0189 per $1 bet\nBased on the exceedance rate, for every $1 bet, you should expect to make $0.1387.\nBased on the distribution, for every $1 bet, you should expect to make $0.0189.<\/code><\/pre>\n\n\n\nSource Code<\/h2>\n\n\n\n
The source code can be found here to run your own analysis. <\/p>\n\n\n\n
- Distribution-Based Analysis<\/strong>: This approach dives deeper into the statistical distribution of monthly returns, considering variance and volatility. If the data shows that other companies have frequently come close to Apple\u2019s growth rates, the odds of an upset increase.<\/li>\n<\/ol>\n\n\n\n
- Probability Based on Exceedance Rate of Returns Over an X-Month Timeframe<\/strong><\/li>\n<\/ul>\n\n\n\n
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