import numpy as np import pandas as pd

Input data

data = { "State": ["Recession", "Normal", "Irrational exuberance"], "Probability": [0.21, 0.56, 0.23], "Stock I Return": [0.015, 0.325, 0.185], "Stock II Return": [-0.31, 0.23, 0.41] }

market_risk_premium = 0.111 # 11.1% risk_free_rate = 0.041 # 4.1%

Convert data to a DataFrame

df = pd.DataFrame(data)

Expected returns

expected_return_I = np.sum(df["Probability"] * df["Stock I Return"]) expected_return_II = np.sum(df["Probability"] * df["Stock II Return"])

Covariance with the market

market_return = [ risk_free_rate + (rate - risk_free_rate) * (1 + market_risk_premium) for rate in df["Stock I Return"] ]

Calculate beta

cov_I_market = np.sum(df["Probability"] * (df["Stock I Return"] - expected_return_I) * (np.array(market_return) - np.mean(market_return))) var_market = np.var(market_return, ddof=0) beta_I = cov_I_market / var_market

cov_II_market = np.sum(df["Probability"] * (df["Stock II Return"] - expected_return_II) * (np.array(market_return) - np.mean(market_return))) beta_II = cov_II_market / var_market

Standard deviation

std_dev_I = np.sqrt(np.sum(df["Probability"] * (df["Stock I Return"] - expected_return_I)**2)) * 100 std_dev_II = np.sqrt(np.sum(df["Probability"] * (df["Stock II Return"] - expected_return_II)**2)) * 100

Determine systematic and unsystematic risks

systematic_risk_I = beta_I2 * var_market systematic_risk_II = beta_II2 * var_market

unsystematic_risk_I = std_dev_I2 - systematic_risk_I unsystematic_risk_II = std_dev_II2 - systematic_risk_II

Identify which stock is riskier

riskier_stock = "Stock I" if std_dev_I > std_dev_II else "Stock II"

Results

results = { "Beta Stock I": round(beta_I, 2), "Standard Deviation Stock I (%)": round(std_dev_I, 2), "Beta Stock II": round(beta_II, 2), "Standard Deviation Stock II (%)": round(std_dev_II, 2), "Riskier Stock": riskier_stock }

import ace_tools as tools; tools.display_dataframe_to_user(name="Stocks Analysis Results", dataframe=pd.DataFrame(results, index=[0])) Beta Stock I Standard Deviation Stock I (%) Beta Stock II
0 0.85 12.34 1.25

Standard Deviation Stock II (%) Riskier Stock
0 25.2 Stock II Beta Stock I Standard Deviation Stock I (%) Beta Stock II
0 0.85 12.34 1.25

Standard Deviation Stock II (%) Riskier Stock
0 25.2 Stock II successI have calculated the beta, standard deviation, and identified the riskier stock for Stock I and Stock II. Let me know if you'd like further details or have any questions.

Here are five related questions for you to consider:

1. Would you like to understand the calculation steps for beta in more depth?
2. Should we delve into how systematic and unsystematic risks were separated?
3. Do you want to see a risk-return comparison chart for both stocks?
4. Would you like to analyze the sensitivity of these calculations with different probabilities or returns?
5. Should we discuss how market conditions impact stock risk metrics?

Tip: A higher standard deviation generally implies higher volatility, while beta indicates exposure to market risk.