Bayesian CAPM Beta Estimation

1_Bayesian CAPM Beta Estimation.md

Bayesian CAPM Beta Estimation

amazon_bayesian.py

import pymc3 as pm

X = stocks["AMZN"]["X"].values
y = stocks["AMZN"]["y"].values

with pm.Model() as model_1:
    
    alpha = pm.Normal("alpha", mu=0, sigma=1)
    beta = pm.Normal("beta", mu=0, sigma=1)

    exp_returns = pm.Deterministic("exp_returns", alpha + beta * X)
    noise = pm.HalfNormal("noise", sigma=1)

    returns = pm.Normal("returns", mu=exp_returns, sigma=noise, observed=y)

    trace_1 = pm.sample(tune=1500)

amazon_bayesian_prob.py

beta_samples = trace_1["beta"]
np.mean(beta_samples > 1.2)
# => 0.32125

amazon_ols.py

import statsmodels.api as sm

X = stocks["AMZN"]["X"].values
y = stocks["AMZN"]["y"].values

X = sm.add_constant(X)

model = sm.OLS(y, X)

results = model.fit()
model.data.xnames = ["alpha", "beta"]
print(results.summary())

data_wrangling.py

# Tickers to get data
tickers = ["MSFT", "GOOG", "AMZN", "FB"]

# Add S&P 500
tickers.append("^GSPC")

# Download data from Yahoo Finance
data = yf.download(
    " ".join(tickers),
    period = "5y",
    interval = "1mo",
    group_by = "ticker",
)

# Store the S&P 500 data
market = data["^GSPC"].dropna().reset_index().set_index("Date")
tickers.remove("^GSPC")

# Get the data for each stock
stocks = {}

for ticker in tickers:
    stock_data = data[ticker].dropna().reset_index().set_index("Date")
    monthly_prices = pd.concat([stock_data["Close"], market["Close"]], axis=1)
    monthly_prices.columns = [ticker, "market"]
    monthly_returns = monthly_prices.pct_change(1).dropna(axis=0)

    stocks[ticker] = {
        "data": stock_data,
        "monthly_prices": monthly_prices,
        "monthly_returns": monthly_returns,
        "X": monthly_returns["market"],
        "y": monthly_returns[ticker]
    }

ols.py

for ticker in stocks.keys():

    X = stocks[ticker]["X"].values
    y = stocks[ticker]["y"].values

    X = sm.add_constant(X)

    model = sm.OLS(y, X)

    results = model.fit()

    print(f"{ticker}: ", results.params[1])

results.md

Stock	Yahoo! Finance	OLS	Bayesian
MSFT	0.83	0.808	0.65 - 0.90 (72%)
GOOG	0.99	0.981	0.80 - 1.10 (76%)
AMZN	1.20	1.152	0.90 - 1.30 (70%)
FB	1.18	1.266	1.00 - 1.40 (73%)