Beta Hedging with Oracle (ORCL) and the S&P 500 (SPY)

This repository demonstrates beta hedging using Oracle (ORCL) and the S&P 500 ETF (SPY). It includes explanations of factor models, beta calculation, risk exposure, and hedging implementation.

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Overview

Beta hedging is a strategy to reduce the impact of market movements on a portfolio.

• Beta ($\beta$) measures an asset's sensitivity to a factor, usually the market.
• Alpha ($\alpha$) represents returns independent of the market.
• Hedging creates a market-neutral portfolio, where returns are mostly alpha and volatility is reduced.

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Factor Models

A factor model explains the returns of an asset as a linear combination of factors:

$$ Y = \alpha + \beta_1 X_1 + \beta_2 X_2 + \dots + \beta_n X_n + \epsilon $$

Where:

• $Y$ = asset returns (Oracle in this case)
• $X_i$ = factor returns (market index, sector ETF, etc.)
• $\alpha$ = return independent of factors
• $\beta_i$ = sensitivity to factor $X_i$
• $\epsilon$ = noise

A single-factor model for Oracle vs the market:

$$ R_{ORCL} = \alpha + \beta \cdot R_{SPY} + \epsilon $$

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Beta Formula

$$ \beta = \frac{\text{Cov}(R_{ORCL}, R_{SPY})}{\text{Var}(R_{SPY})} $$

• Measures how Oracle moves relative to the market
• High beta → more volatile, follows the market closely
• Low beta → less sensitive to market swings
• Beta = 0 → market-neutral

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Risk Exposure

• High beta means larger gains in a rising market and larger losses in a falling market.
• Low or negligible beta indicates returns mostly independent of the market.
• Market-neutral portfolios focus on asset-specific performance, providing stable returns across market conditions.

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Hedging Implementation

1. Obtain price data for ORCL and SPY.
2. Calculate daily returns from price data.
3. Estimate beta:

$$ R_{ORCL} = \alpha + \beta \cdot R_{SPY} + \epsilon $$

4. Construct a hedged portfolio:

$$ R_{Hedged} = R_{ORCL} - \beta \cdot R_{SPY} $$

5. Evaluate hedged portfolio:

   • Alpha: independent performance
   • Beta: reduced market exposure
   • Volatility: lower risk

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Market Neutrality

• A portfolio with beta ≈ 0 is market-neutral
• Returns are driven primarily by asset-specific factors (alpha) rather than market movements

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Notes on Estimation

• Beta is estimated from historical data and may change over time.
• Hedging using historical beta may not fully remove market risk.
• Beta estimates have standard errors; frequent recalculation improves hedging accuracy.

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Beta Hedging Example – Oracle (ORCL) vs SPY

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Method

1. Download Data: Daily prices for ORCL and SPY using yfinance.

2. Compute Returns: Calculate daily percent changes.

3. Estimate Beta: Linear regression of ORCL returns against SPY returns to find alpha and beta.

4. Construct Hedged Portfolio:

   Hedged Portfolio = ORCL returns - (beta × SPY returns)
   

5. Analyze Portfolio: Compare volatility, average return, and alpha before and after hedging.

6. Out-of-Sample Test: Apply the hedge to a future period to test stability.

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Results

• Reduced Volatility: The hedged portfolio is smoother than ORCL alone.
• Market Neutral: Beta ≈ 0 — the portfolio no longer follows SPY movements.
• Alpha Preserved: Small positive returns remain, independent of the market.

Metric	ORCL	Hedged ORCL
Average Daily Return	-0.000038	0.000592
Volatility (Std Dev)	0.0193	0.0136
Beta vs SPY	1.0+	~0

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Conclusion

This example demonstrates how beta hedging can isolate a stock’s intrinsic performance, reduce market-driven risk, and create a more stable, market-neutral portfolio.

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Libraries Used

• yfinance – for historical stock prices
• numpy – numerical operations
• matplotlib – plotting
• statsmodels – regression analysis

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