Introduction

Pair trading is a classic market-neutral strategy that involves taking opposing positions in two correlated assets. This post walks through a simple example and connects it to portfolio theory.

Example: Alpha & Omega

Imagine two tech firms, Alpha and Omega. We construct a pair trade:

• Short Omega
• Long Alpha

Initial Trade

After 3 Months

Performance

• Alpha ($50 →$45): 10% drop
• Omega ($40 →$35): 12.5% drop

Position Types

• Long Position: Profit when price rises
• Short Position: Profit when price falls

Scaling Up: Portfolio Construction

Pair trading can be extended to a portfolio of carefully chosen stocks. The goal is to use mathematical models to balance risk and return, factoring in correlations.

Mean-Variance Optimization

The standard way to build a portfolio is through mean-variance optimization:

• Return Vector: $\vec{\mu} = (\mu_1, \mu_2, ..., \mu_n)$
• Covariance Matrix:

• Weight Vector: $\vec{w} = (w_1, w_2, ..., w_n)$

Portfolio Returns

• Expected Return:

  $$ext{Expected Return} = \vec{w} \cdot \vec{\mu}$$

• Portfolio Variance:

  $$\sigma^2 = \vec{w}^T \Sigma \vec{w}$$

• Objective Function (Loss Function):

  $$\vec{w} \cdot \vec{\mu} - \lambda \vec{w}^T \Sigma \vec{w}$$

The objective is to find weights $\vec{w}$ that maximize this function, balancing return and risk according to your preferences.

Portfolio Constraints

Alternative Data

Coming soon...

Conclusion

References

• QuantRocket: Pairs Trading
• YouTube: Pairs Trading Explained