Zero-Beta Portfolio

A zero-beta portfolio is constructed so its systematic risk (beta) relative to a reference market index is zero. In theory, a portfolio with beta = 0 has no correlation with market movements and, under CAPM assumptions, should have an expected return equal to the risk-free rate.

Key takeaways

• A zero-beta portfolio has zero systematic risk — its portfolio beta equals 0.
• Beta measures sensitivity to movements in a chosen market index; beta > 1 is more volatile than the market, beta < 1 is less volatile, and beta < 0 indicates movement in the opposite direction.
• Because it has no market exposure, a zero-beta portfolio typically underperforms in bull markets and may be of limited appeal compared with simply holding risk-free assets.
• Perfectly eliminating market risk is theoretical; practical constructions aim for an approximate zero beta.

Understanding beta

Beta quantifies an investment’s sensitivity to a reference market index:
Beta = Covariance(Stock return, Market return) / Variance(Market return)

Interpretation:
* Beta > 1: investment tends to amplify market moves.
* Beta = 1: investment moves in line with the market.
* Beta between 0 and 1: investment is less volatile than the market.
* Beta < 0: investment tends to move opposite the market.

Beta depends on the chosen index; a security can have different betas relative to different market measures.

Building a zero-beta portfolio

For a fully invested portfolio, choose weights w_i such that the weighted sum of asset betas equals zero:
sum(w_i * beta_i) = 0 (and typically sum(w_i) = 1)

This can be achieved with a mix of positively and negatively correlated assets or via long-short constructions. Note that transaction costs, estimation error in betas, and changing correlations mean the resulting portfolio will usually only approximate zero beta.

Example

A manager has $5 million and considers five assets with these betas:
* Stock 1: beta 0.95
* Stock 2: beta 0.55
* Bond 1: beta 0.20
* Bond 2: beta −0.50
* Commodity 1: beta −0.80

An allocation:
* Stock 1: $700,000 (14%) → weighted beta = 0.95 × 0.14 = 0.133
* Stock 2: $1,400,000 (28%) → weighted beta = 0.55 × 0.28 = 0.154
* Bond 1: $400,000 (8%) → weighted beta = 0.20 × 0.08 = 0.016
* Bond 2: $1,000,000 (20%) → weighted beta = −0.50 × 0.20 = −0.100
* Commodity 1: $1,500,000 (30%) → weighted beta = −0.80 × 0.30 = −0.240

Sum of weighted betas ≈ −0.037, which is effectively a near-zero beta portfolio.

Practical considerations

• Alternatives: In many situations, holding true risk-free instruments (e.g., short-term government securities) is cheaper and simpler than constructing a zero-beta portfolio.
• Market conditions: Zero-beta strategies may be more attractive when downside protection is a priority (bear markets) but will generally lag in rising markets.
• Estimation risk: Betas are estimated from historical data and can change over time; portfolios should be rebalanced and monitored.

Conclusion

A zero-beta portfolio aims to neutralize market exposure by combining assets with offsetting betas. While useful conceptually and for certain hedging purposes, practical limits (estimation error, costs, and changing correlations) make truly zero systematic risk difficult to sustain, and simpler risk-free alternatives often suffice.