Definition, Formula, and Example of a Zero-Beta Portfolio
What Is a Zero-Beta Portfolio?
A zero-beta portfolio is a strategic investment portfolio designed to eliminate systematic risk, indicated by a beta of zero. Such a portfolio is structured to offer the same expected return as the risk-free rate, with no correlation to market movements. This implies that while higher-beta portfolios may yield higher returns, a zero-beta portfolio provides stability and protection against market fluctuations.
In bullish markets, a zero-beta portfolio may not garner significant investor interest due to its lack of market exposure, potentially leading to underperformance compared to diversified portfolios. However, during bear markets, some investors may consider it as a safe haven. Yet, questions arise about whether investing in risk-free assets would be a more cost-effective alternative to a zero-beta strategy. Ultimately, achieving a completely risk-free investment is theoretically unattainable.
Key Takeaways:
- A zero-beta portfolio mitigates systematic risk by maintaining a beta of zero.
- Beta quantifies an asset’s sensitivity to market index movements.
- Zero-beta portfolios, devoid of market exposure, may not be appealing during bullish markets.
Understanding Zero-Beta Portfolios
Beta and Formula
Beta is a metric assessing a security’s sensitivity to the price movements of a designated market index. It gauges whether an investment is more or less volatile than the benchmark index being evaluated.
A beta exceeding one indicates higher volatility than the market, while a beta below one suggests lower volatility. Negative betas signify movements opposite to the market performance.
For instance, a stock might exhibit a beta of 0.97 compared to the S&P 500 index, 0.7 relative to the Russell 2000 index, and a negative beta against an unrelated index like an emerging market debt index.
The formula for beta is: Beta = Covariance of Market Return with Stock Return / Variance of Market Return
A Simple Zero-Beta Example
To illustrate a zero-beta portfolio, imagine a scenario where a portfolio manager aims to create a zero-beta position against the S&P 500. Given $5 million to invest, the manager contemplates the following:
- Stock 1: beta of 0.95
- Stock 2: beta of 0.55
- Bond 1: beta of 0.2
- Bond 2: beta of -0.5
- Commodity 1: beta of -0.8
Through a strategic allocation, a portfolio with a near-zero beta can be constructed as follows:
- Stock 1: $700,000 (14%, beta of 0.133)
- Stock 2: $1,400,000 (28%, beta of 0.154)
- Bond 1: $400,000 (8%, beta of 0.016)
- Bond 2: $1 million (20%, beta of -0.1)
- Commodity 1: $1.5 million (30%, beta of -0.24)
This diversified portfolio would yield a beta close to zero, portraying a low correlation with market movements.
