How Long and Short Weights Determine Portfolio Beta

Summary

Portfolio beta is calculated as the weighted sum of the constituent assets’ betas. If the assets have positive betas, a portfolio made only of long positions generally has positive beta; combining long and short weights can offset those exposures and bring portfolio beta toward zero. This explains why a zero-beta portfolio is often built as a long-short portfolio, while a conventional long-only portfolio may be designed to have beta near one.

The answer also points out that a portfolio’s beta need not be one just because it is long-only: a 130/30 portfolio can have beta around one, depending on the assets and their weights. The example illustrates the distinction between net exposure and market sensitivity. The explanation assumes positive stock betas and does not give a specific portfolio calculation. It also notes a practical constraint: shorting individual stocks may be difficult for mutual funds and individual investors.

Key ideas

• Portfolio beta is the sum of each asset’s beta multiplied by its portfolio weight.
• Long positions in positive-beta stocks generally produce positive portfolio beta.
• Long and short positions can offset market exposure and produce beta near zero.
• A 130/30 portfolio can have beta around one, depending on its holdings.
• Shorting individual stocks may be difficult for some investors and funds.

Tags

# Beta = 1 and 0. Type of portfolios


# Beta = 1 and 0. Type of portfolios












I read in E. Quian's "Quantitative Equitity Portoflio Management" the following:

> A traditional long-only portfolio [with unit beta] would have most of its risk in the market risk. However, a zero beta portfolio, typically a long-short market-neutral portfolio, would have no systematic risk.

Why are Beta=1 portfolios typically long-only and why are Beta=0 portfolios typically long-short and market neutral?

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/26311

Portfolio beta is a linear combination of each asset's beta times the weight of the asset in the portfolio. Thus in general we have $$ \beta = \sum_{i=1}^N w_i \beta_i $$ where $w_i$ is the weight of asset $i$ and $\beta_i$ its beta. If we assume that for stocks the betas are positive then $\beta$ above is positive for positive weights. If you have positive and negative weights then you can get $\beta=0$.

If you have a 130/30 portfolio - thus positive weights that sum to 130% and negative ones that sum to -30% then you can have a beta of approx 1.

Note that for mutual funds and individual investors it is not that easy to have short exposure to single stocks.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.