# 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?

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.

• Thanks @Richard this is helpful, but I am having a hard time relating your answer to my question. Let me know if there is anything I can do to clarify it.
– Josh
Commented May 29, 2016 at 15:25
• Is is because the more positive Beta is, the more long the portfolio is?
– Josh
Commented May 29, 2016 at 15:27
• How do you measure beta? Ex-post it has something to with the performance of the assets that you hold, right? In a first approximation (which is also true ex-ante) the beta is what my formula above says. If you are long then you are long the market - an indication by how much is given by beta. What is your understanding of beta? Commented May 29, 2016 at 17:52
• The beta of a typical stock is 1.0. What is the lowest beta stock that you know of? The lowest I know is Hawaii Electric (HE) with beta 0.4. I suppose with some effort I could find some a little lower than that. How are you going to combine together stocks with Beta of 0.4 or 0.3 into a portfolio with a beta of zero? You can't do it unless you short some stocks... Commented May 30, 2016 at 1:38
• Yes, of course... This is what my answer says... Commented May 30, 2016 at 4:44