In finance, the beta (β or market beta or beta coefficient) is a measure of how an individual asset moves (on average) when the overall stock market increases or decreases. Thus, beta is a useful measure of the contribution of an individual asset to the risk of the market portfolio when it is added in small quantity. Thus, beta is referred to as an asset's non-diversifiable risk, its systematic risk, market risk, or hedge ratio. Beta is not a measure of idiosyncratic risk. Interpretation of values By definition, the value-weighted average of all market-betas of all investable assets with respect to the value-weighted market index is 1. If an asset has a beta above (below) 1, it indicates that its return moves more (less) than 1-to-1 with the return of the market-portfolio, on average. In practice, few stocks have negative betas (tending to go up when the market goes down). Most stocks have betas between 0 and 3. Treasury bills (like most fixed income instruments) and commodities tend to have low or zero betas, call options tend to have high betas (even compared to the underlying stock), and put options and short positions and some inverse ETFs tend to have negative betas. Importance as risk measure Beta is the hedge ratio of an investment with respect to the stock market. For example, to hedge out the market-risk of a stock with a market beta of 2.0, an investor would short $2,000 in the stock market for every $1,000 invested in the stock. Thus insured, movements of the overall stock market no longer influence the combined position on average. Beta thus measures the contribution of an individual investment to the risk of the market portfolio that was not reduced by diversification. It does not measure the risk when an investment is held on a stand-alone basis. Technical aspects Mathematical definition The market beta of an asset , observed on occasions, is defined by (and best obtained via) a linear regression of the rate of return of asset on the rate of return of the (typically value-weighted) stock-market index : where is an unbiased error term whose squared error should be minimized. The coefficient is often referred to as the alpha. The ordinary least squares solution is where and are the covariance and variance operators. Betas with respect to different market indexes are not comparable. Relationship between own risk and beta risk