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In finance, the beta (β) of an investment is a measure of the risk arising from exposure to general market movements as opposed to idiosyncratic factors. The market portfolio of all investable assets has a beta of exactly 1. A beta below 1 can indicate either an investment with lower volatility than the market, or a volatile investment whose price movements are not highly correlated with the market. An example of the first is a treasury bill: the price does not go up or down a lot, so it has a low beta. An example of the second is gold. The price of gold does go up and down a lot, but not in the same direction or at the same time as the market. A beta greater than one generally means that the asset both is volatile and tends to move up and down with the market. An example is a stock in a big technology company. Negative betas are possible for investments that tend to go down when the market goes up, and vice versa. There are few fundamental investments with consistent and significant negative betas, but some derivatives like equity put options can have large negative betas. Beta is important because it measures the risk of an investment that cannot be reduced by diversification. It does not measure the risk of an investment held on a stand-alone basis, but the amount of risk the investment adds to an already-diversified portfolio. In the capital asset pricing model, beta risk is the only kind of risk for which investors should receive an expected return higher than the risk-free rate of interest. The definition above covers only theoretical beta. The term is used in many related ways in finance. For example, the betas commonly quoted in mutual fund analyses generally measure the risk of the fund arising from exposure to a benchmark for the fund, rather than from exposure to the entire market portfolio. Thus they measure the amount of risk the fund adds to a diversified portfolio of funds of the same type, rather than to a portfolio diversified among all fund types. Beta decay refers to the tendency for a company with a high beta coefficient (β > 1) to have its beta coefficient decline to the market beta. It is an example of regression toward the mean. ==Statistical estimation== Beta is estimated by regression. Given an asset and a benchmark that we are interested in, we want to find an approximate formula : where ''r''a is the return of the asset and ''r''b is return of the benchmark. Since the data are usually in the form of time series, the statistical model is :, where ε''t'' is an error term (the unexplained return). Click here for a definition of Alpha (α). The best (in the sense of least squared error) estimates for α and β are those such that Σε''t''2 is as small as possible. A common expression for beta is :, where Cov and Var are the covariance and variance operators. This can also be expressed as : where ρa,b is the correlation of the two returns, and σa and σb are the respective volatilities. Relationships between standard deviation, variance and correlation: Beta can be computed for prices in the past, where the data is known, which is historical beta. However, what most people are interested in is ''future beta'', which relates to risks going forward. Estimating future beta is a difficult problem. One guess is that future beta equals historical beta. From this, we find that beta can be explained as "correlated relative volatility". This has three components: *correlated *relative *volatility Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the sensitivity of the asset's returns to market returns, its non-diversifiable risk, its systematic risk, or market risk. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. In fund management, measuring beta is thought to separate a manager's skill from his or her willingness to take risk. The portfolio of interest in the CAPM formulation is the market portfolio that contains all risky assets, and so the ''r''b terms in the formula are replaced by ''r''m, the rate of return of the market. The regression line is then called the security characteristic line (SCL). : is called the asset's alpha and is called the asset's beta coefficient. Both coefficients have an important role in modern portfolio theory. For example, in a year where the broad market or benchmark index returns 25% above the risk free rate, suppose two managers gain 50% above the risk free rate. Because this higher return is theoretically possible merely by taking a leveraged position in the broad market to double the beta so it is exactly 2.0, we would expect a skilled portfolio manager to have built the outperforming portfolio with a beta somewhat less than 2, such that the excess return not explained by the beta is positive. If one of the managers' portfolios has an average beta of 3.0, and the other's has a beta of only 1.5, then the CAPM simply states that the extra return of the first manager is not sufficient to compensate us for that manager's risk, whereas the second manager has done more than expected given the risk. Whether investors can expect the second manager to duplicate that performance in future periods is of course a different question. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Beta (finance)」の詳細全文を読む スポンサード リンク
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