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What are the beta and alpha indicators in finance? How to express it by formula?
Alpha index is an index to measure the investment performance of fund portfolio, and beta index is an index to measure the systemic risk of portfolio.

The fund's income can be considered to be composed of two parts: the income brought by the overall market rise and the income brought by the fund's stock strategy. The gain brought by the market rise is the beta gain. To put it bluntly, this is the harvest brought by the high tide. High beta returns do not mean high level of fund managers. The income from stock selection is alpha income, which is the real value of fund managers.

Fund income = alpha income+beta income+residual income

Where beta rate of return = beta coefficient × benchmark rate of return. Residual income is a random variable with an average value of 0, which can be skipped.

In the eyes of quantitative investors, income and risk are two sides of the same coin. Risk brings benefits, and benefits mean risks. Income and risk can be used interchangeably in the formula. So the above formula can also be written as:

Fund risk = alpha risk+beta risk+residual risk

When the beta coefficient is large (for example, greater than 1), the fluctuation of fund income has a great influence, the market rises, the fund income rises sharply, the market falls, and the fund income falls sharply. Hedge funds can reduce the beta coefficient to close to zero by shorting stock index futures, eliminating the beta risk and giving up the beta income.

In this way, the fund's income becomes an alpha income that is not affected by the broader market. The level and fluctuation of alpha income are determined by the quality of fund stock selection/timing strategy. A good hedge fund can bring alpha income through bull market and bear market.