# How does Beta reflect systematic risk?

Systematic risk, or total market risk, is the volatility that affects the entire stock market across many industries, stocks, and asset classes. Systematic risk affects the overall market and is therefore difficult to predict and hedge against.

Unlike with unsystematic risk, diversification cannot help to smooth systematic risk, because it affects a wide range of assets and securities. For example, the Great Recession was a form of systematic risk; the economic downturn affected the market as a whole.

Investors can still try to minimize the level of exposure to systematic risk by looking at stock’s beta, or its correlation of price movements to the broader market as a whole. Here, we take a closer look at how beta relates to systematic risk.

## Beta and Systematic Risk

Beta is a measure of a stock’s volatility in relation to the market. It essentially measures the relative risk exposure of holding a particular stock or sector in relation to the market.

If you want to know the systematic risk of your portfolio, you can calculate its beta. Beta effectively describes the activity of a security’s returns as it responds to swings in the market. A security’s beta is computed by dividing the product of the covariance of the security’s returns and the market’s returns by theÂ varianceÂ of the market’s returns over a specified period, using this formula:

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begin{aligned} &text{Beta coefficient}(beta) = frac{text{Covariance}(R_e, R_m)}{text{Variance}(R_m)} \ &textbf{where:}\ &R_e=text{the return on an individual stock}\ &R_m=text{the return on the overall market}\ &text{Covariance}=text{how changes in a stock’s returns are} \ &text{related to changes in the market’s returns}\ &text{Variance}=text{how far the market’s data points spread} \ &text{out from their average value} \ end{aligned}

â€‹BetaÂ coefficient(Î²)=Variance(Rmâ€‹)Covariance(Reâ€‹,Rmâ€‹)â€‹where:Reâ€‹=theÂ returnÂ onÂ anÂ individualÂ stockRmâ€‹=theÂ returnÂ onÂ theÂ overallÂ marketCovariance=howÂ changesÂ inÂ aÂ stockâ€™sÂ returnsÂ arerelatedÂ toÂ changesÂ inÂ theÂ marketâ€™sÂ returnsVariance=howÂ farÂ theÂ marketâ€™sÂ dataÂ pointsÂ spreadoutÂ fromÂ theirÂ averageÂ valueâ€‹ï»¿

Note that beta can also be calculated by running a linear regression on a stock’s returns compared to the market using the capital asset pricing model (CAPM). In fact, this is why this measure is called the beta coefficient, since statisticians and econometricians label the coefficients of explanatory variables in regression models as the Greek letter ÃŸ. The formula for CAPM is:

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## What Does Beta Tell You?

Once you’ve calculated the beta of a security, it can then be used to tell you the relative correspondence of price movements in that stock, given the price movements in the broader market as a whole.

• A beta of 0 indicates that the portfolio is uncorrelated with the market. In other words, movement of the stock or stocks held move randomly in relation to the broader market.
• A negative beta (i.e., less than 0) indicates that it moves in the opposite direction of the market and that there is a negative correlation with the market.
• A beta between 0 and 1 signifies that it moves in the same direction as the market, but with less volatilityâ€”that is, smaller percentage changesâ€”than the market as a whole.
• A beta of 1 indicates that the portfolio will move in the same direction, have the same volatility and is sensitive to systematic risk. Note that the S&P 500 index is often used as the benchmark for the broader stock market and the index has a beta of 1.0.
• A beta greater than 1 indicates that the portfolio will move in the same direction as the market, and with a higher magnitude than the market. Stocks with betas above 1.0 are quite sensitive to systematic risk.

In reality, you won’t have to go about calculating beta yourself in most cases. Beta is commonly listed on freely available stock quotes from several online financial portals, as well as through your broker’s website.

## Example

Assume that the beta of an investor’s portfolio is 2.0 in relation to a broad market index, such as the S&P 500. If the market increases by 2%, then the portfolio will generally increase by 4%.

Likewise, if the market decreases by 2%, the portfolio generally decreases by 4%. This portfolio is therefore sensitive to systematic risk, but the risk can be reduced by hedging. This can be achieved by obtaining other stocks that have negative or low betas, or by using derivatives to limit downside losses.