Calculating Beta
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What information is contained within risk and beta measures and how these numbers are calculated.
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Glossary
Beta portfolio risk Standard Deviation VolatilityTranscript
Models of risk and return in finance require us to estimate the exposure of a firm to Market risk.
Beta is a measure of that market risk. It indicates how sensitive an Investments returns have been to movements in the market over a specific period of time in other words. It indicates how the assets value has reacted to either a movement up or a movement down in the market because it is essentially a comparison it only measures relative risk and not total risk or absolute risk.
Let's look at a company with higher systematic risk positive macro events will result in Greater gains negative macro events will result in Greater losses a beta greater than 1 indicates that an investment has higher systematic risk than the market which means that it tends to see higher returns than the Benchmark index in an upmarket scenario in lower returns than the benchmarket index in a down Market scenario. All of the things being equal. For example, if the market return above the risk-free rate is 10% a smaller company that may be more sensitive to economic fluctuations might have an asset beta of 1.4 that would imply a return above the market return in this case 14% The reverse is true for Investments with beta is less than one which have lower systematic risk than the market. They tend to underperform in up Market scenarios, but protect better on the downside all of the things being equal in general bigger companies with more predictable earnings and dividends will carry a lower beta value Banks and insurance stocks utilities and large conglomerates all tend to have lower betas. These lower betas result in a lower than Market return as we see here with an asset beta of point eight resulting in a return of only eight percent.
Let's now take a look at historical betas by sectors as you expect utilities shows the lowest beta given its low sensitivities to Market factors beta measures sensitivity to the market in Broad Market factors, not total variation sectors that are less sensitive to the macroeconomic environment tend to have lower systematic risk and therefore lower betas.
Sectors that are more sensitive to the macroeconomic environment tend to have higher systematic risk and therefore higher betas.
Beta data is widely available by many financial data providers. But how is it calculated while there are many ways to estimate systematic risk, the most practical and common is a regression analysis the beta for an asset class can be estimated by regressing the returns on any asset against the Returns on an index representing the market portfolio over a reasonable period of time. This is a statistical process that evaluates the historical relationship between a given asset that dependent variable and one or more other independent variables.
Regressions allow us to describe the returns of an individual security the dependent variable compared to the returns of the market in general the independent variable.
Y is the return on Apple stock beta is the slope of the regression line it is the level of movement in returns of a given security for each unit of movement in the market in general X is the return of the S&P the alpha return or a in the regression equation of a security represents the Securities propensity to move independent of the market if the S&P has a 10% return over the risk-free rate, then we would expect Apple to have a return of 1.369 times 10 plus 0.0116, which equals 3.7% over the market return the past is not the future. So historical data is obviously not a perfect forecast of current and future risk also in choosing a time period for beta estimation it is worth noting the trade off involved by going back further in time. We get the advantage of having more data points in the analysis, but this could be offset by the fact that the firm itself might Had recent major changes therefore it is necessary to recognize that estimates of beta whether obtained through calculation or regression analysis may or may not represent current or future levels of an assets systematic risk.
Regression analysis is similar to plotting all combinations of the assets return and the market return and then drawing a line through all points with the smallest possible set of distances between itself and each data point in addition to being widely available. Luckily beta calculations can also be done in Excel with the slope function without running a full regression analysis.
Betas can be used to measure the sensitivity to multiple factors not just Market sensitivity while traditional Market beta indicates the extent to which a portfolio is exposed to the market the portfolio return that is related to Beta represents compensation for bearing Market risk, but there are other betas many investors have found success with more complex multi-factor models using multiple betas allowing more than one variable to be considered in estimating returns models can also be built using extensive list factors that can be categorized as macroeconomic fundamental and statistical factors. We've only covered macroeconomic factors so far.