Beta in Asset Pricing Model

What the Beta is?

Beta is a numeric value that measures the fluctuations of a stock to the changes in the overall stock market. It is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole.

Beta is used in the capital asset pricing model (CAPM), a model that calculates the expected return of an asset based on its beta and expected market returns.

CalculatingBeta in R

  • Downloading the data from Quandl

  • Check the structure:

  • As the intersect function can only be applied to two vectors, we call the Reduce function to identify the common dates in the three time series:

  • Now, let us simply filter all three data frames to the relevant cells to get the vectors:

  • After cleaning the data, we have to calculate the log-returns and risk premium. Creating a function to do so:

  • Once we have both time series; the individual asset’s (MRF) and the official Interest rate of India (BCB/17901), beta can be calculated as:

  • The regression coefficients obtained as:

    Notice the coefficient of risk_premium and the one obtained by ratio of covariance are same which is beta calculated.

  • Plotting, the Security Characteristic Line (SCL) is obtained as follows:

  • Details of line fit:

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