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Systematic risk can be measured using beta. Stock Beta is the measure of the risk of an individual stock in comparison to the market as a whole. Beta is the sensitivity of a stock’s returns to some market index returns (e.g., S&P 500). Basically, it measures the volatility of a stock against a broader or more general market.

It is a commonly used indicator by financial and investment analysts. The Capital Asset Pricing Model (CAPM) also uses the Beta by defining the relationship of the expected rate of return as a function of the risk free interest rate, the investment’s Beta, and the expected market risk premium.

Beta is calculated using correlation or regression analysis.

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**Using the correlation method, beta can be calculated from the historical data of returns by the following formula: **

Where,

r_{im} = Correlation coefficient between the returns of stock i and the returns of the market index

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σ_{i}= Standard deviation of returns of stock i

σ_{m} = Standard deviation of returns of the market index

σ^{2}_{m} = variance of the market returns

**Using the regression analysis, beta can be calculated from the historical data of returns by the following formula: **

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Y = α + βX

Where,

Y = Dependent variable

X = Independent variable

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α and β are constants.

**The above regression equation can also be written as follows: **

R_{i }= α +β_{i} R_{m}

Where,

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R_{i }= Return of the individual security

R_{m} = Return of the market index

Β_{i} = Beta (Systematic Risk) of individual security

α= Estimated return of security when market is stationary

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**The formula for calculation of CC and β are as follows:**

Where,

n = number of items

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X = Independent variable scores (returns of the market index)

Y = Dependent Variable scores (returns of individual security)

**Interpretation of Beta:**

i. A beta of 1 indicates that the security’s price will move with the market.

ii. A beta of less than 1 means that the security will be less volatile than the market.

iii. A beta of greater than 1 indicates that the security’s price will be more volatile than the market.

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For example, if a stock’s beta is 1.2, it’s theoretically 20% more volatile than the market. The Beta of the general and broader market portfolio is always assumed to be 1.

**Example:**

**The rates of return on the security of A Ltd. And market portfolio for 10 periods are given below: **

What is the best security of A?

**Solution:**