CAPM Beta Calculator - Calculator Academy (2024)

FAQs

How do you calculate beta in CAPM model? ›

Beta (β) In corporate finance, beta (β) measures the systematic risk of a security compared to the broader market (i.e. non-diversifiable risk). The beta of an asset is calculated as the covariance between expected returns on the asset and the market, divided by the variance of expected returns on the market.

Subtract the risk-free rate from the market (or index) rate of return. If the market or index rate of return is 8% and the risk-free rate is again 2%, the difference would be 6%. Divide the first difference above by the second difference above. This fraction is the beta figure, typically expressed as a decimal value.

The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between the expected return and risk of investing in a security. It shows that the expected return on a security is equal to the risk-free return plus a risk premium, which is based on the beta of that security.

The pieces of the CAPM formula are the risk-free rate (Rrf), investment beta (βa) and the market return (Rm – Rrf). The value of each piece is dynamic, so the CAPM calculation needs to be updated over time. The formula is represented symbolically as: Ra = Rrf + [βa * (Rm – Rrf)], with Ra being the expected return.

Beta effectively describes the activity of a security's returns as it responds to swings in the market. A security's beta is calculated by dividing the product of the covariance of the security's returns and the market's returns by the variance of the market's returns over a specified period.

In this context, covariance refers to the measure of a stock's return relative to that of the market, and variance refers to the measure of how the market moves relative to its mean. Once those figures are identified, beta is calculated by dividing covariance by variance (Beta = Covariance/Variance).

The first is to use the formula for beta, which is calculated as the covariance between the return (r_a) of the stock and the return (r_b) of the index divided by the variance of the index over three years.

Beta = covariance/variance

Covariance is a measure of a security's returns relative to the market's returns. Variance is a measure of the market's return relative to its mean or average.

According to the theory behind the CAPM, those numbers should be able to tell how a stock will perform on the market. Based on the equation, the expected return of an investment will equal the risk-free rate + (the beta * equity risk premium).

What is risk-free rate in CAPM? ›

The risk-free rate signals an investment that has no risk; the investor will not lose money. The rate is the main component of many famous theories, such as the capital asset pricing model (CAPM), modern portfolio theory (MPT), and the Black-Scholes model.

Another disadvantage in using the CAPM in investment appraisal is that the assumption of a single-period time horizon is at odds with the multi-period nature of investment appraisal. While CAPM variables can be assumed constant in successive future periods, experience indicates that this is not true in the real world.

The CAPM formula describes the expected return for investing in a security that's equal to the risk-free return plus a risk premium. In the formula, the risk premium—a rate of return that's greater than the risk-free rate—represents an investor's compensation for taking on systemic risk that can't be diversified away.

Conversely, the capital asset pricing model (CAPM) evaluates if an investment is fairly valued, given its risk and time value of money in relation to its anticipated return. Under this model, Cost of Equity = Risk-Free Rate of Return + Beta × (Market Rate of Return – Risk-Free Rate of Return).

50 years on from its introduction, CAPM is still one of the most widely studied and accepted pricing models but in that timespan, it has generated several critics. Its assumptions have been derided from the outset as unrealistic in real market conditions.

We are going to focus on one particular aspect of CAPM: beta. Beta, as we noted above, is the beta coefficient of an asset that results from regressing the returns of that asset on market returns. It captures the linear relationship between the asset/portfolio and the market.

Beta. The measure of systematic risk (the volatility) of the asset relative to the market. Beta can be found online or calculated by using regression: dividing the covariance of the asset and market's returns by the variance of the market.

The alpha formula derives from the Capital Asset Pricing Model (CAPM), with the CAPM formula for alpha reading as Alpha= r - Rf - beta(Rm - Rf). Alpha can be positive or negative. Beta, the volatility of a stock in comparison to the overall market, is part of the formula to calculate an investment's expected returns.