CAPM Beta Calculator
Calculate the Beta coefficient for an asset relative to a market index using historical return data. Beta is a measure of systematic risk, indicating how sensitive an asset's returns are to overall market movements.
Enter a series of historical returns for your asset and the corresponding historical returns for a market index (e.g., S&P 500) over the exact same periods. Enter one return value per line or separated by commas. Ensure you have a sufficient number of data points for a meaningful calculation (at least 2, though typically 30+ are used in practice).
Enter Historical Returns
Understanding CAPM Beta
What is Beta?
In finance, Beta (β) is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole. Systematic risk refers to the risk inherent to the entire market or entire market segment. It's a risk that cannot be diversified away.
The Capital Asset Pricing Model (CAPM)
Beta is a key component of the Capital Asset Pricing Model (CAPM), which describes the relationship between systematic risk and expected return for assets, particularly stocks. The CAPM formula is: E(Ri) = Rf + βi * (E(Rm) - Rf), where E(Ri) is the expected return of the investment, Rf is the risk-free rate, βi is the beta of the investment, and (E(Rm) - Rf) is the market risk premium.
Beta Formula
Beta is statistically calculated using the following formula:
β = Cov(Ra, Rm) / Var(Rm)
Where:
Cov(Ra, Rm)is the covariance between the asset's return (Ra) and the market's return (Rm). Covariance measures how two variables change together.Var(Rm)is the variance of the market's return (Rm). Variance measures the dispersion of a set of data points around their mean.
This formula essentially measures the extent to which an asset's returns are correlated with the market's returns, adjusted for the market's own volatility.
Interpreting Beta Values
- Beta = 1: The asset's price activity is strongly correlated with the market. An asset with a beta of 1 has average systematic risk.
- Beta > 1: The asset is more volatile than the market. If the market goes up by 1%, the asset is expected to go up by more than 1%. These stocks are often considered more aggressive or risky.
- Beta < 1 (but > 0): The asset is less volatile than the market. If the market goes up by 1%, the asset is expected to go up by less than 1%. These stocks are often considered more defensive.
- Beta = 0: Indicates no correlation with the market (theoretically, like a risk-free asset).
- Beta < 0: The asset moves in the opposite direction of the market (e.g., if the market goes up, the asset tends to go down). This is rare for most traditional assets like stocks but can occur with certain investments like inverse ETFs or gold in some periods.
Beta is based on historical data and is not a perfect predictor of future volatility. The choice of the market index and the time period used for calculation can significantly impact the resulting Beta value.
CAPM Beta Examples
Below are examples illustrating Beta calculation using small sets of hypothetical monthly returns. Enter these values into the calculator to see the result.
Example 1: Asset tracks Market closely (Beta ≈ 1)
Scenario: Asset returns closely mirror market returns.
Asset Returns: 0.02, -0.01, 0.03, 0.005, -0.025
Market Returns: 0.018, -0.009, 0.029, 0.006, -0.024
Calculated Beta: ≈ 1.01 (Expected close to 1)
Example 2: Asset more volatile than Market (Beta > 1)
Scenario: Asset returns show larger swings than market returns.
Asset Returns: 0.03, -0.02, 0.05, 0.01, -0.04
Market Returns: 0.015, -0.01, 0.025, 0.005, -0.02
Calculated Beta: ≈ 1.98 (Expected > 1)
Example 3: Asset less volatile than Market (Beta < 1)
Scenario: Asset returns show smaller swings than market returns.
Asset Returns: 0.01, -0.005, 0.015, 0.002, -0.01
Market Returns: 0.02, -0.01, 0.03, 0.005, -0.025
Calculated Beta: ≈ 0.50 (Expected < 1)
Example 4: Asset returns roughly constant (Beta ≈ 0)
Scenario: Asset returns show little to no correlation with market returns (highly simplified example).
Asset Returns: 0.001, 0.001, 0.001, 0.001, 0.001
Market Returns: 0.02, -0.01, 0.03, 0.005, -0.025
Calculated Beta: ≈ 0.00 (Expected close to 0)
Example 5: Asset moves opposite to Market (Beta < 0)
Scenario: Asset returns tend to go down when the market goes up, and vice-versa (highly simplified example).
Asset Returns: -0.02, 0.01, -0.03, -0.005, 0.025
Market Returns: 0.02, -0.01, 0.03, 0.005, -0.025
Calculated Beta: ≈ -1.00 (Expected < 0)
Example 6: Using different data points (3 points)
Scenario: Calculate Beta with a minimum number of points.
Asset Returns: 0.05, -0.03, 0.01
Market Returns: 0.04, -0.02, 0.005
Calculated Beta: ≈ 1.29
Example 7: Using different data points (7 points)
Scenario: More data points for potentially higher accuracy.
Asset Returns: 0.01, 0.02, -0.005, 0.03, -0.01, 0.005, 0.025
Market Returns: 0.008, 0.015, -0.003, 0.028, -0.008, 0.006, 0.022
Calculated Beta: ≈ 1.09
Example 8: Asset slightly less volatile than Market (Beta just under 1)
Scenario: Asset is slightly defensive.
Asset Returns: 0.018, -0.009, 0.027, 0.004, -0.023
Market Returns: 0.02, -0.01, 0.03, 0.005, -0.025
Calculated Beta: ≈ 0.90
Example 9: Asset significantly more volatile than Market (Beta much > 1)
Scenario: Asset is aggressive.
Asset Returns: 0.04, -0.03, 0.06, 0.015, -0.05
Market Returns: 0.015, -0.01, 0.025, 0.005, -0.02
Calculated Beta: ≈ 2.65
Example 10: Market with little movement
Scenario: If the market has very low volatility, the Beta calculation becomes unstable (potential division by near zero).
Asset Returns: 0.02, -0.01, 0.03, 0.005, -0.025
Market Returns: 0.001, -0.0005, 0.0015, 0.0002, -0.001
Calculated Beta: Approx 20.08 (Highlights instability with low market variance)
Understanding Investment Risk
Investment risk can be broadly categorized into two types: systematic risk and unsystematic risk...
Why Beta Matters
Beta is a key metric for investors looking to understand the market risk exposure of an asset...
Frequently Asked Questions about Beta
1. What does a Beta of 1 mean?
A Beta of 1 means the asset's price is expected to move in lockstep with the overall market. If the market rises by 5%, the asset is expected to rise by approximately 5%.
2. What does a Beta greater than 1 mean?
An asset with Beta > 1 is considered more volatile than the market. It is expected to experience larger percentage gains than the market in up periods and larger percentage losses in down periods.
3. What does a Beta less than 1 (but greater than 0) mean?
An asset with Beta < 1 is considered less volatile than the market. It is expected to experience smaller percentage gains than the market in up periods and smaller percentage losses in down periods. These are often called "defensive" stocks.
4. Can Beta be zero or negative?
Yes. A Beta of zero means there is theoretically no correlation between the asset's returns and the market's returns. A negative Beta means the asset's returns tend to move in the opposite direction to the market, though this is rare for most common assets.
5. What is the standard time period and frequency for calculating Beta?
Common practice often involves using 5 years of monthly return data, or 3 years of weekly return data. However, different analysts and data providers may use different periods and frequencies, which can lead to different Beta values for the same asset.
6. What market index should I use?
The choice of market index should be relevant to the asset being analyzed. For U.S. stocks, the S&P 500 is a very common market proxy. For assets in other countries or specific sectors, a more relevant local or sector index should be used.
7. Is Beta a measure of total risk?
No, Beta only measures systematic risk (market risk). It does not account for unsystematic risk (specific risk) which is unique to an individual company or asset and can typically be reduced or eliminated through diversification.
8. How reliable is historical Beta in predicting future volatility?
Beta is based on historical data and assumes that the historical relationship between the asset and the market will continue. While useful, it is not a perfect predictor of the future and should be used in conjunction with other analytical tools.
9. Why might my calculated Beta differ from sources like Yahoo Finance or Google Finance?
Differences can arise due to varying factors: the market index used (e.g., S&P 500 vs. NYSE Composite), the time period of historical data (e.g., 3 years vs. 5 years), the frequency of data (e.g., daily vs. weekly vs. monthly), and slight variations in the statistical methodology.
10. Can I calculate Beta for a portfolio?
Yes. The Beta of a portfolio is the weighted average of the Betas of the individual assets within the portfolio, where the weights are the proportion of the portfolio's total value that each asset represents.
