Analysis: Beta

Definition:

This indicator reflects the sensitivity of the portfolio’s return to benchmark fluctuations and measures its systematic risk relative to it.

Interpretation:

Beta = 1: The asset moves in sync with the market. If the market rises or falls by 1%, the asset is likely to change by the same 1%.
Beta > 1: The asset is more volatile than the market. If the market rises by 1%, the asset’s price changes more — for example, by 1.5% (β = 1.5).
Beta < 1: The asset is less volatile than the market. With the same 1% market movement, the asset changes by a smaller percentage, for example 0.5% (β = 0.5).
Beta = 0: No correlation with the market. The asset’s movements are independent of the general market trend.
Beta < 0: Inverse relationship. When the market rises, the asset falls and vice versa. This behavior is typical, for example, of certain defensive assets or instruments like inverse ETFs.

Example:

Portfolio:

Risk Free Rate (RFR) = 2%
2025-01-01 deposit of 1000
2025-03-03 purchase of NASDAQ:AAPL (qty:1, price: 190, commission: 0)
2025-04-11 Beta calculation date. Last price of AAPL = 198.15

Beta = −0.39, i.e., we have a portfolio with inverse correlation: when the benchmark rises by 1%, the portfolio on average decreases by 0.39%. When the benchmark falls, the portfolio increases by 0.39%, respectively.

Note: It’s important to account for the short-term nature of the period used for simplification of the calculation.

Calculation:

Beta is calculated over the entire period covered by the portfolio using monthly returns (monthly performance) of the portfolio and the selected benchmark. Beta is displayed on a scale from 0 to 2, where the benchmark value is always fixed at 1, as it is the standard.

Formula: β = Covariance(Perf Bench, Perf Portfolio) / Variance(Perf Bench)where:

Covariance — covariance of portfolio and benchmark returns
Variance — variance of benchmark returns
Perf Bench — monthly returns of the benchmark
Perf Portfolio — monthly returns of the portfolio

Beta calculation example based on the interpretation’s portfolio:

Perf Portfolio:
1. January: 0
2. February: 0
3. March: 3.2% (obtained: pv as of March 31 ((1032.13-1000)/1000)*100)
4. April: −2.3% (obtained: ((1008.15-1032.13)/1032.13)*100)

Avg = (0 + 0 + 3.2 − 2.3) / 4 = 0.225%

Perf Bench:
1. January: 0
2. February: 0
3. March: −0.773% (obtained: pv as of March 31 ((992.27-1000)/1000)*100)
4. April: −0.813% (obtained: ((984.2-992.27)/992.27)*100)

Avg = (0 + 0 − 0.773 − 0.813) / 4 = −0.3965%

Covariance(Perf Bench, Perf Portfolio): Deviations from averages for each month:
1. January: (0 − 0.225)(0 − (−0.3965)) = (−0.225)(0.3965) = −0.0892
2. February: (0 − 0.225)(0 − (−0.3965)) = (−0.225)(0.3965) = −0.0892
3. March: (3.2 − 0.225)(−0.773 − (−0.3965)) = (2.975)(−0.3765) = −1.1201
4. April: (−2.3 − 0.225)(−0.813 − (−0.3965)) = (−2.525)(−0.4165) = 1.0517

Covariance = (−0.0892 + (−0.0892) + (−1.1201) + 1.0517) / 4 = −0.062

Variance(Perf Bench):
1. Squared deviations from the benchmark mean:
2. January: (0 − (−0.3965))² = 0.1572
3. February: (0 − (−0.3965))² = 0.1572
4. March: (−0.773 − (−0.3965))² = 0.1417
5. April: (−0.813 − (−0.3965))² = 0.1735

Variance = (0.1572 + 0.1572 + 0.1417 + 0.1735) / 4 = 0.157

Covariance(Perf Bench, Perf Portfolio) / Variance(Perf Bench): β = −0.062 / 0.157 = −0.39

Note:

Beta helps assess systematic (non-diversifiable) risk associated with market volatility but does not account for the asset’s fundamental characteristics.
When interpreting the result, it is important to ensure that the selected benchmark is relevant to the assets included in the portfolio.
If all transactions were made in the current month relative to the date of the Beta calculation, the indicator will not be calculated because there is no completed calendar month.