> ## Documentation Index
> Fetch the complete documentation index at: https://kalpi.ai/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Beta Metric

> Evaluate your portfolio's structural volatility relative to the broader market index.

**Beta (**$\beta$**)** measures the systematic risk (or volatility) of your algorithmic strategy compared to a benchmark index (like the Nifty 50).

While Standard Deviation measures *absolute* risk in a vacuum, Beta measures *relative* risk. It tells you exactly how sensitive your portfolio is to macro market movements.

## The Mathematical Formula

Beta is calculated by dividing the covariance of the portfolio and the benchmark's returns by the variance of the benchmark's returns:

$\beta = \frac{Cov(R_p, R_m)}{Var(R_m)}$

## Interpreting Your Beta Score

When reviewing your backtest, use the benchmark value of exactly **1.0** as your baseline:

| Beta Value             | Market Sensitivity     | Tactical Reality                                                                                                                                                            |
| :--------------------- | :--------------------- | :-------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **Exactly 1.0**        | Neutral                | The portfolio moves perfectly in sync with the benchmark. If the market drops 5%, your portfolio drops 5%.                                                                  |
| **Greater than 1.0**   | High Beta (Aggressive) | The portfolio is structurally more volatile than the market. A Beta of 1.5 means if the market rises 10%, the portfolio rises 15% (but also falls 15% if the market drops). |
| **Between 0 and 1.0**  | Low Beta (Defensive)   | The portfolio is insulated from market shocks. A Beta of 0.5 means the portfolio only experiences half the volatility of the broader market.                                |
| **Below 0 (Negative)** | Inverse Beta           | The portfolio structurally moves in the opposite direction of the market, serving as a direct hedge.                                                                        |