Beta

Sensitivity to benchmark moves -- how beta is calculated, what values mean, and why it matters for leveraged strategies.

What is Beta?

Beta measures how much your strategy moves when the asset moves. Think of it as a dial that describes the relationship between the two: when the asset goes up 1%, does your strategy go up 1% as well? More? Less? Not at all?

A beta of 1.0 means your strategy moves in lockstep with the asset. A beta of 0.5 means your strategy captures about half the asset's movement on average. Beta is the companion metric to alpha -- together they describe both the relationship your strategy has with the asset and the value it adds beyond that relationship.

The Key Thing to Understand

Beta is calculated across every candle in your backtest -- including candles where your strategy has no open position. When your strategy is out of the market, it returns 0% on that candle while the asset continues to move. These zero-return candles are included in the calculation, which pulls beta toward zero.

This means beta reflects two things at once: how your strategy moves relative to the asset when it's positioned, and how much time it spends positioned at all. A strategy that perfectly tracks the asset when in a trade but is only in the market half the time will have a beta closer to 0.5 than to 1.0.

Green dots track the asset closely (slope near 1.0). Red dots sit at 0% because no position was open. The flat candles pull the overall beta down to 0.57.

Why is my beta so low when my trades follow the asset closely?

If your strategy's exposure is below 100%, your beta will be pulled down by the candles where you're sitting flat. A strategy with 60% exposure that closely tracks the asset when positioned will have a beta in the neighborhood of 0.6, not 1.0. This is by design -- beta measures your overall relationship with the asset, not just the relationship during active trades.

How It's Calculated

Simula calculates beta by looking at the candle-by-candle returns of your strategy and the asset, then measuring how they move together. The formula is:

Beta

beta = covariance(strategy returns, asset returns) / variance(asset returns)

In plain English: look at each candle and ask two questions. First, when the asset goes up, does your strategy also go up? And by how much? That's the covariance -- it measures whether the two move in the same direction and how strongly. Second, how much does the asset move around on its own? That's the variance. Dividing the first by the second gives you beta: a single number that says"for every 1% the asset moves, my strategy moves roughly X%."

If your strategy amplifies the asset's moves, beta will be above 1. If it dampens them (or spends time flat), beta will be below 1.

Worked Examples

Fully invested strategy

A strategy that is always in the market and amplifies the asset's moves:

Asset returns over 5 candles: +2%, -1%, +3%, -2%, +1%
Strategy returns: +2.6%, -1.3%, +3.9%, -2.6%, +1.3%

On every candle, the strategy's return is exactly 1.3 times the asset's return. When the asset goes up 2%, the strategy goes up 2.6%. When the asset drops 1%, the strategy drops 1.3%. The relationship is perfectly consistent.

Beta = 1.3. For every 1% the asset moves, the strategy moves about 1.3% in the same direction.

Strategy that trades in and out

A strategy that is positioned about 50% of the time:

Asset returns over 6 candles: +2%, -1%, +3%, -2%, +1%, +2%
Strategy returns: +2%, -1%, +3%, 0%, 0%, 0%

On candles 1-3, the strategy tracked the asset perfectly. But on candles 4-6, the strategy had no position -- it returned 0% while the asset kept moving. Beta sees all six candles and concludes: overall, this strategy only captures about half the asset's movement.

Using the formula: covariance(strategy, asset) = 2.13, variance(asset) = 3.77. Beta = 2.13 / 3.77 = 0.57. (Covariance and variance across all six candles are tedious to work out by hand -- the takeaway is the result, not the arithmetic.) Even though the strategy matched the asset perfectly when positioned, the three flat candles pull the overall relationship down. Exposure here is 50%, and beta is in a similar range.

Reading Your Results

Beta above 1

Your strategy amplifies the asset's movements. When the asset goes up, your strategy goes up more; when the asset goes down, your strategy goes down more.

Beta around 1

Your strategy moves roughly in line with the asset.

Beta between 0 and 1

Your strategy captures only a portion of the asset's movement. This is common for strategies that spend time out of the market.

Beta around 0

Your strategy's returns have little relationship to the asset's returns.

Negative beta

Your strategy moves in the opposite direction of the asset. A negative beta means that when the asset goes up, your strategy goes down, and vice versa.

Beta and Alpha

Beta and alpha are always calculated together. Beta describes the relationship between your strategy and the asset; alpha measures whether your strategy added value beyond that relationship.

In the formula alpha = strategy return - (beta * asset return), alpha's calculation uses beta to set the expected return. If your beta is 0.6 and the asset returned 20%, the expected return is 12%. Any return above 12% is positive alpha; anything below is negative.

Things to Watch Out For

Beta is not the same as exposure

Beta and exposure are related but measure different things. exposure counts what fraction of candles have an open position. Beta measures the statistical relationship between your strategy's returns and the asset's returns. They will be in a similar range for strategies that closely track the asset when positioned, but they can diverge when the strategy's trading behavior is more complex -- for example, if the strategy uses leverage or trades against the trend.

Beta is an average

The beta you see is a single number summarizing the entire backtest. The actual relationship between your strategy and the asset may vary across different market conditions within that period. A strategy might behave differently in trending markets than in choppy ones, but beta averages all of that into one figure. Walk-forward analysis can reveal how beta shifts across different market phases within your backtest.

Alpha -- measures the return your strategy added beyond what beta would predict. Alpha and beta are always calculated together.

Exposure -- the percentage of candles with an open position. Helps explain why beta is below 1 for strategies that trade in and out.

Volatility -- measures total variation in your strategy's returns. Beta and volatility are related but distinct: beta measures the relationship to the asset, while volatility measures overall return variation regardless of what the asset did.