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Beta & Alpha

Beta and alpha are two of the most widely used concepts in portfolio analysis. Beta tells you how much an asset tends to move relative to a benchmark. Alpha tells you whether that movement produced excess returns, or just rode the benchmark's coattails.

Beta​

Definition

Beta measures the correlation and magnitude of an asset's price moves relative to a benchmark. A beta of 1.5 means the asset historically moves 1.5% for every 1% move in the benchmark.

Visualizing Beta​

Drag the slider to change the asset's beta and see how its price movement changes relative to the benchmark.
Beta1.5
0 (uncorrelated)3.0 (3x amplified)
BenchmarkAsset
When benchmark moves +10%, this asset moves
+15.0%
Amplifies benchmark moves by 1.5x

Beta Ranges​

Beta
Meaning
Example
0
Uncorrelated. Moves independently of the benchmark.
Gold vs. S&P 500 (in some regimes)
0.1 - 0.9
Dampened. Moves in the same direction but with smaller magnitude.
Utility stocks vs. S&P 500
1.0
Moves in lockstep with the benchmark.
S&P 500 index fund vs. S&P 500
1.1 - 2.0
Amplified. Same direction, larger swings.
ETH vs. BTC (~1.3-1.8)
> 2.0
Highly amplified. Much larger moves than the benchmark.
Small-cap altcoins vs. BTC
< 0
Inverse. Moves opposite to the benchmark.
VIX vs. S&P 500 (negative beta)

Beta in Crypto​

Beta is especially useful in crypto because assets within the space are highly correlated, but the magnitude of their moves varies significantly.

BTC vs. S&P 500

Cross-asset beta

  • Beta ranges from ~0.5 to ~1.2 depending on regime
  • Higher beta during risk-on periods (macro correlation rises)
  • Lower beta during crypto-specific events (FTX collapse, halving)
  • Not stable enough to use as a reliable hedge ratio

ETH vs. BTC

Intra-crypto beta

  • Beta typically ranges from ~1.3 to ~1.8
  • ETH amplifies BTC moves in both directions
  • During alt season, ETH beta to BTC can exceed 2.0
  • During BTC-dominance rallies, ETH beta can compress toward 1.0
💡
Beta Is Not Constant

Beta is calculated from historical data and changes with market regime. During calm periods, BTC might show low beta to equities. During a liquidity crisis, correlations spike and so does beta. Always specify the lookback window (30 days, 90 days, 1 year) when citing a beta value, and treat it as descriptive rather than predictive.

Alpha​

Definition

Alpha is the return you got that beta cannot explain. If your portfolio outperformed what its benchmark exposure alone would predict, the excess is positive alpha. If it underperformed, the excess is negative alpha.

The Formula​

α = Ractual - (β × Rbenchmark)

Take what the benchmark did, scale by beta, subtract from your actual return. The remainder is alpha.

Alpha Calculator​

Enter your portfolio return, beta, and benchmark return to calculate alpha.
expected_return = 1.2 x 10% = 12.0%
alpha = 15% - 12.0% = +3.0%
Alpha
+3.0%
Outperformed what beta alone would predict.

Practical Example​

Suppose your crypto portfolio returned 15% over the past month. The benchmark (BTC) returned 10%, and your portfolio's beta to BTC is 1.2.

  • Expected return = 1.2 x 10% = 12%
  • Alpha = 15% - 12% = +3%

You generated 3% of return above what your beta exposure to BTC would explain. That 3% came from something else: asset selection, timing, or strategy.

Where Alpha Comes From​

In crypto, common sources of alpha include:

SourceHow It Works
Asset selectionHolding tokens that outperform the broad market on a risk-adjusted basis
Basis tradingCapturing the basis between perps and spot
Vol tradingBuying or selling implied volatility when it is mispriced relative to realized vol
Funding rate captureEarning positive funding while hedging directional risk
TimingEntering or exiting positions ahead of regime shifts
⚠️
Alpha Is Hard to Sustain

Most apparent alpha in crypto comes from taking hidden risks that have not yet materialized (illiquidity, smart contract risk, tail events). True alpha, excess return that persists after accounting for all risk factors, is rare and tends to diminish as more participants pursue the same strategies.

Beta and Alpha Together​

Beta and alpha are complementary. Beta tells you how much of your return came from market exposure. Alpha tells you how much came from skill (or luck).

High Beta, Low Alpha

Riding the market

  • Portfolio moves with the market but does not outperform it
  • Returns are explained entirely by benchmark exposure
  • Common for leveraged index positions or high-beta altcoin portfolios
  • Not necessarily bad. You captured market upside.

Low Beta, High Alpha

Skill-driven returns

  • Portfolio generates returns independent of market direction
  • Most return comes from strategy, not exposure
  • Common for market-neutral, basis, or vol trading strategies
  • Harder to achieve but more resilient in drawdowns

Test your understanding before moving on.

Q: ETH has a beta of 1.5 to BTC. If BTC drops 20% in a week, what would you expect ETH to do?
Q: Your portfolio returned +8%. BTC returned +12% and your beta to BTC is 0.9. What is your alpha?
Q: Why is beta not a reliable predictor of future moves?

💡 Tip: Try answering each question yourself before revealing the answer.

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