How does crypto change a portfolio's risk?

Cryptocurrencies such as Bitcoin and Ether have been far more volatile than stocks, bonds or gold: their prices have repeatedly multiplied within months and fallen by 70–80% in bear markets. Adding them to a portfolio changes its risk out of proportion to their weight — and how much it changes can be calculated.

Volatility and correlation

Bitcoin's volatility has historically been around 60–80% a year, roughly four times that of global stocks. Its correlation with stocks has varied: close to zero in its early years, and positive in more recent ones, particularly in sell-offs such as 2022, when crypto and stocks fell together.

The volatility of a portfolio with a crypto share $w_c$ is:

\sigma_p = \sqrt{(1 - w_c)^2 \sigma_s^2 + w_c^2 \sigma_c^2 + 2 \, w_c (1 - w_c) \, \rho \, \sigma_s \sigma_c}

where $\sigma_s$ is the volatility of the rest of the portfolio, $\sigma_c$ that of crypto, and $\rho$ their correlation.

A simple illustration

A portfolio with 15% volatility adds crypto with 70% volatility and a correlation of 0.4 with the rest:

Crypto share	Portfolio volatility	Share of the portfolio's risk from crypto
0%	15.0%	none
2%	15.3%	about 4%
5%	16.0%	about 13%
10%	17.5%	about 28%

A 5% crypto position adds about one point of volatility and carries around an eighth of the portfolio's total risk. At 10%, crypto accounts for more than a quarter of it.

Drawdowns

Volatility understates the effect on drawdowns. In a crypto bear market with a 75% fall, a 5% position costs the portfolio about 3.75% on its own — and more if stocks fall at the same time, as they did in 2022.

0.05 \times (-75\%) = -3.75\%

Things to keep in mind

Position size is the main risk control. Because crypto is so volatile, its weight — more than the choice of coin — determines most of its effect on the portfolio.
Weights drift quickly. After a strong rise, a 3% position can become 10% within months; rebalancing keeps its risk in check.
Correlations are unstable. Crypto has not reliably diversified stock portfolios in sell-offs.
Specific risks — exchange failures, loss of access to wallets, regulation — come on top of the price swings and are not captured by the formulas.

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