How Much Bitcoin in a Portfolio? The Correlation Analysis

Short answer: Until 2019 bitcoin moved almost independently of stocks. Since 2020 it has moved noticeably with them: over the last 52 weeks its correlation with the S&P 500 was 0.33, with the Nasdaq 0.41, and with gold only 0.16. At the same time bitcoin has calmed down; its volatility fell from over 100% to around 45% a year. For your portfolio this means: 1 to 5% bitcoin barely raises the overall risk, while from 10% upwards bitcoin carries a large part of it.

How many percent you want to hold in bitcoin at all, and how to work through a crash for that, is covered in Bitcoin portfolio allocation. This article adds two numbers professionals use to build portfolios: correlation and volatility.

What correlation means

Picture two assets and check every week whether each went up or down. If they almost always rise and fall together, they are strongly correlated. If they sometimes move together and sometimes against each other, with no pattern, they are uncorrelated.

Correlation is a number between −1 and +1:

Two misunderstandings are common.

Correlation says nothing about size. A correlation of 0.3 does not mean bitcoin follows 30% of the stock market's move. It only says how reliably the direction matches. How strongly an asset swings is measured by volatility.

Correlation says nothing about the long run. Bitcoin and stocks can have little to do with each other week by week and still both rise over ten years. Correlation measures short moves, not the trend.

How bitcoin's correlation has changed

We compared bitcoin's weekly closes (this site's daily prices) with the S&P 500, the Nasdaq Composite and the gold future (all in US dollars, Yahoo Finance), every Friday from July 2010 to 6 November 2026. Bitcoin's volatility comes from daily returns.

Over longer periods, where chance plays a smaller role:

Until 2019: a market of its own

In its first nine years bitcoin had practically nothing to do with stocks. The buyers were mostly private individuals and tech enthusiasts, and the price followed its own events: exchange collapses such as Mt. Gox, halvings, hype. What happened on Wall Street hardly mattered. Using daily data for 2017 to 2019, the International Monetary Fund found a correlation of 0.01.

Since 2020: part of the risk assets

In March 2020 investors around the world sold everything that swings. On 12 March 2020 the S&P 500 fell 9.5% and bitcoin 40%. The link remained afterwards. The IMF measured a correlation of 0.36 for 2020 and 2021. Our weekly data show the highest 52-week value in July 2026 at 0.54 and the lowest in December 2019 at −0.22.

The reasons are clear: since 2020 funds, companies and, since January 2024, US spot ETFs hold bitcoin. The same investors who buy tech stocks buy bitcoin, and they sell both when money gets tighter. This was particularly clear in 2022, when central banks raised rates quickly and stocks and bitcoin fell together. How the policy rate and the bitcoin price are connected is explained in Interest rates, central banks and bitcoin.

That the Nasdaq usually correlates a little more than the S&P 500 fits this picture: bitcoin is traded like a growth asset, not like a safe haven.

Gold: not a twin

Bitcoin is often called "digital gold". In the short run it does not behave like it. The correlation with gold was 0.08 over the whole period and hovered around zero from year to year; only in 2020 was it higher at 0.45, when everything fell together in the crash and then rose again. Whether bitcoin takes over gold's role in the long run is a different question from weekly moves. It is covered in Bitcoin vs. gold.

For your portfolio the low correlation with gold is good news: if you hold both, you have two assets that pull each other along very little.

How volatility has changed

Volatility is the typical swing in a year. 45% roughly means: in two out of three years the price ends no more than 45% above or below what the trend would suggest. Stocks such as the S&P 500 come to 12 to 20%, more in crisis years.

Bitcoin's volatility has clearly fallen over the years:

• 2011 to 2013: 80 to 172%. Single days brought +49% or −49%.
• 2017 to 2021: 68 to 93%.
• 2023 to 2026: 42 to 53%. The biggest daily gain in 2025 was 9.5%, the biggest loss 8.5%.

This comes from the larger market: the more money sits in bitcoin, the more it takes to move the price. The bear markets also became shallower, though not harmless. How deep and long each crash was is shown in this comparison, covered in detail in All bitcoin bear markets compared:

Important for the calculation below: bitcoin still swings almost three times as much as a stock index. We therefore calculate with 50%, slightly more than in the last two years.

What this means for a small bitcoin share

Now both numbers come together. How strongly a portfolio of stocks and bitcoin swings depends on three things: how strongly each part swings, how large the bitcoin share is and how correlated the two are.

The basic idea: because bitcoin does not move perfectly with stocks, moves partly cancel out. A small share swings strongly, but often in a different direction from the rest. It therefore adds less risk than its volatility would suggest.

The result for three correlations:

The table shows three things.

Up to 5% the volatility stays almost the same. At today's correlation it rises from 17.0 to 17.1%. Bitcoin then contributes around 6% of the risk.

From 10% bitcoin has a say. A tenth of the money carries a sixth of the risk, a fifth of the money almost two fifths.

The higher correlation has shrunk the "free" range. When bitcoin still moved independently (ρ = 0), the volatility of a stock portfolio even fell up to about 10% bitcoin. Today that effect ends at 1.5%.

Does the formula match reality? We recalculated a portfolio of the S&P 500 and bitcoin with weekly prices, reset to the target share every week:

The picture is the same: up to 5% the volatility did not change, from 10% it rose, and from 20% clearly.

The limits of the calculation

Correlation and volatility are averages over normal weeks. For your decision they are not enough, for three reasons.

Correlation rises in crashes. In March 2020 stocks, bitcoin and, for a few days, even gold fell at the same time. Exactly when diversification should help, it helps least.

The numbers change. Within months the correlation with stocks jumped from −0.2 to over 0.4. Anyone who had planned their share with ρ = 0 was using wrong numbers from 2020 on. So calculate with a value that is rather too high.

Bitcoin crashes are bigger than its volatility suggests. A volatility of 50% sounds like declines of at most 50 to 60%. In fact bitcoin fell by more than three quarters in every major bear market. The formula does not capture these outliers.

Which share fits which goal

Correlation and volatility give three ranges. They do not replace your personal loss limit; they show what a share does to the portfolio.

The banks that recommend 1 to 4% arrive at their number in a similar way. BlackRock, for example, justifies its 2% limit with the risk contribution in a mixed portfolio.

Once bitcoin carries a large part of your risk, a fixed rule becomes important: if bitcoin rises strongly, its share grows by itself, and with it the risk. How to sell back to your target by rule is covered in Taking bitcoin profits. Why diversification matters with bitcoin in other places too, in custody and emergency savings, is shown in Why diversification works differently with bitcoin.