*(Informational purposes only. This post is not intended to be investment advice.)*

A question that I’ve frequently gotten is, **“how money should I allocate to Bitcoin?”** ** I’m not a cryptocurrency fan**, but the folks who ask are usually already very interested and to them, it’s not a question of if they invest but rather how much to invest.

So in today’s post, let’s take a look at how an allocation to Bitcoin might impact the risk of your portfolio. If you need a primer on portfolio strategy and risk, you can read this post by yours truly first:

## Understanding Portfolio Optimization

towardsdatascience.com

The two things to consider when deciding how much of an investment to add to your portfolio (once you’ve decided it merits inclusion) are:

- The investment’s volatility.
- The investment’s correlation with the rest of your portfolio.

In finance, volatility is a reasonable proxy for risk. The higher the volatility of something, the more it’s price will whip around, and the more likely it is that you will experience large drawdowns when things go bad. Large drawdowns might not bother someone like Warren Buffett, but for many investors it can cause panic and bad decision making. So think carefully before exposing your portfolio to excessive volatility.

# Bitcoin Is Way More Volatile Than Stocks

This should be obvious, but Bitcoin is massively more volatile than stocks — **Bitcoin has an annualized volatility of 98% while the S&P 500 has an annualized volatility of 18%**. You can see this in the following boxplot where Bitcoin makes stocks (normally considered a risky asset) look like a Treasury bond.

So we would expect a portfolio with equal amounts of Bitcoin and stocks to have its variance driven mainly by Bitcoin (due to its significantly higher volatility).

# Bitcoin Is More Correlated To Stocks Than You Would Think

Bitcoin is regarded as a diversifier. Yes, as incredibly volatile as it is, like gold its considered a diversifier due to a low correlation historically to traditional risky assets like stocks, corporate bonds, and real estate.

**Well, it hasn’t been that uncorrelated to stocks lately:**

Noticeably, when markets declined last March, Bitcoin took a dive as well (no diversification provided then):

Granted, there are not many assets that provide a true hedge during the darkest times — put options, VIX futures, Treasury bonds, Swiss Francs, the Japanese Yen, and gold are probably it. But even so, it’s disappointing that Bitcoin’s supposed diversification occurred only during good times.

# Sizing Your Bitcoin Investment

Taking all the above into consideration, the most sensible and systematic way to size a Bitcoin allocation is by calculating its risk contribution.

The risk contributions of a portfolio decompose the portfolio’s volatility into its individual drivers (here’s a helpful primer on risk decomposition). In this case, **we want to decompose a portfolio’s risk into the portion from Bitcoin and the portion from stocks**. Here’s some code to do this:

import numpy as np import pandas as pd# w is the weight of bitcoin in the portfolio w = 0.2 # 1-w is the weight of stocks W = np.array([[w, 1-w]])# Calculate the portfolio's weekly volatility # gbtc returns is a dataframe that whose columns are # 1) Bitcoin returns and 2) S&P 500 returns port_vol = (([email protected]_returns.cov()@W.T)**0.5).loc[0,0]# Calculate marginal contribution to variance mctv = gbtc_returns.cov()@W.T# Calculate marginal contribution to risk by scaling mctv by portfolio weights mctr = (mctv/port_vol*W.T)*(52**0.5)

The bar chart below shows the risk contributions when w=0.2 (20% Bitcoin, 80% stocks). The sum of the bars is the total risk (a.k.a. volatility) of the portfolio, which is 26%. That’s significantly riskier than the stock market, which has a volatility of just 18%.

Let’s vary our Bitcoin weight and see what happens to its risk contribution (the total height of the bar, both blue and orange parts, is the total risk of the portfolio):

Once you go beyond a Bitcoin weight of around 15% or so, it quickly starts to dominate the risk of the portfolio. Bitcoin HODLers might not care, but having a bubble asset like Bitcoin contribute more than half of your portfolio’s risk is extremely risky (for lack of a better word).

**My recommendation based on seeing these numbers is to have at the very, very most 10% of your wealth in something like Bitcoin.** And if you must invest, keep in mind that besides its ridiculous volatility, Bitcoin is also more correlated to stocks than you think. Moreover, in the years ahead as we ebb and flow between money printing rallies and rate hike declines, Bitcoin and stocks will probably become even more correlated. So HODL at your own risk!