Before we talk about risk from crypto exposure, let’s cover the higher level topic of Modern Portfolio Theory. Straight from the wiki: “Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk.”

The premise upon which MPT is built is that investing in multiple assets (indexing) is less risky than owning just one or a few (individual stock picking). More technically, you can reduce the risk of your investment portfolio by diversifying your holdings into assets that are negatively correlated.

This has been conventional wisdom for a long time and shouldn’t be news to anyone with interest in personal finance, financial independence, or investing in general.

Harry Markowitz introduced MPT in the 50s, along with the concept of the Efficient Frontier (Figure 1).

The frontier itself is a set of all the optimal portfolios that offer the highest level of returns for a given level of risk. Any portfolio along the line is optimal, while any portfolio in the area below and to the right of the line is suboptimal. The X-axis is risk, measured as the standard deviation of annual returns, while the Y-axis is annual returns. The main idea I’d like to reiterate is that you can reduce the standard deviation (risk) of a portfolio’s returns by investing in assets with low or negative covariance. For a given level of risk, there are innumerable portfolios that can be constructed to generate higher or lower returns. Your goal as an investor should be to find a portfolio that sits on the curve, so that you’re getting the maximum amount of return possible for your chosen level of acceptable risk.

NOTE: Check out these articles on Investopedia if you want to learn more about MPT and the Efficient Frontier.

The standard deviation of an assets returns can also be called risk or volatility. A stock whose returns deviate greatly from the mean is said to carry more risk. The first step in trying to quantify this risk is to pull some financial data of various assets and calculate their returns. For this example, I’ll use:

• ^GSPC, the ticker for the SP500, to represent stocks.
• BND, a Vanguard Total Bond Index fund, to represent bonds.
• and BTC-USD, AKA Bitcoin.

For this analysis, I chose a 2 year period as the timeframe. Next, we’ll find the logarithmic return of each asset so that we can examine them separately in the specified timeframe.

Uh oh! It’s the methodology police. There are a LOT of different pros and cons for calculating either logarithmic or simple returns. An appropriate method for this example is to calculate the arithmetic mean of the logarithmic returns of the assets, as I’ve done here. Another appropriate method could be to calculate the geometric average of the simple returns. An arguably incorrect method for comparing asset performance is to calculate only the arithmetic mean of the simple returns. If this all sounds confusing, here’s a good discussion of the topic. The important thing to note is that due to the complex nature of compounding returns and the fact that, for example, +5% and -5% do not cancel out to 0%, there are many of considerations involved in making an appropriate calculation. Seeing as this post is for demonstrative purposes only, I’m OK with the selected method.

This shows us the daily log returns of the assets. To see an annualized amount, multiply the mean daily returns by the number of trading days in a year for each asset: 250 for stocks and bonds, 365 for Bitcoin. (252 is technically more accurate, but the difference is negligible.)

For calculating standard deviation, we can use the Pandas .std() method. Following the same logic as before, we need to annualize this number. However, instead of simply multiplying by the number of trading days, we also need to take the square root of the number of trading days due to the algebra involved in converting variance to standard deviation:

From here we can summarize the data visually in Tableau — showing that Bitcoin has had significantly higher returns, while also carrying significantly more risk (Figure 2).

From this graph we can answer our first question from earlier — how risky is Bitcoin compared to the typical stock and bond indices?

During this specific two year period, BTC provided a return that was about 3.7x higher than that of the SP500. With higher return is an expectation for greater volatility, which is also present — BTC’s standard deviation was 3.3x higher than the SP500.

It’s time for everyone’s favorite financial disclaimer: past performance is no guarantee of future results. Notice how I am not making any claims about what could happen in the future — I am simply stating the results of my specific analysis over this given timeframe. Despite the high returns, this is absolutely not a suggestion to lever up and go 100% Bitcoin.

One interesting point from Figure 2 is that BTC provided a greater increase in return per unit increase of risk relative to stocks and bonds. Because of that, it appears BTC would have been a “good” investment in this timeframe. This conclusion is corroborated by my own Roth IRA portfolio over a similar period (Figure 3 below). (Note that the time period in Figure 3 is not the exact same as the one used in the analysis above, because my Roth IRA account was created in November of 2019 and thus has no data between June-October 2019.)

This graph is a screenshot from my own Charles Schwab Roth IRA account which depicts the risk and return of various benchmark portfolios along with my own (green square). If you imagine a linear regression line of best fit based on the benchmark portfolios, you can see that my own would lie above the line, indicating that it outperformed the predicted risk-return relationship by generating a greater-than-expected return for a given level of risk. The reason that my portfolio risk (and subsequent return) is so high is that I had significant exposure to BTC (via GBTC) in this account. Based on the data we calculated in Figure 2, this exposure to BTC affected my portfolio in exactly the way we expected — higher risk, but higher reward.

Notice how Figures 1, 2, and 3 agree with one another nicely. Figure 1 shows the theoretical efficient frontier, Figure 3 shows a real application of that frontier, and Figure 2 is just a subset of Figure 3 that we calculated ourselves.

The conclusion for this section is that BTC was an extremely volatile asset over the given 2 year period. Despite this, it did provide enough return to justify the risk.

One last note before we move on. I want to emphasize that I treat Bitcoin and other cryptos as highly speculative assets. It’s hard to tell from the context given, but I never had more than 5% of my liquid net worth in Bitcoin at any given time. My Roth IRA is labeled as an “extremely aggressive” portfolio based on my allocation because I wanted to utilize the tax advantages of the account. In reality, my total portfolio (when you consider both my Roth IRA and my taxable investment accounts) is much more conservative.

Coinsmart. Beste Bitcoin-Börse in Europa
Source: https://medium.com/swlh/how-much-bitcoin-should-you-reasonably-own-ae9b66cfb3d?source=rss——-8—————–cryptocurrency