Crypto-currencies as an Asset Class

Introduction


 

Last time we looked at market capitalization of the digital assets and how a buy-and-hold portfolio would have performed over the last four years. Digital assets have experienced influx of capital and along that attention from media. Although it might be hard not to take any sides or argue on the validity of the price actions we have seen in the past year or so, we would like to stay objective in these articles. I do believe in systematic strategies, but I also think best investing strategies emerge from fundamental reasons. Human behavioral biases, market microstructure inefficiencies or even the good old deep value strategy all have one factor in common, a valid fundamental inefficiency which makes the performance of the strategy more relevant in the future. The question that in particular I am after is how much, if anything, one should allocate to digital assets? I am assuming that the total market capitalization of digital assets is going to expand as it gets more attention. Astronomical returns would attract more capital until we reach equilibrium (unless you believe there is no place for cryptos and blockchains in the economy. But let’s assume there is for the sake of this article).

Modern Portfolio Theory was born to answer a similar question. If we take the same framework and apply it to a market-cap weighted portfolio of cryptos, we should have a better understanding of its correlation with markets. In this article we have limited our study to a few ETFs that are designed to follow different sectors of the market. Below we have a list of ETFs.

SPY: US Large Cap
XLE: US Energy
XLF: US Financials
XLU: US Utilities
XLK: US Technology
XLB: US Basic Materials
XLP: US Consumer Non-cyclicals
XLV: US Healthcare
AGG: US, Broad Market Investment Grade
HYG: US, Broad Market High Yield
GSG: Commodities Broad Market
VNQ: US, Real Estate
VIX: SPX 30-day Volatility Index

While the list above by no means is not exhaustive, we have intended to capture various sectors of the market as well as asset classes. Our analysis is divided into three parts. First, we perform a correlation analysis. Both on the panel and rolling correlation to capture any linear relationship that might exist between these portfolios. Second, we look at the risk-return characteristics of these portfolios. We also compare the diversification benefit that a crypto buy-and-hold strategy might add to a buy-and-hold US large cap portfolio. Last, we put aside all distributional characteristics of a passive crypto portfolio and look at the co-dependence of a passive crypto strategy and a passive equity strategy.

 

Data


 

Since Yahoo Finance has made some changes to their API, we have turned to AlphaVantage for free ETF data. Although AlphaVantage offers data on digital assets, we decided to reuse the data we had to have a consistent analysis. Thus, all the data relating to digital assets is coming from CoinMarketcap. You can find further information here.

Analysis


In the first part of our analysis we examine whether there is any linear correlation between a marketcap-weighted portfolio of cryptos and the ETF’s listed in the Introduction. We perform the analysis on all three correlation definitions. You can find detail regarding the details of the definitions here. The passive crypto portfolio is CRP here.

pearson
Figure 1. Pearson correlation of a market-cap weighted portfolio of top ten largest cryptos and various market sectors.
spearman
Figure 2. Spearman correlation of a market-cap weighted portfolio of top ten largest cryptos and various market sectors.
kendall
Figure 3. Kendall rank correlation of a market-cap weighted portfolio of top ten largest cryptos and various market sectors.

Surprisingly, the CRP portfolio, regardless of correlation definition, has no correlation with any of the portfolios. The above plots are calculated over the time frame that CRP portfolio was made (For construction of the CRP portfolio please go to here). Our next step would be looking at rolling correlations. There might be strange dynamics between these portfolios that has turned very close to zero on average but is far from zero over different time periods.

rolling_1
Figure 4. Rolling Pearson correlation of a market-cap weighted portfolio of top ten largest cryptos and various market sectors. The window size is 60 days.
rolling_2
Figure 5. Rolling Pearson correlation of a market-cap weighted portfolio of top ten largest cryptos and various market sectors. The window size is 60 days.
rolling_3
Figure 6. Rolling Pearson correlation of a market-cap weighted portfolio of top ten largest cryptos and various market sectors. The window size is 60 days.

In general, the rolling correlations are very tamed. It is rare to see a value above 0.2. All the time series show mean-reverting behavior and the sixty-day window should have a reasonable accuracy, one standard deviation is about 10% of true value, for volatility/estimation to trust the above results (You can read more about the standard error of volatility estimates in here). It does seem that the digital assets are not correlated to the general market. If indeed the correlations are low, we should see very significant benefits in allocating a percentage of bankroll to digital assets. Of course, this is assuming the correlation would stay low in the future.

efficient_frontier
Figure 7. Annualized return versus annualized volatility of CRP versus various sectors of the market.

Figure 7 shows a Markowitz style risk-return plot. While we are well aware of the pitfalls in implementation and distributional assumptions behind the Modern Portfolio Theory, it is still a powerful tool to understand the efficient frontier and optimal portfolio. In fact, the plot above is screaming about two products that investors should add to their allocations. Volatility products and digital assets. The optimal portfolio with and without these allocations would certainly show a very different risk-return behavior.

To assess the diversification benefits of an allocation to digital assets, we should look at the drawdown curves as well.

DrawDown
Figure 8. Drawdowns of CRP portfolio versus SPY in percentage terms.

Figure 8 is very insightful. Surprisingly it shows smaller but much longer drawdowns in CRP portfolio compared to SPY. In other words, the diversification comes not only at a cost of much higher volatility but also prolonged periods of drawdown.

We have not performed any analysis on distributional characteristics of the returns in digital assets compared to stocks, commodities, currencies or etc. Intuitively, we expect high kurtosis and fat tails. If we put the distributions aside and simply look at the co-dependence between a marketcap-weighted portfolio of US large cap stocks and CRP, we have Figure 9. In short, we have used the Copula Theory to factor in distributional features of CRP and SPY portfolios.

Copula
Figure 9. CRP and SPY copula.

The scatter plot looks very much like a two-dimensional uniform distribution. Put differently, the plot shows that there is zero to little co-dependence between CRP and SPY.

 

Final Remarks


 

The entire analysis points us to one conclusion. Digital assets are a rising asset class with little to zero correlation to traditional asset classes. It is hard to believe that these low values would persist in the future as high returns would almost certainly attract capital. The fact that we have not seen any significant correlation does not automatically mean that we should allocate a sizable portion of our bankroll to digital assets. The diversification benefit comes at the cost of significantly high volatility and very long drawdowns. However, had we solved a quadratic optimization on the allocation among these portfolios, cryptos would most probably get a weight significantly higher than zero.

 

Codes


The codes for this analysis is in here.

Disclaimer


None of the ideas posted on this blog are investment advice. Use at your own risk/discretion.

 

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Passive Investing in Cryptos

Setting The Benchmark

There has been a lot of hype about bitcoin and cryptocurrencies lately. Most of the general public is in shock and awe for missing out on astronomical returns. Some early adopters, however, have made a hefty chunk of money. Should we look at them as the next generation of (crypto) hedge fund managers? or they have been simply lucky? let me ask this question differently, how much return (and volatility) is good for a strategy in cryptos?

Cryptos
Figure 1. Are cryptocurrencies the future?

So it is becoming a little more obvious where I am going with this post (which is also my first). Like any other market, we need a benchmark in this market. This would allow us to assess the performance of active strategies. An index that is serving as a benchmark, by construction, helps to quantitatively assess extra return and volatility of superior manager with impressive “alpha”.

So let’s get to it. I am going to look at the equity curve of a market capitalization-weighted passive strategy. But first, a few technicalities.

  1. Yes, I understand there would be limitations going back in time and the index would mostly consist of bitcoin, but let’s say for a moment we have accepted these practical issues. Particularly, we just want to know how much one would have earned if he had made a cap-weighted portfolio of top ten largest currencies (by market capitalization) and rebalanced every day.
  2. I also understand that companies follow a certain methodology to construct widely-followed indices (you can look at S&P US Indices Methodology for S&P methodology on their indices), but here we are going to accept the fact that we did not have a big universe of cryptos back in 2013. So I am going to take the top ten currencies today, go as far back as I can and build the portfolio.
  3. Yes! there is forward-looking bias! You could argue that in 2014 I could have not known that ETH (Ethereum) would be a big cryptocurrency. Just bear with me here, I think the bias is actually not material and the performance would not suffer dramatically. Remember that this is a passive strategy, we are not trying to actively beat the market.

I used the data from Coin Market Cap which goes back to 2013. The strategy simply holds the coin that has higher market value and rebalances the portfolio daily. For example, if BTC has twice the market capitalization of ETH, and we have only these two coins, the weights in our portfolio would be 2/3 and 1/3 respectively. For this exercise we have only looked the top 10 coins with the highest market cap. The results should be more or less robust if someone looks at a portfolio that holds all 1000 or so coins. This is due to the enormous market cap of BTC and ETH compared to the rest.

Figure below shows the equity curve for a passive cap-weighted strategy.

 

pnl_capweighted.png
Figure 2. The equity curve of a $1 invested in a market-cap weighted portfolio. The universe consists of top 10 coins by market capitalization.

 

In the next post, we will look at a few statistics for this basic strategy. It would also be interesting to look at diversification benefits of holding this portfolio and its relative performance compared S&P500.

Happy trading,

HD