## 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.

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.

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.

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.

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.

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.