Bitcoin & Crypto | Monetary Policy & Inflation | US

## Summary

We investigate what impact minor allocations (1% to 5%) of crypto in a portfolio of well-diversified assets have on the overall portfolio performance.

Three versions of a model portfolio aimed at European investors are considered: a Eurozone portfolio (calculated in EUR, Table 1), a Swiss Portfolio (calculated in CHF, Table 2), and a UK portfolio (calculated in GBP, Table 3), with the bond ETF used the only difference between the three. The results of the analysis are calculated in each respective currency.

Some key considerations involved in the study include:

- All data is obtained from Bloomberg.
- Each portfolio starts on 2 August 2010 and ends on 11 July 2023.
- Each portfolio simulates the progression of a 100 EUR/CHF/GBP investment.
- The crypto component in each portfolio is the MSCI Global Digital Assets Select Top 20 Capped Index backdated to 2010 using bitcoin prices.
- Weights and returns are calculated in EUR. CHF, and GBP for each of the three portfolios, respectively.

- We use total returns for each asset.
- Monthly, quarterly, and yearly rebalancing (with fractions) are considered.
- We perform a bootstrapped analysis to arrive at distributional estimates for performance metrics to try and mitigate the path-dependency of portfolio returns.
- Trading costs are ignored.

(* This report was originally produced for ETC Group.*)

## Model Portfolio Weights with and Without Crypto

The model portfolios are split into a risk component (60%) and a risk averse component (40%). Their structure and asset allocation is not the result of our portfolio analysis – it rather represents a pattern that can be found very often in discretionary portfolios and DIY portfolios.

- The risk component (60%) contains all assets except the bond ETF.

- The risk averse component (40%) contains the respective bond ETF only.

- We introduce crypto weightings (1% to 5%) to each portfolio by reducing the 60% risk component proportionally across all the risk assets (the risk averse component remains 40%).

Examples of the weightings for the EUR portfolios with crypto allocations from 1% to 5% are shown in Charts 1 to 6. Notably, all risk components are reduced proportionally, and the bond ETF is left untouched. The same is true for the CHF and GBP portfolios.

## Crypto Correlations

Cryptocurrencies can serve well as an extra source of diversification in a portfolio of well-diversified assets. Here are the details on crypto correlations through time:

**From the inception of crypto:**The correlation between crypto (proxied by the MSCI Global Digital Assets Select Top 20 Capped Index which has been backdated using bitcoin prices obtained from Bloomberg) and other assets considered in the model portfolios is low. Since the inception of crypto (c. 2010), it has been most correlated to the Global Equity Index (+10%) and the Global EM Equity Index (+7%) while being uncorrelated to rest (Chart 7).

**When crypto became mainstream:**Crypto became more mainstream from 2017 onward and prices peaked (locally) in December 2017 with the launch of CME bitcoin futures. Looking at data from 2017 onward reveals the crypto components correlation to the Global Equity Index is +23%.

**Institutional flows:**Another pivotal moment in the history of crypto as an asset class was when the first US Bitcoin ETF (based on CME Bitcoin futures) started trading on 19 October 2021 which made it easier for institutional investors to participate in the space. Looking at all data from this date onward reveals the crypto components correlation to the Global Equity Index is +46%.

**Where are we now?**Year to date the correlation of the crypto component to the Global Equity Index (+16%) remains low (Chart 8). A correlation between crypto and equities exists, but the relationship is more nuanced and often more overstated than reality when looking at the big picture.

In terms of any patterns we observe in the correlation structure between crypto and the other assets we find that:

- Crypto’s correlation to developed market equities (Global Equity) and emerging market equities (Global EM Equity) generally moves in the same direction over time as shown by the rolling 3-month correlation (Chart 9). Indeed, we show the percentage of days per year the sign of the correlation to each of the equity ETFs differed (Chart 10). From 2017 onward, with the exception of the Covid pandemic that started in 2020, the percentage has been relatively low (sub 15%).

- The correlation between crypto and the Eurozone, Swiss, and UK bond ETFs has some bias for moving in the same direction, though there are more frequent instances where the sign of the correlations differs when compared to that of the equity ETFs (Charts 11 and 12). Standout years include 2017 where almost 70% of the year saw these correlations move in different directions.

- The relationship between crypto’s correlation to gold and commodities is more intermittent, with instances recently where the correlations have diverged completely (Chart 13 and 14).

## EUR Portfolio Performance

Tables 4 to 6 show the performance of the Eurozone model portfolios over the period (2 August 2010 – 11 July 2023) for all crypto weightings and rebalancing frequencies considered (*we provide an in-depth analysis for the Eurozone portfolio, but the following analysis is similar for the CHF (Tables 9-11) and GBP (Tables 12-14) portfolios).*

In terms of risk-return comparisons, we find that:

**Returns:**As expected, including the crypto component increases the CAGR (Compound Annual Growth Rate) and percentage returns over the period for all crypto weightings and rebalancing frequencies considered.

**Portfolio risk:**With a monthly rebalance frequency the portfolio volatility increases slightly when using 3%+ crypto weightings. Portfolio volatility increased significantly for all crypto weightings when using a quarterly or yearly rebalance, compared to monthly rebalancing.

**Risk-adjusted returns:**All scenarios led to higher Sharpe ratios (and better Calmar and Sortino ratios). The largest increase is seen in the 5% weighting for a monthly rebalance – there is an over +142% uplift in the Sharpe Ratio (0.97) when compared to that of the no crypto portfolio (0.40).

**Drawdowns:**For monthly rebalancing, the maximum drawdown over the period for the portfolios that include a crypto component are comparable to the no crypto portfolio. For quarterly and yearly rebalancing, the maximum drawdowns increase significantly as we increase the crypto weight.

Another observation alongside the uplift in risk adjusted returns is the increase in the skew (of the returns) as the crypto weight is increased. Skew refers to the distribution of returns, particularly the likelihood and magnitude of extreme gains or losses.

- Positively skewed returns will generally have more losing days than those of negatively skewed returns but the losing days will be relatively small in magnitude.

- Negatively skewed returns will have fewer down days, but the losses on those days will be larger. Positive skew is attractive as it focuses on generating a higher frequency of smaller gains while minimising the likelihood of large losses.

- The model portfolio without crypto has a negative skew (unfavourable), but when incorporating crypto the skew increases (favourable) which helps the portfolio enhance the potential for outsized profits while managing the risk of significant losses.

### Observations on Rebalancing

More often rebalancing allows for more control of portfolio risk but also increases trading costs (which we do not consider in this study). A trade-off between the two must be made. To show how much extra risk is being born by adopting lower frequency rebalancing, we show the evolution of the asset weights for the 3% crypto component portfolio for the three rebalancing frequencies (Charts 15 to 17).

The average weight of the crypto component for the monthly rebalance is 3.2%, compared to 4.1% for the quarterly and 8% for the yearly (Table 7). Furthermore, at times the crypto weight becomes unacceptably large for the quarterly and yearly rebalance frequency with the maximum weight of the crypto component being 54% and 76%, respectively.

If we look at all instances where the weight of crypto exceeds 10% (which is over 3 times its intended weight of 3%) we can get a better understanding of how long the extreme allocations have lasted historically. Table 8 shows the number of days per year this occurred for the 3% crypto Eurozone portfolio – 2013 stands out with 206 days for the yearly rebalance, 40 for the quarterly, and 5 for the monthly. Moreover, in 2013 the allocation for crypto exceeded 50% on 31 occasions for the yearly rebalance.

### Bootstrapped Performance Metrics

The performance metrics displayed so far relate to a single sample path – we are considering only one thread of history. While this is useful to understand at a high level what crypto can do for a portfolio, it introduces a path dependency which makes the metrics sensitive to the start date of the sample. Put another way, had we chosen a different start date, we would see different metrics (though we would expect the conclusions to be the same in this study).

To reduce the sensitivity of the metrics to the starting date, we run the following procedure to bootstrap performance metrics and obtain distributional estimates **(monthly rebalancing is considered in this analysis):**

- Choose a random starting date such that there is at least three years of data available after this date.

- Evaluate the no crypto portfolio and 3% crypto portfolio metrics over the following three years.

- Repeat the process 1,000 times.

We focus on the following three metrics:

**Sharpe ratio:**The Sharpe ratio evaluates the risk-adjusted return of an investment or portfolio, indicating the (excess) return earned per unit of risk taken. A higher Sharpe ratio signifies better risk-adjusted performance.

**Calmar ratio:**The Calmar ratio assesses the risk-adjusted return in relation to maximum drawdown, representing the downside risk. A higher Calmar ratio implies better risk management, as it demonstrates the ability to recover from losses more efficiently.

**Sortino ratio:**The Sortino ratio, similar to the Sharpe ratio, measures risk-adjusted returns but focuses solely on downside risk, particularly the volatility of returns below a target level

Across all 1,000 trials we find that the distribution of the Sharpe, Calmar, and Sortino ratios favour the 3% crypto component portfolio over the no crypto portfolio (Charts 18 and 19). In particular, we find that:

- The average Sharpe ratio for the 3% crypto component portfolio (0.84) is 75% higher than that of the no crypto portfolio (0.48).

- The average Calmar ratio for the 3% crypto component portfolio (0.59) is 79% higher than that of the no crypto portfolio (0.33).

- The average Sortino ratio of the 3% crypto portfolio (1.14) is 81% higher than that of the no crypto portfolio (0.63).

- The above conclusions are also generally true across the portfolios with the other crypto weightings. Moreover, the difference between the mean ratios for the crypto and no crypto portfolios are statistically significant under a T-test.

- A scatter plot of CAGR versus volatility for all 1,000 samples for the no crypto and 3% crypto portfolios reveals that adding crypto leads to higher CAGR values for a comparatively small increase in the portfolio volatility (Charts 20 and 21). This is consistent with higher risk adjusted returns.

- The skew of portfolio returns in the samples is also higher for the crypto portfolios with 208 samples out of 1,000 (20.8% of the total samples) having skew greater than 0 for the 3% crypto portfolios compared to just 8 (0.8% of the total samples) for the no crypto portfolios (Charts 20 and 21).

## CHF Portfolio Performance

## GBP Portfolio Performance

## Conclusion – Should You Allocate Cryptocurrencies to Your Portfolio?

**An allocation to crypto boosts (risk adjusted) returns.** The analysis has shown that a minor allocation to crypto in a well-diversified portfolio enhances risk-adjusted returns. Indeed, in most cases a crypto allocation of around 3% with monthly rebalance frequency has led to a doubling of the Sharpe ratio with a very small increase in the total portfolio volatility (usually around 1 percentage point). Moreover, the bootstrapped analysis confirms the uplift in risk adjusted returns is statistically significant. This gives a good idea for the future use of crypto in the portfolio.

**Crypto allocations can help increase skew. **Aside from increasing the risk-adjusted returns, an allocation to crypto has been shown to increase the skew of portfolio returns. Therefore, a minor allocation to crypto should help well diversified portfolios enhance the potential for outsized profits while managing the risk of significant losses.

**Crypto appears to be a good candidate for portfolio diversification **and the growing number of cryptocurrency sectors (smart contract platforms, privacy coins, metaverse etc.) adds to the** **diversification effect. However, crypto’s correlation to macro markets is not zero which does present some risks. Moreover, the correlation structure between crypto and macro is not always stable which adds to those risks.

**The rebalancing frequency plays a critical role** in ensuring that the weight of crypto component does not become unacceptable large, which we find occurs at times for quarterly and yearly rebalancing. A trade-off between transaction costs and how much risk an investor is willing to bare is needed.

*This report was originally produced for **ETC Group**. *