Since the introduction of Bitcoin in 2009 crypto currency has occupied the imaginations of many investors, in large part due to its relatively high returns: since 2014, Bitcoin has had an average annual return of approximately 61%, while Ethereum has had an average annual return of 55% since 2017. Moreover, as of 31/01/2022 the total capital globally held in crypto currency adds up to approximately $1.7 trillion.

Despite the understandable investor interest in crypto currency, a number of open issues remain. These issues are both practical and theoretical. From the practical perspective, investors’ main question is to determine how much capital to allocate to crypto currency versus other investments? The often-debated but principle theoretical question is what is the fundamental economic underpinning of crypto returns?

This note develops a structured framework that addresses the allocation to crypto currency relative to other investment choices. We start with the practical issue for two reasons: first, our framework builds on models that should be familiar to most investors; second, this framework provides a foundation for considering the theoretical issues. Subsequent notes will focus more specifically on these fundamental points.

The Basic Building Blocks of Investing - Risk and Return

By now, most investors are familiar with finding capital allocations to multiple asset classes by using risk and expected return assumptions. Those assumptions include each asset class’s volatility of return, its correlation with the return to all of the other asset classes and its expected return. In our minds, a reasonable starting point for the analysis is to calculate the historical volatility of crypto currencies with standard asset classes and existing fiat currencies. 

As an illustrative example, Exhibit 1 shows the historical volatility of monthly returns for Bitcoin (1) Ethereum was omitted simply because we opted for a longer sample period. ; US equities (as measured by the Vanguard Total Stock Market Index ETF); US Treasury bonds (as measured by the iShares US Treasury Bond ETF); Tesla; Gold, and the USD/EUR exchange rate. Tesla was chosen because it is another asset that has generated high returns and significant public attention, while Gold and the USD/EUR exchange rate were chosen as illustrative of perceived alternative substitutes to bonds. The exhibit shows the average return over the sample period for each asset or currency, as well as the beta against the equity market and the Sharpe ratio. All returns are excess returns (over the 3-month treasury bill). The statistics are measured with monthly returns over the period Oct 1, 2014 through December 31, 2021.

Exhibit 1 - Historical Return and Risk

Three points are clear from the exhibit, and likely to be known by all investors considering crypto currency:

• First, cryptocurrency returns have been more volatile than any of the other assets and USD/EUR.

• Second, the average cryptocurrency return has exceeded (vastly) the average return on all of the assets and USD/EUR.

• Third, this higher realized return seems to aligned with the higher risk: crytpo currency has about the same realized risk-adjusted return, as measured by the Sharpe Ratio (2) The Sharpe ratio is the ratio of the average excess return divided by the volatility of returns. It is a risk-adjusted return on risky assets. In our calculations, all excess returns are over the 3-month Treasury Bill. , as Tesla and the broad equity market.

Each asset's beta to the equity market (3) An asset’s beta relative to an index is the covariance between its return and the index return, divided by the index’s variance. Beta values of one mean that the asset’s return should track the index (all else equal), while betas in excess of one mean that the asset will outperform the market during market rallies (all else equal). Betas less than one mean that the asset will underperform the market during market selloffs (all else equal). and the historical correlation between asset returns, shown in Exhibit 2, provide more information about the relationship between returns. Several observations are in order:

• Bitcoin and Tesla returns were positively correlated with equity market returns. Hence, Bitcoin and Tesla holders should expect to have positive returns when the market has positive returns, all else equal.

• Bitcoin and Tesla betas were significantly larger than 1.0, indicating that all else equal, their returns will outperform the market during rallies and underperform during selloffs, all else equal.

• Gold, bonds and the USD/EUR exchange rate are all risk-reducing assets, as they have correlations to equities that are close to zero or negative. In addition, bonds and the USD/EUR rate are significantly less volatile than the other asset classes.

• The negative correlation between Bitcoin and bonds and USD/EUR suggests that Bitcoin is not (yet) trading as a currency substitute. Close currency substitutes should have correlations closer to 1.0, significantly lower volatility, and significantly lower or negative correlation with the equity market.

Exhibit 2 - Historical Correlations and Equity Market Beta

Finding Capital Allocations with Risk Budgets

We propose to address the issue of capital allocations to crypto currency through an analysis of alternative risk budgets (4) This approach builds on the idea of risk budgeting. See, for example, Risk Budgeting and the Currency Hedge, Kurt Winkelmann, GSAM White Paper, 2001. , rather than finding allocations through the use of standard mean-variance optimization (5) The issues with standard mean-variance optimization are well-known, with the main issue being that optimal allocations are very sensitive to the expected return assumptions. Approaches such as the Black-Litterman model have helped to produce optimal portfolios that dampen the impact of extreme expected return assumptions. .

By contrast, focusing on risk budgets means that investors can make use of more easily estimable quantities such as volatility and correlation (for example, the data in Exhibits 1 and 2). Moreover, they can use these data to answer three questions:

1. How much risk is embedded in the current portfolio?

2. How much risk is allocated to each investment?

3. What happens to risk levels and risk allocation if capital is reallocated?

For example, Exhibit 3 shows the allocations, risk levels and risk attributions for four different portfolios. In the first portfolio, capital is split 50/50 between Bitcoin and Tesla. In the second portfolio, capital is reallocated from Bitcoin to Tesla so that the contributions to portfolio risk are split equally between each investment. The third portfolio is a standard allocation to equities and bonds, with 70% held in equities. In the final portfolio, 1% of capital is reallocated away from the equity market and into the risk balanced Bitcoin/Tesla portfolio. 

Exhibit 3 - Alternative Portfolio Risk Budgets

None of the results in Exhibit 3 should be seen as especially surprising. Shifting allocations away from Bitcoin into Tesla reduces overall portfolio volatility from around 50% to just over 48%, with a more diversified portfolio. The risk reduction is due primarily to the lower volatility of Tesla relative to Bitcoin and the low correlation between the two return series. Similarly, it shouldn’t be surprising that a standard 70/30 portfolio has a much lower overall volatility than the Bitcoin/Tesla portfolio. Finally, it shouldn’t be surprising that even a small allocation to the Bitcoin/Tesla portfolio increases overall portfolio risk.

To be clear, this example doesn’t propose to answer the question of which portfolio is best. Each investor needs to make that determination on the basis of their own risk tolerance and their own views about relative investment returns. Rather, the example is meant to illustrate a practical approach that investors can take to differentiate between alternative portfolios. 

Caveats and Conclusions

The purpose of this note is to illustrate an approach to the challenge of determining allocations to crypto currency. Our intention was not to advocate for crypto currency (nor Tesla). Ultimately, what drives allocations to crypto currency are investor-specific views on relative returns and risk. 

We propose to address the underlying economics of crypto currency risk and return in our next note. More specifically, that note will consider the open fundamental questions, and how alternative resolutions to those questions could affect forward looking risk and return views for crypto currency.