Cryptocurrencies are never out of the news. That news lurches from woeful pessimism to exuberant optimism giving rise to substantial volatility. Elon Musk punts cryptos passionately, then retracts, then endorses them again. China cracks down heavily on crypto traders then pushes its own digital yuan. The Eurozone plans to regulate cryptocurrencies then a member of the G8 – Germany – permits local institutional investors to weight portfolios up to 20% in cryptos. And while that is going on, the European Central Bank funds research to install a digital euro.

Investigation

We did some investigation of our own using standard investment procedures and metrics on eight years of monthly data (2013 – 2021) sourced from the JSE ALSI TRI index, the JSE ALBI index and Bitcoin. Our results showed some interesting features.

The end date was simply the most recent data available, but also happens to be 38% off the all-time high of Bitcoin for the analysis period. This, combined with the long analysis period of 99 months, should yield robust conclusions that are not the result of cherry-picking data or periods

Correlations

The investigation shows that the ALBI and ALSI are lowly, but positively correlated which is not unexpected for an emerging market economy. Even in developed markets, the correlation between stocks and bonds tends to be unstable at best (PIMCO, 2013). ZAR Bitcoin returns and the ALSI are uncorrelated while the ZAR Bitcoin returns and the ALBI are negatively correlated. It is possible that this negative correlation arises because Bitcoin unaffected by SA monetary policy while the ALBI is strongly influenced by it. If prevailing interest rates are low globally (discouraging deposits), the lack of individual investment alternatives for investors seeking to hedge against the vagaries of monetary policy decisions may push them into investing in cryptocurrencies where their money can see a return while being protected from inflation.

Using the Markowitz efficient frontier an “optimal” portfolio may be identified. Markowitz’s framework constructs a parabolic frontier in portfolio risk/return space such that, at every level of portfolio risk there is a corresponding maximum possible portfolio return. This is achieved by adjusting constituent asset weights. The resulting curve is a ‘frontier’ because higher portfolio returns than those depicted on the curve are impossible, no matter the combination of constituent weights. Markowitz’s technique also identifies an optimal portfolio – i.e. the maximum risk adjusted return portfolio or the highest ratio of excess portfolio return (over the bank, or risk-free, rate) per unit of risk taken to generate that return.

Using the eight years of monthly data indicated above, the (annualised) results are shown below for an average risk-free rate of 5.9% measured over the period 2013 – 2021 (based off 3M JIBAR). The graph represents the coordinates of the maximal returns for each risk level (the efficient frontier), the optimal (or tangent) portfolio, the minimum variance portfolio (situated at the parabola’s turning point and indicating a portfolio which enjoys the lowest risk: no other portfolio comprising these constituents could be assembled in a way which reduced the portfolio risk further).

ALSI and ALBI risk/return coordinates are also shown with returns of 10.0% and 7.1% respectively, given the high risk-free rate.

Bitcoin’s coordinates are not plotted because they are literally “off the chart” with an annualised return of 107% and an annual risk of 117%.

Constituent weights for the respective portfolios are shown below.

The optimal (tangent) portfolio generates an average annual return of 15.4% using only 7.0% allocated to Bitcoin and roughly equal weights in the ALSI and ALBI. No other combination generates a higher quotient of excess return and risk.

The minimum variance portfolio allocates – not surprisingly – most weight to the ALBI but – somewhat surprisingly – it still allocates 0.5% weight to Bitcoin despite its considerable volatility (see below and note that bitcoin annualised volatility is plotted on the right-hand axis, on a scale  that of the left hand axis for the ALSI and ALBI).

This is because although Bitcoin’s volatility is considerable, its negative correlation with the ALBI helps to lower the minimum variance portfolio’s standard deviation by a tiny fraction (6pbs) and at the same time, boosts the minimum variance portfolios return (46bps). Mathematically, it is not the model’s intention to achieve more return in the minimum variance portfolio, this is just a coincidence and consequence of including Bitcoin.

Cumulative returns are somewhat as expected and it can be seen that the inclusion of Bitcoin is not without risk, the Tangent portfolio value does dip below the return of the risk-free rate mid-2013 due to a large drop in the Bitcoin price after which it recovers. It can also be seen that the minimum variance portfolio does indeed have the most stable returns.

Practical Implications

Note that this is a simple analysis comprising only three assets, ignoring transaction costs and assuming reinvestment of gains or losses, and constant re-weighting for the minimum variance and tangent portfolios. Instruments negatively correlated with the market should theoretically offer returns lower than the risk-free rate as it is tantamount to buying portfolio insurance, the most obvious of these being long a future on the South African Volatility Index (SAVI). However, if Bitcoin were to be considered a legitimate investment, it seems to have similar properties that warrant its inclusion in an optimal and even a minimum variance portfolio.

If all of Germany’s investment funds were to take full advantage of the 20% crypto weight allowance, another US$415bn would flow into cryptocurrencies. The current (August 2021) net value in cryptos is currently larger than the Canadian annual GDP (having passed the GDP of the Netherlands in March 2021 and South Korea’s in April). Pizzas, beer and school fees can already be paid for in Bitcoin in New York and bonuses are soon to be awarded to employees in at least one of the Big Four global accounting firms.

Investors need to answer the question for themselves: is it likely that cryptos will collapse completely? Or continue their explosive and volatile growth?

Works Cited
PIMCO. (2013). The Stock-Bond Correlation.

Contributing authors: Francesca Bell & Kyle Singh

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