How to improve the efficient frontier!

n previous articles we have talked about the history of Gold (Inflation is the main threat to the containment of purchasing power for everyone, bar none.), how Gold is a great hedge for stock markets and therefore makes sense to include in an investment portfolio, how Gold protected against inflation during the very high inflation period of the 1970s-80s (Inflation, the Well-Known Phenomenon), but also about Bitcoin and its ability to outperform any asset over the last 8 of 10 years (Gold, Bitcoin or both?). 

Then we also explained that if I want to create a risk parity strategy, it is better to use the Ulcer Index (Ulcer Index, a practical application) instead of the abused volatility that fails to recognise whether there is a positive or negative trend. 

Using the Ulcer Index, we have created an index composed of Gold and Bitcoin that has a track record (albeit back-tested, stellar), now it is time to see how a Bitcoin & Gold index can increase the risk-adjusted return (i.e., the risk-adjusted return assumed) of a traditional portfolio composed with varying percentages of the world stock market and a popular global bond index, namely the Global Aggregate Bond Index. 

To do this, we first calculated the 10-year return and volatility of both indices, and then combined them in incremental steps of 10%. 

Figure 1: Efficient Frontier with Equity and Bond with Variable Weights 

In fact, the first portfolio, which is dark red, has 100% in Global Aggregate Bond and 0% in MSCI World, then the lighter red has 90% in bonds and 10% in equities, and so on down to the purple one which has 100% invested in MSCI World and 0% in Global Aggregate Bond. 

Obviously, these portfolios are arranged along the so-called efficient frontier, i.e. a curve where return is maximised or risk is minimised according to the percentage of each asset in the portfolio. 

Now the question is: can this risk/return ratio improve if I introduce a 5% share of BTCG, i.e. the Diaman Bitcoin & Gold index into the portfolio? 

Before answering this question, it is correct to analyse the correlations between the various parties involved, to understand whether Bitcoin or Gold make sense to be introduced in an investment portfolio 

Figure 2: Correlation Matrix of Key Asset Classes versus BYCG

As can be seen, both Bitcoin and Gold have a low correlation with the stock markets and even less with the bond market, a feature that bodes well for an improvement of the efficient frontier in Figure 1, especially with the introduction of the BTCG Index, i.e. the Diaman Bitcoin & Gold Index. 

Figure 3: Impact of 5% BTCG in an Equity and Bond portfolio 

In fact, it can be observed that the introduction of a mere 5 per cent not only increased the (past) return, but also reduced the volatility, an effect that leaves no doubt as to the importance of including both Bitcoin and Gold, actively managed like this index in an investment portfolio. 

Figure 4: Effect of including 10% BTCG in a portfolio 

This effect becomes even more pronounced if we include 10% BTCG in the portfolio, as can be seen in the graph above. 

But then, if I put 20% in the portfolio, what effect would I get? 

Figure 5: how a portfolio changes with 20% BTCG instead of equities 

In fact, as the percentage of BTCG increases, the expected return increases and volatility decreases, although from 10% to 20% volatility remains almost unchanged compared to only 10% weight in portfolios. 

20% of an index composed of Gold and Bitcoin might seem like a lot, in reality there are many so-called 'Lazy Portfolios' that make use of such percentages and sometimes more Gold in the portfolio. 

The Lazy Portfolios originated from the idea of Ray Dalio, founder of Bridgewater, one of the largest and most famous hedge funds in the United States, to create a portfolio that is good for any market situation, which he called All Weather, or all seasons. 

Over time, different versions of the Lazy Portfolio have evolved and been presented, the most famous being the Golden Butterfly and the Permanent Portfolio. 

While in 2023 Ray Dalio was quite sceptical about Bitcoin (although he had bought a little bit of it for his hedge fund), by 2024 he had completely changed his mind, as witnessed in this infographic:

Figure 6: How Ray Dalio changed his mind about Bitcoin 

Without wishing to go into the merits of his legitimate and opportune change of mind (only fools never change their minds), let us try to see how BTCG might impact a Lazy portfolio, starting with Ray Dalio's own portfolio:

Figure 7: All Weather over the last 10 years 

The All Weather consists of 30 per cent Large Cap equities, 40 per cent in long-term bonds, 15 per cent in medium-short term bonds, 7.5 per cent in commodities and 7.5 per cent in Gold. 

Over the past 10 years, this portfolio has returned 5.1% with a volatility of 8.5%. 

How would the return and risk have changed if BTCG at 7.5% had been inserted instead of Gold? 

Figure 8: All Weather with 7.5% BTCG instead of Gold 

The return would be 6.3% with a volatility of 8.2%, in fact the choice would be 'no brainer' i.e. no further analysis would be required to replace Gold with BTCG. 

If, on the other hand, we tried to consider Bitcoin a commodity and thus also put that 7.5 per cent on BTCG, the average annual return would have skyrocketed to 8.1 per cent with the volatility virtually unchanged from the starting portfolio. 

Figure 9: All Weather with $15% BTCG instead of Commodity and Gold 

Now let us try to see the impact of replacing Gold with the Diaman Bitcoin & Gold Index on the Golden Butterfly, a portfolio that invests 20% in 5 different asset classes, i.e. one part in large-cap stocks, one part in small-cap stocks, a third part in long-term bonds, one part in short-term bonds and finally the last 20% in Gold. 

In this case, the return over the last 10 years would have been 6.9% with a volatility of 7.4%, so considerably better than the All Weather (which, however, was invented well before the Golden Butterfly..). 

How does the portfolio change if I invest in BTCG instead of Gold? 

Figure 10: pure Golden Butterfly strategy 

In this case, 20% of the Diaman Bitcoin & Gold Index raises the return to 10.5% with a slight increase in volatility to 8 per cent, which is amply justified by the increase in expected return. 

Figure 11: Golden Butterfly Strategy with BTCG in Portfolio 

Again, if not the entire Gold component of the portfolio, it would be good to replace at least 50% of it with BTCG. 

We conclude this overview with the permanent portfolio, where Gold has a weight of even 25%. 

Figure 12: Permanent Portfolio Strategy with 25% BTCG 

As can be seen, the return increases from an average of 6% per annum to 10.4%, if one introduces the Diaman Bitcoin & Gold Index into the portfolio with an increase in volatility from 7.4% to 8.2%, thus an expected return increase of 4% at the cost of 1% more volatility, again a really easy decision to make. 

By the end of this roundup of articles, which I encourage you to read if you missed them, we have realised that introducing Bitcoin and Gold into your portfolio is crucial, especially if through a tool that actively manages the exposure of one or the other based on market trends, beautifully captured by the Ulcer Index. 

The Diaman Bitcoin & Gold Index is calculated daily by Compass, a company that makes Benchmarks for third parties, and is taken from an ETP company and listed on Euronext Paris, but I won't tell you the name so as not to get into financial instrument promotion, if you want to know, you can ask me in the comments. 

Good investments to all.