Application of Modern Portfolio Theory (MPT)
Modern Portfolio Theory (MPT), developed by Harry Markowitz, provides a framework for optimizing the risk-return relationship of a diversified portfolio.
In essence, the theory demonstrates that the return and risk of an individual asset matter less than the behavior of the portfolio as a whole, because by combining assets with imperfect correlations, it is possible to reduce total risk without sacrificing return.
The fundamental principle of MPT is efficient diversification: by including different assets, we seek to maximize expected return for a given level of risk (or, alternatively, minimize risk for a given return). The result of this optimization is the so-called efficient frontier, which represents all optimal combinations of investments – that is, those portfolios that offer the highest possible return for each possible level of risk (volatility).
In our case, we calculated the efficient frontier for the four crypto assets (BTC, ETH, BNB, SOL) using expected returns and covariances estimated from historical data. Practically speaking, this involved mean-variance optimization algorithms that sought the best proportions of each asset in the portfolio. The resulting cryptocurrency efficient frontier confirms the intuition that:
Bitcoin and Ethereum (the highest market cap assets) tend to make up a significant portion of the lower risk portfolios, given that they have relatively lower volatility and are seen as 'blue chips' in the crypto market.
BNB and Solana (high growth altcoins) appear in larger proportions in the higher expected return portfolios, as they have historically high returns, although they come with substantially higher risk.
For a moderate risk profile, the goal is to find an intermediate point on this efficient frontier – a portfolio that is not so conservative as to excessively sacrifice return but also does not assume the highest levels of volatility.
In Markowitz terms, it would be a portfolio close to that of the highest Sharpe Ratio, which most efficiently balances return against risk (considering, for simplicity, a risk-free rate of ~0).
In practice, this moderate portfolio tends to be positioned in the middle of the efficient frontier, capturing some of the returns from more aggressive altcoins while mitigating risks with a good dose of BTC/ETH. The figure below illustrates the estimated efficient frontier for the four assets and highlights the position of the optimal portfolio for a moderate investor:
Observing the chart, we see that the moderate portfolio (green point) indeed lies on the efficient frontier (i.e., it is optimal according to the mean-variance criterion) and is positioned between the minimum risk portfolio and the maximum return portfolio. This means that:
If the investor were extremely conservative, they would end up choosing a portfolio close to the left corner of the frontier (minimum volatility ~49% per year in the example, mostly composed of BTC) – but their expected return would be much lower (~22-23% per year in this case).
On the other hand, an aggressive investor focused on maximum return would be at the upper right corner (100% in SOL, volatility ~70% per year, return ~40% per year, but with a high chance of severe fluctuations).
The moderate investor, however, chooses the green point, which offers approximately 29% expected return with ~52% volatility, a much more attractive commitment in terms of return per unit of risk than the extremes.
This moderate portfolio captures part of the risk premium of the altcoins (SOL, BNB) but dilutes the shocks by maintaining almost half of the allocation in more stable assets (BTC, ETH). As the theory suggests, no other combination of assets offers a higher return for this same level of risk.
Recommended Allocation
Based on the optimization described, we arrived at the ideal investment proportions in each cryptocurrency to compose the moderate portfolio.
Here is the recommended percentage allocation and translates these percentages into dollar values for the weekly contributions of $250 (as stipulated).
This distribution of 30/20/30/20 is approximate, representing the 'best balance' between risk and return identified for the moderate profile.
It reflects a reasonable tilt towards Bitcoin and BNB (30% each), while Ethereum and Solana receive slightly smaller slices (20% each).
This mix offers diversification: approximately 50% of the portfolio in more established assets (BTC/ETH) and 50% in higher growth assets (BNB/SOL).
As a result, the portfolio is expected to capture a good part of the appreciation potential of the crypto market, but with more controlled volatility than a portfolio 100% concentrated in the more volatile altcoins.
It is worth noting that this allocation derives from historical data and the return assumptions used; if the investor has specific views (for example, more optimistic about ETH, or more cautious about SOL), they can slightly adjust the percentages while maintaining the moderate balance.
Translating to weekly contributions: from each $250 weekly, approximately $75 would be allocated to BTC, $50 to ETH, $75 to BNB, and $50 to SOL.
Practically speaking, every week the investor would buy these amounts of each asset. This discipline of regular contributions, known as a dollar-cost averaging strategy, helps reduce the short-term impact of volatility – buying more units when prices fall and fewer when they rise, which tends to result in an advantageous average purchase price over time.
In summary, by applying Markowitz's theory, we were able to outline the efficient frontier of the four crypto assets and identify the optimal portfolio suitable for the moderate investor profile, maximizing its expected return given a risk level compatible with its tolerance.