# Modern Portfolio Theory for Cryptocurrency

Observations about the cryptocurrency market give the impression that “when Bitcoin sneezes, the cryptocurrency market catches a cold.” From a technical perspective, it can be difficult to diversify risk in a portfolio composed entirely of cryptocurrencies. Building a portfolio of two highly correlated assets exposes investors to greater risk and loss of wealth. When two assets have a strong correlation coefficient, they tend to move in the same direction. If two assets in the same portfolio move in the same direction, the gains will be greater and the losses worse. This may be why investors try to build portfolios with negatively correlated assets. If one asset in a portfolio composed of two negatively correlated assets goes down, the other asset in the portfolio should go up. This should reduce the maximum amount of assets in the portfolio that could be lost.

One only has to examine the prices of digital assets on cryptocurrency exchanges to see how highly correlated they are with each other. If Bitcoin is red on the day, almost every cryptocurrency on the homepage will be red, while if Bitcoin is green, so will the others. This is why it is said that “even the most incompetent boat floats with the rising tide.”

Correlation of Bitcoin with other top cryptocurrencies

In particular, the Modern Portfolio Theory advocates diversification of securities and asset classes or the benefits of not putting all your eggs in one basket.

**Contents**show

**Introduction to Modern Portfolio Theory (MPT)**

Modern portfolio theory is based on the variance and covariance between expected returns and asset returns. Investors seek to construct a portfolio that generates the highest expected return but does not exceed a certain level of risk, as measured by the portfolio variance.

While the expected return of a portfolio is a weighted average of the expected returns of its assets, the variance of a portfolio can be less than the average variance of its assets because assets can move in opposite directions. If one asset gains and another loses, the overall volatility of the portfolio will be lower because the movements of the assets will cancel each other out.

MPT suggests that the way to overcome this dilemma is through diversification, that is, the allocation of funds among different asset classes and investments. According to MPT, an investor may hold a certain type of asset or investment that is inherently risky, but when combined with many other types of assets or investments, the portfolio as a whole can be balanced, making it less risky than the individual risks of the underlying assets or investments.

Instead of focusing on the risk of each individual asset, Markowitz shows that a diversified portfolio is less volatile than the sum of its individual parts. Although each asset can be quite volatile on its own, the volatility of the portfolio as a whole can be quite low.

**Calculations**

The expected rate of return of a portfolio is calculated as a weighted sum of the rates of return of individual assets. If a portfolio contains four balanced assets with expected rates of return of 4 percent, 6 percent, 10 percent and 14 percent, the expected return of the portfolio is.

Portfolio risk is a complex function of the deviation of each asset pair and the correlation of each asset pair. To calculate the risk of a portfolio with four assets, the investor needs the deviation and six correlation values for each of the four assets because there are six possible combinations of two assets with the four assets. Because of the correlations among the assets, the total portfolio risk, or standard deviation, is lower than the risk calculated with the weighted sum.

**Correlation**

La diversificazione è una strategia di allocazione del portafoglio che mira a minimizzare il rischio idiosincratico attraverso la detenzione di attività non perfettamente correlate tra loro. La correlazione è semplicemente la relazione tra due variabili, misurata dal coefficiente di correlazione, che varia da -1 ≤ ρ ≤ 1.

- A correlation coefficient of -1 demonstrates a perfect negative correlation between two assets. It means that a positive movement in one is associated with a negative movement in the other.
- A correlation coefficient of 1 demonstrates a perfect positive correlation. Both assets move in the same direction in response to market movements.

A perfectly positive correlation between assets in a portfolio increases the standard deviation/risk of the portfolio. Diversification reduces idiosyncratic risk by holding a portfolio of assets that are not perfectly correlated with each other.

For example, suppose a portfolio consists of assets A and B and the correlation coefficient between A and B is -0.9. This indicates a strong negative correlation: losses from A are likely to be offset by gains from B. This is the advantage of a diversified portfolio.

**Kinds of Risk**

Modern portfolio theory states that there are two risk components to individual asset returns.

- Systematic risk: this refers to market risk that cannot be mitigated by diversification, i.e., the possibility that the market and the economy as a whole will suffer losses that will have a negative impact on investments. It is important to note that MPT does not claim to be able to mitigate this type of risk, as it is inherent in the market as a whole or in some parts of it.
- Unsystematic risk: Unsystematic risk, also known as specific risk, refers to individual assets and can be diversified as the number of assets in the portfolio increases.

In a diversified portfolio, the risk of each asset-or the average deviation from the mean-contributes little to the risk of the portfolio. Instead, it is the difference-or covariance-between the risk levels of individual assets that determines the overall risk of the portfolio. Investors therefore benefit from holding a diversified portfolio rather than individual assets. Therefore, assets with low correlation tend to be good diversifiers in a portfolio, while assets with negative correlation are portfolio hedgers.

**The Efficient Frontier**

Although the benefits of diversification are obvious, investors need to determine the level of diversification best suited to them. This can be determined using the so-called efficient frontier, which is a graphical representation of all possible combinations of risky securities for a given level of risk to achieve the optimal level of return.

The efficient frontier is the cornerstone of MPT. It can be seen below. Different cryptocurrencies generate different returns. Assuming you have chosen three cryptocurrencies for your portfolio, the efficient frontier represents the best combination of these three cryptocurrencies. Each point on the efficient frontier represents the maximum expected return for a given level of risk.

Any portfolio outside the efficient frontier is considered suboptimal for two reasons: it is either too risky relative to its return or too small relative to its risk. Portfolios below the efficient frontier do not offer adequate returns relative to their level of risk. Portfolios to the right of the efficient frontier have a higher level of risk for the observed returns.

**How to diversify away risk in crypto portfolios?**

Although digital assets are highly correlated, it is possible to diversify the risk of pure crypto assets by adding more crypto assets to a portfolio. Moving from a portfolio of one asset to a portfolio of two assets; from a portfolio of two assets to a portfolio of three assets, to a portfolio of four assets, and so on has the potential to reduce the standard deviation.

Although cryptocurrencies are highly correlated, the reason for being able to differentiate risk in a portfolio with only cryptocurrencies may be that there are different types of risk.

- Risk to personal assets: risk of project failure, risk of delisting on the stock market, risk of government bans, huge rejection because of a major shareholder who one day decides to sell all his holdings.
- Average industry growth: if you only invest in one or a few assets, it’s like playing the lottery. Your assets may perform differently: one may grow rapidly while another may only do +10%, and that’s it. Therefore, by diversifying your portfolio, you can benefit from the growth of the entire market rather than relying on one currency.
- You can build different portfolios (e.g., high risk, medium risk, low risk) and make an “average” profit depending on the type of risk.

Despite its volatility, Bitcoin has not shown significant correlations with other traditional asset classes such as commodities, stocks, or fixed income since its inception in 2009 (with an average correlation coefficient of less than 0.10 with other asset classes). Binance Research has modeled various techniques to allocate Bitcoin into existing diversified multi-asset portfolios.

All simulated portfolios that include Bitcoin generally show a better risk-return profile than traditional multi-asset portfolios. These results suggest that Bitcoin offers positive diversification benefits for all global investors pursuing multi-asset strategies. Therefore, be sure to back-test your strategy to assess its historical value.

**Criticism of Modern Portfolio Theory (MPT)**

Perhaps the most serious criticism of MPT is that it evaluates portfolios based on variance rather than downside risk. According to modern portfolio theory, two portfolios with the same level of variance and return are considered equally desirable. A portfolio may exhibit this difference because of frequent small losses. In contrast, such differences in other areas may be due to spectacular declines that occur infrequently. Most investors prefer small and frequent losses, which are more tolerable. Post-Modern Portfolio Theory (PMPT) seeks to improve modern portfolio theory by minimizing downside risk rather than variance.

It concludes that spreading assets across multiple assets, rather than placing them in a single asset, allows for the distribution of idiosyncratic risk specific to a particular digital asset. Moreover, in terms of managing transaction risk, the more diversified one can be, the more one can be protected from losses in a cryptocurrency portfolio. There are many strategies for minimizing risk in cryptocurrency trading, but you simply need to find the one that works best for you.

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**Until next time!**