Given the acceptance of Bitcoin as an investment and its rising importance, modeling Bitcoin price volatility becomes important to investment decisions and risk management. However, volatility is only a natural consequence of lower market liquidity. We have already witnessed crucial changes in this respect. Blockdata report shows that Bitcoin has processed 62% more transactions, in terms of dollar value, than PayPal in 2021. However, Mastercard and Visa still remain the runaway leaders with respect to this metric. The new information comes as critics continue to discuss the viability of Bitcoin for a global level of payments.

The data was revealed by Blockdata, which published a report on Nov 23 comparing Bitcoin with payment Mastercard and Visa.

Another approach to tackle excessive volatility is to pursue generally higher returns. In discussing future returns, the two metrics most often referenced are the geometric expected mean (average growth of compounded wealth) and the arithmetic expected mean (probability-weighted average of all possible future states of return).

History shows the benefits of a well-diversified investment portfolio: one asset class generates a better return than another one. Although it may seem attractive to always invest in the best-performing asset classes, this is not a sensible way to invest. It is often only clear after the fact which asset class generates the best return. Various studies use a number of methods and find that Bitcoin has a very low correlation with conventional assets such as bonds, commodities, and equities

**To sum up the value-seeking task, we inevitably end up with Value-at-risk. **Value-at-risk is a statistical measure of the riskiness of financial entities or portfolios of assets. It is defined as the maximum dollar amount expected to be lost over a given time horizon, at a pre-defined confidence level. For example, if the 95% one-month VAR is $1 million, there is 95% confidence that over the next month the portfolio will not lose more than $1 million.

VaR can be calculated using different techniques. Under the parametric method, also known as a variance-covariance method, VAR is calculated as a function of mean and variance of the returns series, assuming a normal distribution. With the historical method, VAR is determined by taking the returns belonging to the lowest quintile of the series (identified by the confidence level) and observing the highest of those returns. The Monte Carlo method simulates large numbers of scenarios for the portfolio and determines VAR by observing the distribution of the resulting paths.

Let’s analyze the relationships between volatilities of five cryptocurrencies, U.S. equity indices (S&P500, Nasdaq, and VIX), oil, and gold. The results of the Markowitz model show evidence of a higher volatility spillover between cryptocurrencies and lower volatility spillover between cryptocurrencies and financial assets.

Another very important mechanism, **autocorrelation**, sometimes referred to as serial correlation in the discretionary-time case, is the correlation of a signal with a **delayed copy of itself as a function of delay**. Informally, it is the similarity between observations as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its **harmonic frequencies**. It is often used in signal processing for analyzing functions or a series of values. Let’s look at how autocorrelation works in the cases of the two most popular cryptocurrencies, Bitcoin and Ethereum.

Bitcoin autocorrelation shows a still-acceptable-amplitude, but much more choppy pattern:

The **relative strength momentum** model invests in the best-performing assets in the model based on each asset’s past return. The momentum can be based on a single timing period or multiple weighted timing periods. Additionally, the model supports using moving averages as a risk control to decide whether investments should be moved to cash. Tactical asset allocation model results from Jan 2020 to Oct 2021 are based on a relative strength model holding the best performing asset. The model uses a single performance window of 10 calendar months. Tactical asset allocation model trades are executed using the end-of-month close price each month based on the end-of-month signals. The time period was constrained by the available data for Ethereum Market Price USD (^ETH) [Sep 2015 – Oct 2021].

Drawdowns for Momentum Model | |||||||

Rank | Start | End | Length | Recovery By | Recovery Time | Underwater Period | Drawdown |

1 | Feb-20 | Mar-20 | 2 months | May-20 | 2 months | 4 months | -31.34% |

2 | May-21 | Jun-21 | 2 months | Aug-21 | 2 months | 4 months | -17.97% |

3 | Sep-20 | Sep-20 | 1 month | Nov-20 | 2 months | 3 months | -17.58% |

4 | Sep-21 | Sep-21 | 1 month | Oct-21 | 1 month | 2 months | -11.22% |

5 | Jun-20 | Jun-20 | 1 month | Jul-20 | 1 month | 2 months | -2.29% |

Drawdowns for Equal Weight Portfolio | |||||||

Rank | Start | End | Length | Recovery By | Recovery Time | Underwater Period | Drawdown |

1 | Mar-20 | Mar-20 | 1 month | May-20 | 2 months | 3 months | -32.74% |

2 | May-21 | Jun-21 | 2 months | Aug-21 | 2 months | 4 months | -27.84% |

3 | Sep-20 | Sep-20 | 1 month | Oct-20 | 1 month | 2 months | -12.80% |

4 | Sep-21 | Sep-21 | 1 month | Oct-21 | 1 month | 2 months | -9.02% |

5 | Jun-20 | Jun-20 | 1 month | Jul-20 | 1 month | 2 months | -2.63% |

We clearly observe that by applying the momentum model as opposed to the equal weight model to our portfolio the depth of drawdowns is reduced, although in observations #3 and #4 in September 2020 and September 2021 we contemplated slightly worse drawdowns in our Momentum model applied to those periods vis-a-vis the Equal weight model. We have a hypothesis, that the RSI model works better over the first halves of a year, as opposed to the Equal weights that are better looking during the second halves. All-in-all, using the RSI model diminished our resulting annual drawdown by almost 5 percentage points, which is not bad.

**Conclusion:** Keeping cryptos in our individual portfolios is both a wise and yield-enhancing approach, while various smoothening methods can tangibly reduce both factual and expected volatility while preserving elevated returns and return expectations.

Finally, let’s take a look at the multiasset diagram plotted with the assistance of *Portfoliovisualizer.com*’s data:

Reading and studying this diagram is simple: Everything located higher of the R-Square Curve is considered a poor choice for an active VaR-enhanced portfolio, as these asset classes tend to unveil higher volatilities while promising relatively modest yields going forward. In distinction, another set of assets – such as corporate high-growth Euro bonds, government bonds in Euro, U.S. mutual funds, etc. – offer much better VaR characteristics showing, conversely, suppressed levels of volatility, while delivering still-higher returns. We also outline the special positions of Bitcoin and Ethereum on this chart. Literally, they both face no competition from other typical asset classes, even though their implied volatilities still leave to desire more.