Portfolio Optimization With BNB

• Like Bitcoin, BNB displayed a null correlation with all traditional financial assets, like equities and commodities, in the long-term. However, BNB also exhibited a lower than average correlation with other large-cap cryptocurrencies like Bitcoin (BTC) and Ethereum (ETH).

• This report analyzed the performance of traditional US equity + fixed-income portfolios, (1) without crypto, (2) with BNB, and (3) with BNB & BTC; different rebalancing techniques were also used in this study.

• Thanks to their low correlations with other financial assets, the inclusion of cryptoassets to traditionally diversified portfolios drastically improved the risk-return characteristics of these portfolios, as measured by their higher Sharpe ratios.

• While both the BNB and BNB + BTC portfolios outperformed the crypto-free portfolio , the BNB portfolio outperformed the BNB + BTC on similar metrics, despite an increased level of volatility.

• Tolerance-based rebalancing allows investors to limit their exposure to cryptoassets, while a monthly rebalancing sometimes leads to significant deviations from a portfolio’s target exposure to cryptos (e.g., during the January 2018’s bull run).

• With non-normal returns, skewness must also be considered in regard to large negative tail risks. Unlike other cryptocurrencies, BNB displayed positively skewed daily returns, which may be useful for investors to manage downside tail risk better, especially in a portfolio composed of negatively skewed assets.

1. Overview of BNB

1.1 BNB: the fuel of the Binance ecosystem

BNB powers the Binance ecosystem and is the native coin of Binance Chain. BNB is a cryptocurrency created in June 2017, launched during an ICO in July, and initially issued as an ERC-20 token. Designed to be used for fee reductions on the Binance exchange, its scope was extended over the years.

BNB powers the Binance Chain as its native chain token. For instance, it is used to pay fees on the Binance DEX, issue new tokens, send/cancel orders, and transfer assets.

At the core of the economics of BNB, there is a burn system leading to periodic reductions of its total supply (~ every three months). From the initial maximum supply of 200 million, burns will keep occurring until the supply reaches 100 million.

In addition to its on-chain functions, BNB has multiple additional use-cases, as it offers fee discounts on Binance.com, can be used as a payment asset on third-party services and entails participation rights for Binance Launchpad.

The full breakdown of organizations and projects in the BNB ecosystem is displayed below.

As discussed before, BNB is the native asset of the Binance Chain and is used to perform operations on the network, such as sending orders on the Binance DEX, transferring assets from one wallet to another, and issuing new assets.

However, the full scope of the Binance Chain is much larger, as displayed below.

After implementing the BEP-3 standard in late 2019, Hash Time-Locked Contract functions and further mechanisms have been made available to handle inter-blockchain token pegging. This is likely to further increase the interoperability with other programmable blockchains, like Ethereum.

Finally, the anticipated support of smart-contracts on the Binance Chain will likely foster additional use-cases for BNB, unlocking a new range of opportunities.

1.2 Characteristics and past performance

While BNB is a new financial asset, it displayed extremely large positive returns in its first years, followed by significant drawdowns, and other price rallies.

Chart 1 - Evolution of the price of BNB in USD

Source: Binance.com.

Table 1 - BNB calendar returns

*the ICO price was set at 0.10 USD (per BNB).

Table 2 - BNB quarterly returns

Source: CoinMarketCap, Binance.

1.3 Is BNB correlated to other assets?

1.3.1 Correlation with other cryptocurrencies and digital assets

As illustrated in our previous reports about crypto-correlations, the intensity of the relationships among cryptocurrencies and other digital assets is often positively significant.

Chart 2 - Correlations between large cryptoassets by marketcap in 2019

Source: CoinMarketCap.

In 2019, the average correlation ratio amongst cryptocurrencies stood at 0.72, a high value indicating a strong relationship between the returns of cryptoassets.

Amongst ten of the largest marketcap cryptoasset, BNB was the least correlated asset displaying an average correlation of only 0.58.

BNB displayed a medium positive correlation with other large cryptoassets: only 0.57 with BTC, 0.52 with XRP, 0.64 with LTC, and 0.63 with ETH. In comparison, BTC and ETH, the two largest cryptoassets, displayed a strong positive correlation(0.82).

1.3.2 Correlations with traditional financial assets

Chart 3 - Correlations between BNB, BTC, and traditional financial assets in 2019

Source: CoinMarketCap, Yahoo Finance, Bloomberg.

BNB appears to be a unique asset: not only is it uncorrelated with traditional financial assets, but it is also one of the lowest correlated assets with other cryptocurrencies.

Hence, the next subsection focuses on the construction of model portfolios, including Bitcoin (BTC) and BNB, along with the backtesting of the performance of these portfolios.

2. Methodology and construction of model portfolios

In this report, two general approaches to the construction of a portfolio are being adopted:

• Time-based rebalancing is the rebalancing of a portfolio at fixed, pre-defined intervals. For instance, BNB’s weight is reallocated at the end of each month with different levels of exposure, such as 5%.

• Tolerance-based rebalancing (also termed “Dynamic Boundary Rebalancing”) is the rebalancing of a portfolio, whenever the effective portfolio weight of an asset in the portfolio exceeds target thresholds.

For all assets, transaction fees are included based on empirical data from exchanges and trading venues. For practical reasons, slippage is not considered for this analysis, even though it can be a key variable for large investors. Transaction fees are set at 0.10% for all assets.

The portfolio construction is in line with 21 Shares’ previous research paper (Ige, 2019) and shall be composed of traditional assets to 95%. We adopt a traditional allocation of 60% equities / 40% bonds and focus solely on the US market.

For the cryptocurrency allocation, we target a 5% allocationin this report with two different scenarios1: (1)BNB alone, (2) BNB with BTC.

Henceforth, four portfolios are backtested in the next subsection and benchmarked against two base portfolios with no exposure to cryptoassets.

For all the portfolios, data is backtested from September 30th, 2017, to December 31st, 2019.

Portfolio 1: Monthly Rebalancing with BNB only

• Portfolios are rebalanced, with a target of 5% for BNB, on the last business day of the month.

Portfolio 2: Monthly Rebalancing with BNB & BTC only

• Portfolios are rebalanced, with a target of 2.5% for BNB and 2.5% for BTC, on the last business day of the month.

Portfolio 3: Tolerance-Based Relancing with BNB only

• Portfolios are rebalanced, with a target of 5% for BNB, whenever a boundary is crossed.

• Boundaries are set at 2.5% & 7.5% for rebalancing.

Portfolio 4: Tolerance-Based Relancing with BNB and BTC

• Portfolios are rebalanced, with a target of 2.5% for BNB and 2.5% for BTC, whenever a boundary is crossed.

• Boundaries are set 1.25% & 3.75% for both BNB and BTC.

3. Results and interpretation

In the following section, we present the performance results for both our time-based and tolerance-based rebalancing strategies — by presenting calendar returns, annualized returns, volatiles, Sharpe ratios, and maximum drawdowns for the portfolios. We will then analyze the data in order to better understand to what extent BNB provides further diversification to an investor’s portfolio.

3.1 Time-based rebalancing

Chart 4 - Portfolio Performances (Base = 1000)

Table 3 - Calendar returns

Table 4 - Key metrics for portfolios with time-based rebalancing

Chart 5 - Portfolio weights (5% BNB Portfolio)

Chart 6 - Portfolio weights (2.5% BNB + 2.5% BTC Portfolio)

As expected, the portfolio with additional BNB outperforms both the benchmark and the enhanced portfolio combination of BTC and BNB in the time-rebalancing case. While the BNB portfolio has a much higher level of volatility than the BTC portfolio, this additional volatility is more than compensated for the given excess returns — indicated by the superior Sharpe ratio of 1.081 compared to 0.368 for the benchmark and 0.903 for the BNB + BTC mix portfolio.

Near the tail-end of the 2017-18 bull market, BNB’s allocation within the portfolio briefly reached a high of 14% due to its sudden rise to the low-20 digits (USD) in early January. It is important to note, however, that the large deviation from the ideal BNB allocation of 5% could have unnecessarily given an investor a more-than-ideal exposure to the crypto market during the early months of the 2018 downturn — this would not happen if tolerance-based rebalancing had been used.

3.2 Tolerance-based rebalancing

Chart 7 - Portfolio Performances (Base = 1000)

Table 5 - Calendar returns

Table 6 - Key metrics for portfolios with tolerance-based rebalancing

Chart 8 - Portfolio weights (BNB Portfolio)

Chart 9 - Portfolio Weights (BNB + BTC Portfolio)

We see a similar trend to the monthly-rebalancing portfolio in comparison with the tolerance rebalancing approach. The BNB portfolio performs better than both the benchmark and the BNB + BTC in terms of both, annualized returns and Sharpe ratio, though — once again — the BNB portfolio is subject to a noticeably higher level of volatility than the others.

As expected, the use of a tolerance-rebalancing strategy prevents the BNB allocation within the portfolio reaching levels seen with the monthly-rebalancing analogous portfolio. While this does reduce BNB exposure in the run-up to the 2017-18 price run-up, it also allows the downwards exposure to be reduced during the 2018-19 bear market — this fact is reflected in the greatly reduced volatility in both the BNB and BNB + BTC portfolios. Finally, it seems that a tolerance-rebalancing strategy provides a more reliable way for an investor to ensure their portfolios are never unnecessarily overexposed to the crypto asset industry.

3.3 Skewness

The severe market drawdown on the 12th of March — dubbed as the “Black Thursday”by some within the cryptoasset industry — has highlighted the importance of accounting for tail risk and skewness of returns when building optimal portfolios, especially those with allocations of cryptoassets, such as BNB or BTC.

Generally, modern portfolio theory assumes that the distribution of returns can be adequately understood through the use of the distribution’s mean and standard deviation; within this context, these two metrics allow investors to calculate average returns and volatility. However, the distribution of returns for financial assets rarely, if ever, follows a normal distribution, and this holds true.

The charts below show the distributions of returns of the three sample portfolios we calculated earlier using tolerance rebalancing, whilst comparing them to bootstrapped samples following normal distributions with the same mean, standard deviation, and number of samples.

Charts 10 a/b/c - Portfolio Distributions (Tolerance-Based Relalacing)

As we can see, none of the portfolio’s distributions match closely to the normal distribution. Noticeably, their distributions are negatively skewed and have fatter tails than the normally distributed data set. These two facts can be represented by the metrics Skewness and Kurtosis, where for a normally distributed dataset, its skewness will be 0 and its kurtosis 3.

However, as the table below demonstrates, the skewness and kurtosis of the portfolio’s returns deviate noticeably from metrics that could reasonably suggest their normality. In addition, we use three popular tests for the normality of any distribution — the Shapiro-Wilk, D’Agostino’s K^2, and the Anderson Darling tests — at a 5% significance level to further confirm our doubts of the normality of the portfolio’s returns.

Table 7 - Portfolio Skewness, Kurtosis, and normality tests

The presence of fat-tailed distributions in the returns of the three portfolios and for cryptoasset returns presents an important warning for investors, as modern portfolio theory taken alone — within the consideration of the skewness of returns and tail risk — can lead to a systematic underestimation of downside risk, as was the case on “Black Thursday”. Most equities, Bitcoin, and other “risk-on” assets, generally exhibit negative skewness.

Interestingly, BNB has a positive skewnessof 1.65, which places it into a category of other positively skewed assets (generally) such as VIX and safe-haven assets (in the following example we use the iShares Barclays 1-3 Year Treasury Bond Fund (SHY).

Table 8 - Skewness of different assets

Negatively skewed returns mean that one would generally expect to see the asset produce frequent small gains and infrequent large losses — as is the case with equities in recessionary periods and Bitcoin. Conversely, positively skewed returns mean that one would generally expect to see the asset produce frequent small losses and infrequent large gains. VIX is an easily understood example of this, as it tracks the implied volatility of the S&P500, which generally goes through extended periods of low volatility (e.g., during the post-2008 bull run) before a noticeable, but rare drawdown and heightened volatility phase.

BNB also exhibiting the property of being positively skewed might explain why it could be an especially useful addition to a portfolio that generally consists of negatively skewed assets — helping to bring the overall portfolio skewness closer to 0 and making it more resilient to long-tail events.

4. Conclusion

This analysis has added to the research that suggests that adding small amounts of a cryptoasset to a “traditional” portfolio can drastically improve its risk-adjusted returns. In the context of BNB, we showed how its addition to a balanced portfolio can provide substantial diversification benefits, and both tolerance and monthly rebalanced portfolios with a 5% target allocation of BNB outperforms a portfolio without any cryptoasset. Interestingly, over the study period, the BNB portfolio also outperformed the portfolio with target weights of 2.5% respectively, for both BNB and BTC, despite BNB having a relatively lower than average correlation with Bitcoin.

One under-examined aspect of applying modern portfolio theory to the crypto market has been the effect of skewness and kurtosis of returns on an investor’s risk and expected returns. We showed how - owing to large amounts of skewness and kurtosis - traditional portfolios and portfolios with cryptoassets have returns that do not follow a normal distribution and are generally negatively skewed. This fact can lead to investors underestimating downside risk if they don't properly account for this fact. BNB, interestingly, has had positively skewed returns over the last two years, which allows it to function as a means for investors to further hedge against the present downside tail risk, which is particularly pronounced in portfolios composed of negatively skewed assets.

It was written in collaboration with 21Shares. 21Shares allows investors to take exposure in crypto easily, safely, and in a regulated way on the SIX Swiss Exchange.

References

• Binance Research (2019). Exploring the diversification benefits with Bitcoin. https://research.binance.com/analysis/bitcoin-diversification-benefits

• Binance Research (2020). 2019 - Annual Crypto-Correlations Review. https://research.binance.com/analysis/annual-crypto-correlations-2019

• Hougan, M. (2018). Bitwise Investments. The Case for Crypto In An Institutional Portfolio (2018). https://static.bitwiseinvestments.com/Research/Bitwise-The-Case-For-Crypto-In-An-Institutional-Portfolio.pdf

• Ige, L (2019). Portfolio Optimization With Crypto Assets. https://www.amun.com/img/uploads/amun-portfolio-optimization-with-crypto.pdf

1. There are plenty of other papers (e.g., Hougan 2018, Binance Research 2019), which investigates the diversification benefits of Bitcoin in traditional portfolios.↩