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Portfolio Diversity: A Technical Analysis

14/08/2018
Tatunka

How much value does diversity add to a portfolio?

This is the core question we are looking to address with this article. While nobody can predict the future, we can look into the past to examine trends. This can help us make better decisions when challenging the future.

How is this study different?

While there has been a lot of discussion around the diversification of portfolios, little work has been achieved in constructing a case for diverse portfolios. We hope this will spark further technical analysis of the market.

Exactly one year of market data has been collected from exchanges. The data begins on May 4, 2017 and ends on May 3, 2018. This precise data is used to evaluate trades as they would have happened at the time of trading.

What fee is taken for trades?

All trades include a standard .25% fee.

What is the trade path?

All trades take place using BTC as a intermediary. This means if a trade is happening from ETH to LTC, ETH will first be traded to BTC and then to LTC. In this instance, both of these trades would incur a .25% trading fee.

Rebalance Period

What is a rebalance?

A rebalance is the process of taking some value from coins which perform well over a period and redistributing that value to coins which performed worse. The end result is the portfolio will have the desired percentage of each asset after each rebalance. So, let’s take an example where a portfolio has desired allocations of 50% ETH and 50% BTC. When the market moves, the percent of each holding may become 60% ETH and 40% BTC. Then, when a rebalance takes place it will make trades so the allocations are once again 50% ETH and 50% BTC.

What is a rebalance period?

In the most simple case, a rebalance happens on a designated interval. The specific amount of time between each rebalance is called the rebalance period. This means a rebalance period of 1 day will result in a rebalance at the same time every single day. This study will examine a range of rebalance periods, from 1 hour to 1 month. Learn more about rebalancing for cryptocurrency.

Portfolio Size

This wouldn’t be a study on diversity without varying the portfolio size. In this instance, portfolio size refers to the number of assets in the portfolio.

What is the range of portfolio size?

In this study, we have chosen a portfolio range from 2 to 10. With a step size of 2, this means there are 5 individual portfolio sizes; 2, 4, 6, 8, 10.

What is the weight of each asset in a portfolio?

Each asset is weighted evenly in the portfolio. So a 2 asset portfolio would contain 50% of each asset.

Asset Selection

What assets were included in the study?

There was no intentional selection process for what assets to either include or exclude. The simple criteria was that we needed to have a complete year of data for any asset to be included. This automatically eliminates coins which have not existed for over a year, as well as coins which have missing data during outages. The complete list of coins included in the study can be found in our backtest tool.

How were assets selected when creating portfolios?

Individual assets were selected at random from the asset pool. This process continued until the desired number of assets in the portfolio was reached.

Why are assets selected at random?

Assets are selected at random to remove bias from the portfolio design. We don’t care how individual portfolios perform in this study. We care how all portfolios of one size compare to all portfolios of another size. This gives us a more general comparison from which we can draw conclusions.

Backtest

What is a backtest?

A backtest is the process of testing a trading strategy by using historical market data. This process ensures the quality of the technique before investing funds. Backtesting is similar to a simulation that trades based on the strategy over a designated period of time. The results help illustrate the profitability and risk.

How many backtests did we run?

We ran 1000 backtests for each portfolio size and rebalance period pair. This provides us with a large sample set that can be used to observe trends. Read more about backtests or run your own.

What was the starting value for each portfolio?

At the start of every backtest, the portfolio was allocated with $5,000.

Performance

In this study, we will look at how diversity affects performance in 5 different scenarios: HODL, monthly rebalance, weekly rebalance, daily rebalance, and hourly rebalance. Once we have gone through each of these cases, we will combine the results to construct a complete picture of the performance implications of portfolio diversity.

HODL

We have grouped HODL into 5 seperate groups that differ by the number of assets. The asset number varies from 2 (bottom right) to 10 (top) with a step size of 2. Each histogram represents exactly 1,000 backtests. The x-axis is the value of the portfolio after 1 year in US Dollars. The y-axis is the number of backtests which fell into the value buckets that are defined on the x-axis. (Example: If a backtest was run with 2 assets and the results were a portfolio value of 55k USD. This would result in a 1 being added to the bottom right histogram in the x-axis bucket which has the range 50k to 65k. The process is then repeated 1,000 times for each number of assets in the study.)

HODL is the stuff of legends. A simple strategy, a growing market, and an epic meme. Everyone enjoys a good HODL every so often. Unfortunately, there haven’t been enough studies on how the number of assets in a portfolio affects the performance over time. Without considered the actual assets that are being held, this can put a value on how much diversity affected the performance of portfolios over the last year.

What are the results?

In the case of having 2 assets in your portfolio, we can see from the chart above that there is a large early peak around $20k-$35k. This peak quickly trails off to a sparse number of outliers. This congregation on the low end demonstrates a rather poor distribution of results. Increasing the number of assets in a portfolio trends towards a more even distribution of performance and a decrease in random outliers. This means the results that were seen from increasing the number of assets in a portfolio resulted in more consistent and reliable results.

What we can also see from the performance is that the more assets a portfolio contained, the higher the median value at the end of one year. Combined with the consistency, this suggests higher asset numbers produced more high value portfolios. Since the only variable for these backtests were the number of assets in a HODL, we can safely conclude that over the past year, increasing the number of assets in a portfolio tended to increase value.

Increasing the number of assets from 2 to 10 resulted in an increase in portfolio value by 45% after 1 year.

1 Month Rebalance

We have grouped the 1 month rebalance backtests into 5 seperate groups that differ by the number of assets. The asset number varies from 2 (bottom right) to 10 (top) with a step size of 2. Each histogram represents exactly 1,000 backtests. The x-axis is the value of the portfolio after 1 year in US Dollars. The y-axis is the number of backtests which fell into the value buckets that are defined on the x-axis. (Example: If a backtest was run with 2 assets and the results were a portfolio value of 60k USD. This would result in a 1 being added to the bottom right histogram in the x-axis bucket which has the range 55k to 80k. The process is then repeated 1,000 times for each number of assets in the study.)

The HODL comparison showed convincing evidence that portfolio diversity increases the performance of a portfolio over the long term. Without making any trades after the initial allocation of the assets, diversity is already showing promising results. Continuing this investigation, we will examine if this trend continues with the introduction of rebalances. The first rebalance period we will examine is the 1 month rebalance.

What are the results?

The trend that was observed during the HODL case continues for this analysis. We see a definitive increase in performance as we increase the number of assets in the portfolio.

Increasing the number of assets from 2 to 10 resulted in an increase in portfolio value by 94% after 1 year.

1 Week Rebalance

We have grouped the 1 week rebalance backtests into 5 seperate groups that differ by the number of assets. The asset number varies from 2 (bottom right) to 10 (top) with a step size of 2. Each histogram represents exactly 1,000 backtests. The x-axis is the value of the portfolio after 1 year in US Dollars. The y-axis is the number of backtests which fell into the value buckets that are defined on the x-axis. (Example: If a backtest was run with 2 assets and the results were a portfolio value of 60k USD. This would result in a 1 being added to the bottom right histogram in the x-axis bucket which has the range 56k to 81k. The process is then repeated 1,000 times for each number of assets in the study.)

The next step for our study is to continue decreasing the rebalance period. The reason for this is to determine the long term affects of shorter periods. Although it’s common to have infrequent rebalances for traditional asset classes, the volatility of the crypto market presents a unique opportunity for increasing this frequency in an attempt to improve performance. Large market swings are typical, so rebalancing is the ideal strategy for this situation.

What are the results?

As we continue to decrease the rebalance period, we begin to observe results that were similar to those discussed in our previous article “Rebalance vs. HODL: A Technical Analysis”. To summarize, these results discovered that decreasing the rebalance period had a general tendency to increase portfolio performance over the last year. A 1 week rebalance period not only outperformed HODLing, but also a rebalance period of 1 month.

Increasing the number of assets from 2 to 10 resulted in an increase in portfolio value by 74% after 1 year.

1 Day Rebalance

We have grouped the 1 day rebalance backtests into 5 seperate groups that differ by the number of assets. The asset number varies from 2 (bottom right) to 10 (top) with a step size of 2. Each histogram represents exactly 1,000 backtests. The x-axis is the value of the portfolio after 1 year in US Dollars. The y-axis is the number of backtests which fell into the value buckets that are defined on the x-axis. (Example: If a backtest was run with 2 assets and the results were a portfolio value of 60k USD. This would result in a 1 being added to the bottom right histogram in the x-axis bucket which has the range 53k to 75k. The process is then repeated 1,000 times for each number of assets in the study.)

In the next case, we will continue decreasing the rebalance period to 1 day. Many of the observations that were seen in the previous cases will be revealed here as well. This includes the increase in performance over weekly rebalances, the performance increase that arises from portfolios with more assets, and a more balanced distribution curve when more assets are present.

What are the results?

In the set of 5 charts, we can see a clear trend that increasing the number of assets in a portfolio improves the distribution of value. While 2 asset portfolios are heavily weighted such that the majority of the results congregate towards the lower end of values, 10 asset portfolios have a distribution that provides a more consistent higher portfolio value.

Increasing the number of assets from 2 to 10 resulted in an increase in portfolio value by 68% after 1 year.

1 Hour Rebalance

We have grouped the 1 hour rebalance backtests into 5 seperate groups that differ by the number of assets. The asset number varies from 2 (bottom right) to 10 (top) with a step size of 2. Each histogram represents exactly 1,000 backtests. The x-axis is the value of the portfolio after 1 year in US Dollars. The y-axis is the number of backtests which fell into the value buckets that are defined on the x-axis. (Example: If a backtest was run with 2 assets and the results were a portfolio value of 60k USD. This would result in a 1 being added to the bottom right histogram in the x-axis bucket which has the range 42k to 73k. The process is then repeated 1,000 times for each number of assets in the study.)

The shortest rebalance period we will be evaluating is the 1 hour rebalance. This means we are rebalancing every hour of every day for an entire year. Performed manually, this would be an incredible feat of commitment. Maybe even impossible. Projecting from previous results, the expectation by this point is that 1 hour rebalances will outperform every other case studies this far.

What are the results?

The results demonstrate the highest total portfolio mean value that was observed in this study of $125k. The 1 hour rebalance showed improved performance over all other periods as well as HODL. A 1 hour rebalance period also had the highest increase in portfolio value when increasing from 2 assets to 10 assets.

Increasing the number of assets from 2 to 10 resulted in an increase in portfolio value by 127% after 1 year.

Complete Comparison

With each of these results, we can stitch them together to get a complete view of how the median performances drift based on rebalance period.

The median performance demonstrates that the higher the rebalance period with the higher number of assets presents the highest gains for rebalancing. Each value represents the complete holdings of the median portfolio. This amount is in USD.

Now that we have seen how rebalance period affects the performance of a portfolio, we can combine all of this data to get a general view of how rebalancing performs compared to HODL in general. When we accumulate all of the results from each individual test, we can see a clear trend for both rebalancing and HODL.

With this combined data, we get a combined median for rebalancing of $66k. Combining the results from the HODL tests results in a median of $40.5k. This is a staggering difference of $25.5k.

Rebalancing median: $66k, HODL median $40.5k

Why median?

The median values were used in this comparison because there are a significant number of incredible outliers when examining portfolio results. While these results are possible, we consider these far too unlikely to be factored into a reasonable expectation. We want to present data that encompasses the most possible results.

The median presents a more realistic expectation for results. The median tells us that half of portfolios performed better than that number and half performed worse. Essentially, a 50:50 chance.

In this instance, this means if you had randomly selected assets to include into a portfolio with a random rebalance period, the value of the portfolio had a 50% chance of being OVER $66k after one year.

Why chance?

The presented results are based on random selections of portfolios. This means if you also randomly selected a bunch of portfolios over the same time period, you could find similar results. We hope this is not your strategy for selecting a portfolio. We will continue to provide studies of the market, however is up to you to make smart decisions for which assets to include in your portfolio.

Conclusions

Disclaimer: Past performance does not guarantee future results.

This study evaluated the results of backtests. There is no guarantee for future success using the same methods. Treat this as a tool which can help each of us make better decisions when constructing portfolios in the future.

What did this study reveal?

There are a few clear trends that are revealed in this study. Over the past year, the number of assets played an important role in the performance of a portfolio. Simply increasing the number of assets, whether HODLing or rebalancing, generally improved the performance over a complete year.

Besides the number of assets, there was observed a strong relation between portfolios which were rebalanced more frequently and performance. This means that in the past year, those portfolios which were rebalanced more frequently provided higher returns than those which were not. Taking both of these factors into account, we can see that the optimal portfolio over the last year had a high number of assets and rebalanced frequently.

In the past year, simply increasing the number of assets in a portfolio from 2 to 10 increased performance by a median of 77%.