Summary:

• Back-testing reveals Dollar Cost Averaging (DCA) buy-and-hold bitcoin investing yields lowest return of the four strategies we tested.
• Mayer Multiple and moving average crossover strategies performed better than Dollar Cost Averaging.
• The Upside Signal Rationality Index strategy significantly outperformed all other strategies tested.

The very simplest way to invest in Bitcoin is to buy and hold, and that works. Even buying at the market tops, historically, can deliver a good return, in three to five years. And in fact, there are many Bitcoiners who believe in and promote ‘stacking’ and ‘hodling’ (holding) the largest pile of bitcoin you can. But, bitcoin’s volatility make this a questionable strategy based on our analysis. Famous trader and author Peter Brandt, put it like this:

With the pain of the Bitcoin hodler roller coaster in our bones, we set out to analyze the alternatives. Our challenge? We don’t want to be day traders and yet we don’t want to suffer through 80% declines and long bear markets. Our ideal is a simple system that allows us to occasionally buy the lows and sell the highs, a system that Warren Buffett himself could get behind if he didn’t hate digital assets!

Warren Buffett famously said, “Be fearful when others are greedy, and greedy when others are fearful.” 

But this is extraordinarily difficult! When fear and greed take hold, our natural tendencies are to buy and sell at the wrong time. We are emotional beings, and are instinctively inclined to make errors in the heat of the moment.

We need a system to cool our emotions – to remind us and when the market is euphoric, it’s actually at its point of highest risk. And, when depressed, we’ve reached the point of maximum financial opportunity.

You might be thinking, that’s what Dollar Cost Averaging (DCA) is for. Our back-testing, however, shows it significantly underperforms other strategies, as you will see further on.

The challenge then is to modify it so that it becomes an intelligent or dynamic dollar cost averaging system, buying more at the lows and selling the tops!

The first thing we need is a mathematical model also known as an oscillator to tell us when the market is greedy (prices high) or fearful (prices low). Why do we need math you say? Can’t we just look at the bitcoin price chart?

Nope! We need the mathematical model because being fearful when others are greedy and greedy when they are fearful is harder than it sounds. And, agonizing over charts will eat up time better spent away from your screens.

Bitcoin Price Models

There are many existing bitcoin price models and oscillators, which we find either too simple to produce the highest returns, or too technical for most investors. Our model, the Rationality Index (RI). is designed to be user-friendly in spite of its advanced mathematical foundation. Here, we’ll compare it against existing models by back-testing a number of investment strategies. Below you will find results of our Bitcoin investment strategy back-testing summarized and detailed with charts.

Here are some of those existing bitcoin price models and investment strategies we’ve used as benchmarks along with our in-house index, the Rationality Index:

Mayer Multiple
Dollar Cost Averaging (DCA)
Moving Average crossover indicators 
Rationality Index (RI)

Methodology

Cash Flow

First we need to define the exact methodology used for the back-tests. The initial cash is always $10,000 USD, and additional $1,000 USD are added at the first trading day of each month. Like any professional fund, though, the money is only available at the end of the day, after the trading session (this allows for better accountability).

Fund mode

We use a fund-like strategy to properly calculate the returns on investment. When any back-testing begins, we issue a number of shares that will compose our fund. For example, since all strategies start with $10,000, and we set the starting share price as 100,000, our fund will start with 100 shares outstanding. As the Bitcoin price fluctuates, the share price goes up and down proportionally, but the 100 shares outstanding aren’t affected, and remain untouched. When money is added to the fund, new shares are issued according to the amount that was added, and the share price at that date.

An example: on 2011-02-28, in the Buy and Hold strategy, our fund is valued at $13,922.05 (share price: $126.56, number of shares outstanding: 110). On the next trading day, 2011-03-01, a total of $1,000 are added to the fund, and cash is converted to new shares (1,000 divided by the share price $126.56: 7.90 new shares are issued, so the fund has now 117.90 shares outstanding). Although the new shares are issued on March 1^st, cash will only be available for trading in the next session (March 2^nd).

ROI

How is the ROI calculated? Please see Fool.com’s ROI calculation article.

What are our Holding Period Return (HPR) delimiters? In the example above, our fund was valued at $13,922.05 on Feb 28^th, and that’s our ending value for the period. The next period starts on March 1^st, and the starting value is corrected for the cash flow, i.e. $14,922.05. So all our HPRs are calculated individually, then multiplied all together, and finally 1 is subtracted (corresponds to the initial value).

Orders

Orders have three states until they are completed: submitted, accepted (by the broker) and executed. Since we have only daily prices, our back-testing tool was instructed to execute orders at the exact same price as they were submitted, and in the same day. Also, the order is always fully executed with estimated trading costs at 0.3%.

Results

Our results were obtained from a very large batch of back-tests. Our first focus was to find whether strategies using our Rationality Index performed better than Buy and Hold strategies (either lump sum investment or initial plus monthly cash additions). A do-nothing strategy was used as control.

The Rationality Index requires an initial period of existing price data to be calculated, so the first date when the Index is available is November 2, 2011 or 200 days after BTC genesis. We filtered our trading dataset to remove all data before that, when the Index wasn’t available. We used a fixed 10 year window, for a long-term view of the results, and another window starting right after the bull run peak of the last halving cycle (the day after the peak of $19,641 on December 16th, 2017). The latter is a good illustration of how an investor that jumped in at the worst possible moment (worst at the time, around 2017) could still be very profitable in the long run. An initial value of $10,000 dollars was added to the “available cash”. Decimals have been removed in the results charts for readability.

First, we’ll summarize all the results here:

Now for the details:

Empty strategy

To kickstart our analysis, we executed the empty strategy, to understand how much money was invested. These are the results:

10-year window

2017 peak to mid-2022

Ok, that was expected. The ROI when you don’t make any trades should indeed be zero.

Buy and Hold Strategy

Let’s start with the simplest of all strategies, the ‘hodlers’ strategy, a simple Buy and Hold system. perhaps the most famous of all bitcoin hodlers Is Michael Saylor, CEO of Micro Strategy Corporation Who puts it like this, “. . .when you’re buying bitcoin if you understand it, I don’t think you’re investing and I don’t think you’re speculating, I think you’re saving.” Watch the video to catch the whole discussion. It’s a valid viewpoint useful in helping us flesh out our own personal time horizon, risk tolerance and portfolio preferences. Even if the return is lower on the buy-and-hold strategy, it may be the right choice for you.

Note that in the empty strategy above, for testing purposes, this strategy starts with an initial buy of $10,000 dollars plus monthly additions of $1,000. These are the results:

10-year window

Understanding the chart: in this strategy we are dollar cost averaging into bitcoin over a 10 year period.  That’s why you see so many green buy indicator triangles and no red sell indicator triangles.  This is also the reason that the red cash line at the top of the chart stays flat at zero.  Because every day, we are immediately buying bitcoin with any available cash. Also note that because the portfolio never holds any cash, it’s total value is just the value of the bitcoin at its current price. The great strength of this method is its simplicity, but the cost is performance as buy-and-hold ranks second to last of all methods we back-tested.

2017 peak to mid-2022

Understanding the chart: in this strategy we are dollar cost averaging into bitcoin over a 5 year period.  That’s why you see many green buy indicator triangles starting in 2017 and no red sell indicator triangles.  This is also the reason that the red cash line at the top of the chart stays flat at zero.  Because every day, we are immediately buying bitcoin with any available cash. Also note that because the portfolio never holds any cash, it’s total value is just the value of the bitcoin at its current price. The end result in terms of ROI is rather dismal, of course, thanks to the 2022 earthquake in macroeconomic environment and Federal Reserve monetary policy. Again, the great strength of this method is its simplicity, but the cost is performance as buy-and-hold ranks last of all methods we back-tested.

It would be extremely profitable to time travel to July, 2012 to buy bitcoin. Let’s compare to another potentially profitable strategies.

Mayer Multiple

The Mayer Multiple was originated by Trace Mayer to gauge the current price of Bitcoin and determine whether the cryptocurrency was overbought or oversold. Mayer defined this price tool as follows:

Mayer Multiple = Bitcoin Market Price / 200 day Moving Average

By conducting simulations based on historical data, Mayer concluded that any multiple above a 2.4 threshold had historically signified the beginning of a speculative bubble for Bitcoin.

We ran thousands of simulations to understand which would be the optimal buy / sell thresholds for the Mayer Multiple.

10-year window

Using the 10-year window, the best results were obtained when:

• • buy when the Mayer Multiple is at or below 1.3

• • sell when the multiple is at or above 6.2

Understanding the chart: in this strategy we are buying and selling bitcoin using the Mayer Multiple thresholds as a signal over 10 years. In the chart we see just 2 red sell indicator triangles for the 2013 peaks and curiously none in the 2017 peak or after.  We also note steady buy indicators wherever the price is not rising or falling steeply. This a remarkably strong strategy when you consider it’s simplicity and relative performance. As weaknesses, we note the failure to take profits at the 2017 peak and frequent buying which some may find tedious.

2017 peak to mid-2022

Using the shorter time window, the best results were obtained when:

• • buy when the Mayer Multiple is at or below 0.6

• • sell when the multiple is at or above 2.2

Understanding the chart: in this strategy we are buying and selling bitcoin using the Mayer Multiple thresholds as a signal over 5 years. In the chart we again see just 2 red sell indicator triangles, the first midcycle in June 2019 is very well-timed, and the second, around January 2021 looks a bit premature.  We also note few but well-timed buy indicators. Just like over the 10 year period, the Mayer Multiple shows remarkable strength when you consider it’s simplicity , minimal trades and relative performance. As a weakness, we note the sell signal significantly below the 2021 blowoff top.

Moving Average Crossover

10-year window

The best result for the daily MA Crossover strategy category uses a 10-day fast SMA and a 19-day slow SMA.

Understanding the chart: in this strategy we are buying and selling bitcoin using the 10/19 daily simple moving average crossover signals over 10 years. In the chart we see copious trades, i.e. many red and green buy/sell indicator triangles, as every day we look for a crossover of the moving averages to execute a possible buy or sell signal. This involves a lot of effort, but the end result is the method ranks third just after the Mayer Multiple.  

The traditional daily 9/20 simple moving average crossover also delivers great results.

Understanding the chart: in this strategy we are buying and selling bitcoin using the commonly used 9/20 daily simple moving average crossover signals over 10 years. In the chart we again see copious trades, i.e. many red and green buy/sell indicator triangles, as every day we look for a crossover of the moving averages to execute a possible buy or sell signal. This involves a lot of effort, but the end result is the method ranks 4rth nearly tied for 3rd with the 10/19 sma crossover.

If we use a weekly approach, where the week starts on Monday at 00:00, the best result has a 15-week fast SMA and a 22-week slow SMA.

Understanding the chart: in this strategy we are buying and selling bitcoin using the 15/22 weekly simple moving average crossover signals over 10 years. In the chart we note far fewer trades, i.e. fewer red and green buy/sell indicator triangles, as now, we only look for a crossover of the moving averages to execute a possible buy or sell signal once a week. This involves far less effort, but its comparative return is also substantially lower than the daily crossover.

The weekly 9/20 simple moving average didn’t perform nearly as well as its daily cousin over 10 years.

Understanding the chart: in this strategy we are buying and selling bitcoin using the 9/20 weekly simple moving average crossover signals over 10 years. In the chart we again note far fewer trades than with the daily crossovers (far less effort) but its return is also substantially lower than the 9/20 daily crossover for this 10 year time period.

2017 peak to mid-2022

In the daily MA crossover strategy category, the best result uses a 9-day fast SMA and a 20-day slow SMA. But it is a weak performer.

Understanding the chart: in this strategy we are buying and selling bitcoin using the 9/20 daily simple moving average crossover signals over 5 years. Notice the many red and green buy / sell signal triangles and you will see this method will keep you busy. Yet for all the work involved, its return over the five-year period was not competitive.

 When we used a weekly approach, the results were much better over the five-year window. The best result uses a 15-week fast SMA and a 19-week slow SMA.

Understanding the chart: in this strategy we are buying and selling bitcoin using the 15/19 weekly simple moving average crossover signals over 5 years. In the chart, we note far fewer trades, i.e. fewer red and green buy/sell indicator triangles, as now, we only look for a crossover of the moving averages to execute a possible buy or sell signal once a week. This involves far less effort and this method comes in second place in the 5 year back test category just after our Rationality Index.

The 9/20 simple moving average wasn’t among the best results in the weekly crossover.

Understanding the chart: in this strategy we are buying and selling bitcoin using the 9/20 weekly simple moving average crossover signals over 5 years. In the chart, we note few trades as we only look for a crossover of the moving averages to execute a possible buy or sell signal once a week. We like this but the return is not competitive.

Rationality Index

Now let’s look at our Rationality Index which is based on a logarithmic growth curve model. It is inspired by the work of Harold Christopher Burger and this article. Essentially it boils down to finding the curve that represents the best fit using linear regression on a log-log (both X and y-axes are scaled logarithmically) chart of the bitcoin price data. The result is an oscillator allowing us to represent how ‘overbought’ or ‘oversold’ bitcoin is using a number from 0 to 100.

10-year window

We use a buy signal of 71 (buy 100% using available cash at or below index level 71) and a sell signal of 98 (sell entire position at or above index level 98). After the first selling, re-buy 100% of available cash at or below index level 45. The results are outstanding: having spent $130k cash, our investor would have more than $1.5 billion dollars.

Understanding the chart: in this strategy we are buying and selling bitcoin using Upside Signal‘s Rationality Index signals over 10 years. This is a daily strategy so, on the chart we see many buy signals. Note there are just 4 sell signals which all occur near market peaks. This is a very efficient strategy and the reason why it has the highest return among the strategies we tested. 

2017 peak to mid-2022

We used a buy signal of 21 (buy 100% of available cash at or below index level 21) and a sell signal of 97 (sell entire position at or above index level 97). After the first selling, re-buy 100% of available cash at or below index level 13.

Understanding the chart: in this strategy we are buying and selling bitcoin using Upside Signal‘s Rationality Index signals over 5 years. This is a daily strategy but still, on the chart we see just 2 buy signals. You may wonder why so few relative to the 10 year RI strategy? This is related to the pattern of volatility seen in bitcoin prices since 2017.

Note there is only 1 sell signal which occurred near the 2021 March / April peak. This is a very efficient strategy and the reason why it has the highest return among the strategies we tested. 

Note that this result came from just 1 trade, with 2 buy and 1 sell orders. Less trades mean easier execution and less operational costs (fees, spread, slippage, etc).

Discussion and Conclusions

To us the results seem somewhat remarkable and unremarkable at the same time – remarkable how superior the rationality Index strategy was compared to the alternatives we studied. It is remarkable because dollar cost averaging and buy/hold are so popular. But it is also unremarkable in the light of investing’s bottom line: buy low, sell high. 

Our Rationality Index is just a tool to show us what buy low, sell high really means and how it performs if you can manage to overcome your instinctive emotions around investing and actually implement ‘buy low, sell high’.

The Bitcoin Rationality Index highlights for us our own terrible investing mistakes And reminds us continually of our commitment not to repeat them!