The Phi Algorithm

We spent 10 years developing the Phi Algorithm that creates the Target Price by forecasting when Bitcoin prices are likely fall.


It may not seem possible to predict when Bitcoin prices are likely to fall. People have been educated to believe that prices, like many other aspects of life, are random. Yet prices develop over time as do other systems.

Few people doubt that the pattern that forms an oak leaf will continue to repeat itself as an oak tree grows year after year. No one doubts that sowing the seed of a carrot will produce a carrot. Its shape and size may be influenced by environmental factors such as water, sunlight and nutrients, but no one doubts that a carrot seed will produce a carrot and never a beetroot or onion.

Phi, the irrational number of 1.618…, also called the Golden Ratio and Golden Mean, is the expression of growth in the natural world. The particular way various Phi ratios are combined together determines whether the process of development produces a frog or a rat. Nature is super-efficient in using Phi as the universal expression of growth.

The specific Phi ratios that determine the shape of the wings of this butterfly. Source: Gyorgi Doczi The Power of Limits

“If we look closely at a flower, and likewise at other natural and man-made creations, we find a unity and an order common to all of them. This order can be seen in certain proportions which appear again and again, and also in the similarly dynamic way all things grow or are made – by a union of complementary opposites.”

When the growth of a system is plotted on a graph instead of being drawn as a picture Phi expresses itself in frequencies that are multiples of its value. For example 1.618 * 10 could equal approximately 16 days. 1.168 * 2 could equal approximately 2.6 days. This means that as it develops over time a dataset it likely to be structured with periods of rise and fall that take place at fixed Phi derived frequencies. Like the combination of Phi ratios that give an oak leaf its particular shape, these frequencies represent the unique character of the system. As an oak will always produce an oak leaf, so periods of rise and fall will always be found in a system at its signature frequencies irrespective of environmental factors acting upon the system.

Phi in Action

For example, Rassmussen Reports conducted a daily poll of President Obama’s public approval during his two terms in office. The usual view of the data on the left hand graph below seems to suggest that the approval rating has very little structure to it. However, once one of the Phi-based frequencies have been found the right hand graph shows 3 week periods of rising approval immediately followed by 3 weeks of falling approval. There is then a 6 week interval before the process repeats itself. As the right hand graph shows, once the Phi-based frequency is known the periods of rising and falling approval can be forecast with a better than 50/50 chance.

Left hand graph: the normal view of President Obama's Approval Index during his two terms in office. Right hand graph: the same data segmented at the Phi-based frequency that describes the unfolding of the system.

By way of another example, natural gas is often traded in the United States off prices at the Henry Hub distribution centre at Erath, Louisiana. Henry Hub natural gas prices have historically been very volatile. As the left hand graph below illustrates, the system appears to be a classic example of a random distribution of numbers. However, Henry Hub natural gas prices also have structure. The right hand graph shows the price data divided up into fixed recurring periods of rise and fall at a Phi-based frequency. Even in a market as volatile and seemingly unpredictable as Henry Hub natural gas there is still a Phi based structure to the way prices unfold over time.

Left hand graph: normal view of Henry Hub natural gas futures prices. Right hand graph: the same data when segmented into period of fixed length according to the Phi based frequency at which the market operates.

The Challenge of Forecasting When Bitcoin Prices are Likely to Fall

The price of Bitcoin is also a system unfolding over time. This would suggest that its prices would also by structured by Phi-based frequencies. There are however some challenges to finding these.

First, with just 7 years of data (even though the coin is 9 years old), it may be too early to fully describe the Phi-based frequencies of the system. There may simply not be enough instances of the pattern for it to be discernible.

Second, Bitcoin’s rapid rise is value means that the periods of falling prices are not as obvious as with a system such as Henry Hub natural gas where falling prices occur more frequently.

The first challenge can be overcome by focusing on shorter Phi-based frequencies that have had the opportunity to repeat themselves enough times for the pattern of development to be seen.

The second challenge can be mitigated through the use of filters.

Filters represent environmental factors that affect the development of a system. In the development of an oak leaf adequate water and sunlight will enable the pattern of the leaf to be more visible than if these factors were scarce. In the same way a filter such as the standard deviation of returns can give better clarity as to the underlying pattern of a currency such as Bitcoin.

Simulated Forecast Results

This approach – establishing the Phi-based frequency at which the market operates together with appropriate filters –has yielded a simulated success rate greater than 60% in forecasting when Bitcoin prices are likely to fall.

The result on performance is significant. This is primarily due to the compounding effect of the rapid rise in Bitcoin prices. Modelling the forecast periods from 13th September 2013 when Bitcoin stood at $5.93 demonstrates how effective the compounding effect can be on successful forecasts. By 14th February 2018 the value of Bitcoin had risen to $9,071, an average annual increase of 237%. However during the same period the value of Bitcoin Enhanced would have risen to $136,741, an average annual increase of 21,265%. In this simulation the value of Bitcoin Enhanced improved the value of Bitcoin by a multiple of 15.

IMPORTANT - Simulated results are NOT an indication of predictability. Historical data can be easily fitted to produce good results. Only live trading can demonstrate predictability. Second, past performance, even of live trading, is NOT always a good indicator of future results.

Simulated returns of Bitcoin Enhanced compared to the returns of Bitcoin over 6 and one half years.

The Bitcoin Enhanced Method

This section describes how a market price is established for Bitcoin, how Bitcoin Enhanced ensures the validity of its forecasts, how its Target Price is calculated, and how the actual market price of the tokens is create.

Establishing Bitcoin Prices

Bitcoin prices are sourced from multiple APIs across the exchange network. This reduces the chances of outage as well as provides a representative price for Bitcoin at any given time.

Ensuring Trustless Forecasts

A forecast for a period of falling prices is made before the period begins. To ensure this priority in a trustless way we time-stamp the forecast on a blockchain using a service such as The forecast is then published on the Bitcoin Enhanced website and forums such as Facebook and Twitter in an encrypted form. When the forecast is complete we release the key in order for anyone to validate the forecast was genuine and made before the event.

Calculating the Bitcoin Enhanced Target Price

The Bitcoin Enhanced Target Price is a simulated long/short Bitcoin investment strategy. It is the price, without including fees and slippage, that the strategy would have if Bitcoin and Bitcoin futures had been traded. However, no assets are actually traded and no assets support its value.

The Target price tracks the percentage changes in Bitcoin prices except during forecasts of when Bitcoin prices are likely to fall. Then it simulates shorting Bitcoin (betting Bitcoin prices will fall).

In order that the forecasts are not known until they are over, during a forecast the Target Price continues to track Bitcoin’s price changes until the last day of the forecast period. It then adjusts itself depending on whether the forecast was successful in predicting Bitcoin price falls or not.

This adjustment in the Bitcoin Enhanced price can be expressed as a multiplier – the amount that the Target Price is either above or below the Bitcoin price based on the results of the forecasts.


At the start of a forecast period the Bitcoin price is $10,000. Bitcoin Enhanced price is also $10,000. As the price of both coins are the same the multiplier is 1 (1 * $10,000 = $10,000)

Next a forecast period begins. Bitcoin Enhanced continues to track Bitcoin prices using the existing multiplier until the end of the final day of the forecast period.

Once the forecast period is over the percentage rise or fall of Bitcoin prices during the period is calculated. For example, Bitcoin prices may have fallen 5% during the period. If Bitcoin was $10,000 at the start of the period it is now trading at $9,500. It has lost 5%. However Bitcoin Enhanced, by correctly forecasting the price fall now trades at 5% above its price at the start of the period, i.e. at $10,500. $10,500 is 10.5% greater than $9,500. The multiplier between the two coins is now 1.105 until the final day of the next forecast period.

The Market Price of Bitcoin Enhanced Tokens

The Target Price of Bitcoin Enhanced is aspirational. This means that the purpose of Bitcoin Enhanced tokens is to trade at or close to this price. However, the actual price the tokens trade at depends solely on the value token buyers and sellers give the tokens. There is no formal linkage between the Target Price and the traded price. Bitcoin Enhanced has no control over the traded price and does not intervene in the market to support the price.

Bitcoin Enhanced tokens are created on the Waves blockchain platform. The platform comes with its own exchange where the Bitcoin Enhanced tokens, BE Classic and BE Growth can be bought and sold. This price, not the Target Price represents the value of the tokens at any given time.

Example of the Waves exchange where Bitcoin Enhanced tokens can be bought and sold

The whole point of Bitcoin Enhanced is for people to grow value in a token themselves. If they choose to do so they will have demonstrated that, like Bitcoin itself, people can create wealth without being exposed to the risks of the fiat financial system.