Methodology

Introduction

Cryptocurrency Index

What is Index?

Cryptocurrency index is a standard point of reference. Its purpose is to give an insight of the movements of the crypto market.

Types of Indices

Market Cap Indices :

Market cap indices are capitalization-weighted indices. In market cap indices each component is given a weight based on its market capitalization and each currency weight is directly proportional to the market capitalization.

Equal Weight Indices :

Equal weight indices give the same weight to all the components. The smallest component and the largest component have equal weights and hence they get the same space in index calculations.

Concept of Divisor

The index divisor is one of the crucial things in index calculation. The concept of the divisor is brought into the algorithm to remove the fluctuations in the index due to circulating supply. Divisor basically works as an adjustment factor whenever the circulating supply changes.

Index Constituents

The Index consists of top-x currencies based on their market capitalization where x depends on the type of index.
For each index be it either Market Cap or Equal Weight, the index is calculated for x=10,25,50 and 100 currencies. Which gives indices as:

Market Cap Indices : Cryptoz-10, Cryptoz-25, Cryptoz-50 and Cryptoz-100.
Equal Weight Indices : Cryptoz-EW-10, Cryptoz-EW-25, Cryptoz-EW-50 and Cryptoz-EW-100.

Types Of Indices Calculated

As explained above, we calculate two types of indices Market Cap and Equal Weight as Cryptoz-x and Cryptoz-EW-x respectively.

Market Cap and Equal Weight Indices:

For both Market cap and Equal Weight, four types of Indices are calculated each with different number of Currencies (with x = 10, 25, 50, 100) based on their Market Capitalization:

Cryptoz-10 and Cryptoz-EW-10 - For these indices, the top 10 cryptocurrencies are considered.

Cryptoz-25 and Cryptoz-EW-25 - For these indices, the top 25 cryptocurrencies are considered.

Cryptoz-50 and Cryptoz-EW-50 - For these indices, the top 50 cryptocurrencies are considered.

Cryptoz-100 and Cryptoz-EW-100 - For these indices, the top 100 cryptocurrencies are considered.

Rebalancer :

It is activated on 1st of every month. As already explained in the above examples about its importance and its impact on Indices, it also takes care of an additional task. The constituents of Indices are adjusted based on their market capitalization as on 1st of that month. So lets say if ripple's market Cap falls to number 11, then it will not be considered in the further calculation for Cryptoz-10 or Cryptoz-EW-10,instead a new currency that replaced it will be included.

Crypto Market Cap Indices

Crypto Market Cap Indices are most widely used crypto indices. These are also called capitalization-weighted or value-weighted. The cryptocurrency index is a layout for the crypto market. It gives us information to analyze the cryptocurrency market and to understand the variations in the crypto market.

Formula for Index Calculation

index

where, Pi = Price of a cryptocurrency
    Qi = Circulating supply of that cryptocurrency

Initial Divisor Calculation

Market_cap_formulaes

where, Index0 = initial index chosen to be 1000.
    Market Cap0 = Sum of market capitalizations of the constituents of the Index at start date.

Divisor Adjustments

The value of divisor is adjusted when circulating supply of any of constituents is changed. So the only change in price affects the Index.

divisor

where, Pt = Current price of cryptocurrency
    Ct-1 = Previous circulating supply of the cryptocurrency
    Indext - 1 = Previous Index

Algorithm

Indexes are simply calculated based on the summation of Market caps of their constituents. As explained in the above formula for index calculation.

As each Market Cap involves circulating supply, so a currency with no change in price but a change in circulating supply will affect the Index. To nullify the effects of circulating supply on Index, a divisor is introduced as explained above.

Divisor removes the effect of Circulating Supply from the market capitalization.

Let's see how Divisor does this with an example:

Let's say we have two currencies bitcoin and ripple :

Day 1:

     Price of bitcoin = $1;      Circulating Supply of bitcoin = 10 BTC

     Price of ripple = $10;      Circulating Supply of ripple = 1 XRP

     Since, Market Cap = Price * Circulating supply

     Market cap of bitcoin = 1 * 10 = $10

     Market cap of ripple = 10 * 1 = $10

     Initial Index = 1000

     Divisor = Market cap/Initial Index

     Initial Divisor = 20/1000 = 0.02


Day 2:

     Price of bitcoin = $1;      Circulating Supply of bitcoin = 15 BTC

     Price of ripple = $15;      Circulating Supply of ripple = 1 XRP

     Again, Market Cap = Price * Circulating supply

     Market cap of bitcoin = 1 * 15 = $15

     Market cap of ripple = 15 * 1 = $15


Now we see that the market cap of both the currencies increased by 50%, but one is due to circulating supply and the other is due to price.

As we want our index to vary only according to price. So we nullify the change caused by circulating supply using the formula below,


Divisor = Σ (Pricei-1 * circulating supplyi)/Index i-1


where, Pricei-1 = Previous price of a cryptocurrency
    circulating supplyi = Circulating supply of that cryptocurrency
    Indexi-1=Previous Index

Now whenever there is a change in circulating supply we re-adjust the Divisor according to above formula which nullifies the effect of circulating supply

Here we calculate the Divisor using Price of Day 1 and Circulating Supply of Day 2.

So in Our Case:

     1 * 15 + 10*1 = 25

     Divisor = 25/1000

     Divisor = 0.025

     Index = Σ Market cap/Divisor

     Hence, Index = 30/0.025 = 1200


Effect of circulating supply on Cryptocurrency Index

For a time span of one day

Now let's say we have 2 currencies whose Circulating Supply Increased in a span of 1 day but Price is constant.

Day 1:

     Price of bitcoin = $1;      Circulating Supply of bitcoin = 10 BTC

     Price of ripple = $10;      Circulating Supply of ripple = 1 XRP

     Since, Market Cap = Price * Circulating supply

     Market cap of bitcoin = 1 * 10 = $10

     Market cap of ripple = 10 * 1 = $10

     Initial Index = 1000

     Divisor = Market cap/Initial Index

     Initial Divisor = 20/1000 = 0.02


Day 2:

     Price of bitcoin = $1;      Circulating Supply of bitcoin = 15 BTC

     Price of ripple = $10;      Circulating Supply of ripple = 3 XRP

     Since there is a change in circulating supply we re-adjust the Divisor

     1 * 15 + 10*3 = 45

     Divisor = 45/1000

     Divisor = 0.045

     Index = Σ Market cap/Divisor

     Index = 45/0.045 = 1000


From the above calculations, it can be verified that any Change in Circulating supply will not affect the Index Value

For a time span of one month

Now Let's take into account Month Changes.

When Month changes, we re-adjust the currency list based on the Market Cap it holds on that day. Rebalancer makes sure that any change in Currency Order, Addition/Removal of Currency does not affect Index Value. Basic Rule of rebalancing is that Index Value before and after rebalancing stays the same.

Let's again take the same example:

Day 1(Last day of Month):

     Price of bitcoin = $1;      Circulating Supply of bitcoin = 10 BTC

     Price of ripple = $10;      Circulating Supply of ripple = 1 XRP

     So Market Cap = Price * Circulating supply

     Market cap of bitcoin = 1 * 10 = $10

     Market cap of ripple = 10 * 1 = $10

     Initial Index = 1000

     Divisor = Market cap/Initial Index

     Initial Divisor = 20/1000 = 0.02


Day 2 (1st Day of New Month):

     Price of bitcoin = $1;      Circulating Supply of bitcoin = 15 BTC

     Price of ripple = $10;      Circulating Supply of ripple = 3 XRP

     Index Value will stay the same = 1000

     Divisor = Current Market cap/Index value

     divisor = 45/1000 = 0.045

     Now for Next Index Calculation, this divisor will be used.

Equal Weight Index

Equal weight index is one where every Cryptocurrency has the same weight in the index. An equal amount of money is invested in each currency making it easy for you to track performance. It varies directly with any fluctuations in the price of any of the Index members. Therefore, an Equal Weight Index must be rebalanced from time to time to re-establish the proper weighting.

In these type of Indices, all cryptocurrencies carry equal weight regardless of their Market cap. To achieve this we divide the amount to be invested equally in all constituents of Index.

So we calculate the number of coins that can be bought with money at the start of the month. And for the whole month we keep the number of coins constant and monitor the return based on Price Change.

Formula for Index Calculation

index

where, Pi = Price of Cryptocurrency
    Qi = Circulating Supply of the crypto

Initially Money is Divided as per the formula :

Market_cap_formulaes

Market_cap_formulaes

where

    Pi = Price of the currency at the start of the month.

Algorithm

Let's continue with our previous example

Let's say we have two currencies bitcoin and ripple

Start of Month

Amount to Invest : $1000

This is the amount we choose to start with

Day 1:

Total Currencies we are investing in is 2

Amount to Invest/Total_Currencies

So For each currency we have to invest 500

     Price of bitcoin = $100;      Circulating Supply of bitcoin = 10 BTC

     Price of ripple = $10;      Circulating Supply of ripple = 100 XRP

     Amount to Invest per currency / Price of each currency will give us the number of coin one can buy on Day 1. For Ripple it is 500/10 = 50 For Bitcoin it is 500/100 = 5      So we buy 50XRP and 5 BTC on Day 1


Day 2:

     Price of bitcoin = $90;

     Price of ripple = $15;

     Since, Market Cap = Price * Coins that are bought

     Market cap of bitcoin = 5 * 90 =$450 $15

     Market cap of ripple = 15 * 50 = $750

     So Total Index value as given above is sum of all Market Cap based on the number of coins we invested

    Total_sum = $450 + $750 = $1200

So we Invested $1000 on Day 1 it is now worth $1200 on Day 2 due to rise in price of Ripple, even though there is drop in Bitcoin Price.

At Rebalance For Equal Weight Index the amount that we have on 31st is all Invested into top constituents(by Market Cap) equally as described in this example of Day 1


Rebalancer

1. Change constituents every month on the basis of Market Cap.

2. If a Cryptocurrency is discontinued from the crypto market, we make it insensitive from index calculation till rebalanced data is reached.

3. The Index value is not changed in rebalancer, only Divisor is adjusted.

divisor