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

**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** 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.

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.

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:

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

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.

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** 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.

where,

where, **Index**_{0} = **initial index** chosen
to be 1000.

**Market Cap**_{0}
= Sum of market capitalizations of the constituents of the **Index**
at start date.

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

where,

**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 (Price _{i-1} * circulating
supply_{i})/Index _{i-1}
**

where,

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

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**

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** 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.

where,

Initially Money is Divided as per the formula :

where

PLet'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

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**

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**.