# Indices

### Initial Contract Amount:

The initial contract amount is set to 1000.

### Index Calculation Formula:

$Index_{t}=\frac{\sum_{i=1}^{m^t}P_{i}*N_{i}^t}{Divisor_{t}}*Index_{initial}\ \ (t\ge1)$
$Divisor_{t}=Divisor_{t-1}*\frac{\sum_{i=1}^{m}P_{i}*N_{i}^t}{\sum_{k=1}^{g}P_{k}*N_{k}^{t-1}}$
where:
• $Index_{t}$
: Index of the
$t^{th}$
period
• $P_{i}$
: The current price of the
$i^{th}$
constituent
• $N_{i}^t$
: At time
$t$
, the amount of the
$i^{th}$
constituent in the index
• $Index_{initial}$
: Initial contract amount of the index,
$Index_{initial}$
= 10000
• $Divisor_{t}:$
A stabilizer that ensures a stable and continuous change of the index and eliminates the impact of index rebalancing.
$Divisor_{1}=Index_{initial}$

### Index Calculation Process:

1. 1.
Set the initial index contract amount to 1000;
2. 2.
Determine the index constituents;
3. 3.
Determine the amount of each constituent such that:
$\sum_{i=1}^mP_{i}*N_{i}=Index_{initial}$
4. 4.
Since the price of each token
$P_{i}$
is already known, we need to determine the weight of each token
$W_{i}$
to calculate
$N_{i}$
:
$Index_{initial}*W_{i}=P{i}*N{i}$
. There are various methods to determine
$W_{i}$
• Equal weights:
$\frac{1}{m}$
• Market cap weighted:
$w_{i}=\frac{MarketValue_{i}}{\sum MarketValue}$
• and more.

### A Market Cap Weighted Example

Initial Contract Amount: 1000.
Constituent
Market Cap
Sqrt Market Cap
Current Price
BTC
884,619,116,312
940542.0
46633.22
ETH
445,105,069,241
667162.0
3805.21
BNB
87,541,528,702
295874.2
535.24
SOL
46,972,431,831
216731.2
155.67
MATIC
12,623,182,765
112353.0
1.81
$w_{i}=\frac{\sqrt{MarketValue_{i}} }{\sum MarketValue}$
BTC:
$w_{1}=\frac{940542}{940542+667162+295874.2+216731.2+112353}=\frac{940542}{2232662.4}=0.4213$
$N_1^1=\frac{1000*w_1}{p_1}=\frac{1000*0.4213}{46633.22}=0.00903$
ETH:
$w_{2}=\frac{667162}{2232662.4}=0.2988$
$N_2^1=\frac{1000*w_2}{p_2}=\frac{1000*0.2988}{3805.21}=0.07852$
BNB:
$w_{3}=\frac{667162}{2232662.4}=0.1325$
$N_3^1=\frac{1000*w_3}{p_3}=\frac{1000*0.1325}{535.24}=0.24755$
SOL:
$w_{4}=\frac{216731.2}{2232662.4}=0.0971$
$N_4^1=\frac{1000*w_4}{p_4}=\frac{1000*0.0971}{155.67}=0.62375$
MATIC:
$w_{5}=\frac{112353}{2232662.4}=0.0503$
$N_5^1=\frac{1000*w_5}{p_5}=\frac{1000*0.0503}{1.81}=27.79006$
Constituent
Market Cap
Sqrt Market Cap
Current Price
Weight
Quantity
BTC
884,619,116,312
940542.0
46633.22
0.4213
0.00903
ETH
445,105,069,241
667162.0
3805.21
0.2988
0.07852
BNB
87,541,528,702
295874.2
535.24
0.1325
0.24755
SOL
46,972,431,831
216731.2
155.67
0.0971
0.62376
MATIC
12,623,182,765
112353.0
1.81
0.0503
27.7901
Index Calculation:
$Index_{1}=0.00903*BTC+0.07852*ETH+0.24755*BNB+0.62376*SOL+27.7901*MATIC$