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. Set the initial index contract amount to 1000;

2. Determine the index constituents;

3. Determine the amount of each constituent such that: $\sum_{i=1}^mP_{i}*N_{i}=Index_{initial}$
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: $Index_{1}=0.00903*BTC+0.07852*ETH+0.24755*BNB+0.62376*SOL+27.7901*MATIC$