Question

Analyze the price of stETH in ETH denomination and find meaningful correlations that explain its fluctuation. Possible correlations could be with ETH’s price in USD, ETH’s gas price, volume in the curve pool, Curve stETH/ETH pool composition, etc.

To examine the behavior of the ETH and stETH price charts, we fitted different distribution functions. Among all of them, for ETH and stETH, the JohnsonB distribution function was selected as the best distribution function.

The selection of the best distribution function is based on AIC, SIC and HQIC information criteria. The distribution function that has the lowest value for each of these criteria is selected as the best distribution function. Model Risk software has been used to fit different distribution functions.

stETH Distribution Function

1. stETH Price vs. ETH Price

According to the chart above, the stETH price follows the ETH price almost every day. Therefore, there seems to be a strong correlation between the price of stETH and ETH. For further investigation, a scatter plot is drawn and the correlation coefficient between these two variables is calculated.

The correlation coefficient between the two variables is 0.999. That is, the correlation coefficient between the price of stETH and ETH is very strong and positive.

The johnson distribution function is the best function by which the behavior of the stETH and ETH price charts can be analyzed.

2. stETH Price vs. BTC Price

The correlation coefficient between the stETH price and the BTC price is:

Correlation(stETH_price,BTC_Price)=0.54

The correlation between stETH and BTC prices is moderate and positive.

The chart below shows that on different days the stETH price is affected by BTC price fluctuations, ie with the increase or decrease of the BTC price, the stETH price also decreases or increases.

3. stETH Price vs. ETH Liquidity in Curve Farming Pool

According to the chart below, the price of stETH has been affected several times by changes in ETH liquidity in the Curve pool.

For example, in February 2021, when ETH liquidity fell from 127 ETH to 102 ETH in one week, the price of stETH fell from $ 1985 to $ 1,345. Or when ETH liquidity in the Curve increased from 161 ETH to 265 ETH in early May 2021, at the same time the price of stETH rose from around $ 2600 to $ 4100.

The correlation coefficient between the stETH price and the ETH liquidity is:

Correlation(stETH_price,ETH_Liquidity)=0.621

The correlation between stETH and BTC prices is strong and positive.

4. stETH Price vs. stETH Swap Volume

The correlation coefficient between the stETH price and the stETH swap volume is:

Correlation(stETH_price,stETH_swap_volume)=-0.2

The correlation between stETH price and swap volume is weak and negative.

5. stETH Price vs. Average Daily ETH Gas Price

Given that the ETH gas price chart is highly volatile, there is no correlation at first glance. For further consideration in the next section, the correlation coefficient between the stETH price and the ETH gas price has been calculated.

Correlation(stETH_price,ETH_swap_Gas_Price)=0.041

The correlation between stETH price and ETH gas price is very weak and positive.

ETH Distribution Function

Methodology

• In this dashboard, a correlation of 5 variables with the stETH price is obtained. These variables are:

1. ETH Price

2. BTC Price

3. ETH Liquidity in Curve Farming Pool

4. stETH Swap Volume

5. Average Daily ETH Gas Price

• The correlation coefficient between different variables with the stETH price is determined based on the following classification:

1. Correlation sign:

correlation coefficient>0 ---> Positive correlation (the relationship between the two variables is direct).

correlation coefficient<0 ---> Negative correlation (the relationship between the two variables is inverse).

2. Correlation size:

0-0.19 ---> regarded as very weak.

0.2-0.39 ---> weak.

0.40-0.59 ---> moderate.

0.6-0.79 ---> strong.

0.8-1 ---> very strong correlation.

• To model the price behavior of ETH and stETH, the best distribution function is fitted for them. The selection of the best distribution function is based on SIC, AIC and HQIC information criteria(An information criterion is a measure of the quality of a statistical model. It takes into account: how well the model fits the data and the complexity of the model.). Model Risk software has been used to fit different distribution functions.

• The following tables have been used to extract the data:

1. ethereum.core.fact_hourly_token_prices

2. ethereum.core.fact_transactions

3. ethereum.core.ez_dex_swaps

4. ethereum.erc20_balances

5. ethereum.token_prices_hourly

Result

💡 The correlation between ETH and stETH prices has been very strong so far.

💡 The best distribution function that can model the price behavior of ETH and stETH is the JohnsonB distribution function.

💡 The correlation between ETH liquidity in the Curve Farming pool and stETH price is strong.

💡 The correlation between stETH price and BTC price is moderate.

💡 There was no correlation between swap volume and stETH price or Ethereum gas fee with stETH price.