This week, we conducted a simple statistical analysis based on time series data for different stablecoin prices in order to determine their degree of dispersion from the dollar peg. The model compared the degree of dispersion and ranked different assets based on dollar and price spread.

The 90-day historical price (sample period) was taken from Credmark’s API with a 6-hour time interval, while the price feed was reported by Chainlink oracles.

Let’s walk through the analysis one by one.

Stablecoin Time Series

First, we explored the datasets and price patterns of different stablecoins. The first chart summarizes each stablecoin price during the 90 day period. The second chart shows what it looks like if we removed LUSD due to its large price volatility.

90 Day Range

Next, we quantified the largest dispersion of a stablecoin, specifically the variation between peak and trough. Based on the formula below, we identified the highest and lowest dollar-denominated price for each stablecoin within the 90 day sample period.


    r = Max(prices) - Min(Prices)

90 Day Peg Deviation

Finally, we derived a figure that captured the spread of price data. Rather than comparing the dataset against the mean, we benchmarked the datasets against the $1.00 peg. This allows us to define the spread of token price from the one-dollar peg using the formula below:


    σ2 = ∑ (Xi – P)^2 / N

Where,

Xi = the data point in the price data set

P = the peg, in the case of stablecoin- P is substituted to 1

N = number of data points in the population

We captured a regular standard deviation as shown below.

Key Findings

LUSD demonstrated the largest price fluctuation within the 90 day period. This is followed by ALUSD and MIM.
LUSD also exhibited a much higher peg deviation than the standard deviation. While the token deviated from the one-dollar peg, LUSD price remained in a tighter spread between $1.02 - 1.03
- With the deployment of LUSD Chicken Bonds in October, we expect to perform this analysis again to see the effects of the protocol’s ability to recover the dollar peg with the provision of new LUSD liquidity within Curve pools.
ALUSD showed a high degree of price volatility across multiple periods. However, the price during the 90-day sample period reverted to the mean. This may have been due to arbitrage bots working as intended.
BUSD and USDT both showcased the smallest price clusters - presumably due to market volume on CEXes compared to DeFi counterparts.

It would be helpful to study stablecoin pegs in comparison to volume and liquidity within AMMs, as well as measurements on a longer time horizon. For example, a 180-day period may provide larger insights as stablecoin volatility could be affected by external market-wide events like liquidations and fluctuations across major non-stable trading pairs like ETH or BTC.