While standard deviation provides important information about how data varies over its mean, it is rather difficult to use standard deviation to conduct cross comparisons between different types of tokens. In the previous analysis of financial risk exposures faced by stablecoins, one of the important sources of risk we have identified is the collaterals that back up values of these stablecoins to ensure prices stay at the target level. Hence for stablecoins backed with on-chain assets as collaterals, a potential metric to consider is the collateral pool value. This includes the changes in collateral pool value over time, trends in value growth, volatility and intercorrelation between the various collateralised assets.
Collateral pool value
By definition, total collateral value is simply calculated by summing the products of market price and quantity deposited for all tokens included in the collateral pool. Changes in market prices of collateral assets would directly result in changes of the total collateral value. Hence, it is important to study if there are any trends in how prices of each collateral asset changes, and the impact of such changes on the total collateral value.
Coefficient of variation
The coefficient of variation (CV) is also known as the normalised standard deviation. It is a metric ranging from 0 to 1, calculated by dividing the data’s standard deviation by its mean.
For the ease of calculation and data collection, we will consider the top 10 types of collateral asset that make up the highest value out of collateral pool. For each asset, the normalised coefficient of variation is calculated by dividing the standard deviation of asset price by mean asset price in the past one year.
Next, the coefficient of variation of the whole asset pool is calculated by summing the coefficients for each single asset, according to proportions of value. The data on collateral value can be retrieved from reserve reports or dashboards released by the protocol providers. For example, information on DAI collaterals can be found on
Walk through using example of DAI
According to data from Daistats retrieved in March 2022, the types of assets taking up the largest proportion of the DAI’s collateral are ETH, BTC, USDC.. etc, making up for over 90% of the whole collateral pool. The coefficient of variation for DAI collateral pool will be the weighted sum of the coefficient of variation of these individual assets. This metric gives information on the relative volatility of change in value of the reserve pool. Tokens with lower coefficient of variation will subsequently have lower levels of financial risk exposures.
Below is the normalised CV calculated for a group of 6 stablecoins backed with on-chain collateral assets, using data from March 2022. We see that sUSD has the highest CV, followed by LUSD and DAI, indicating a high level of financial risk exposures. ALUSD has the smallest CV, implying a relatively lower level of financial risk exposures.
Fig 1. CV of top collaterals of six stablecoins
From the results, we can clearly see the merits of tokens accepting multiple types of assets as collaterals from the lower CV. Out of the 6 tokens being compared, DAI, VAI and MIM use multiple types of assets as collateral, while sUSD, LUSD and ALUSD only accept a single type. In general, collateral pools made up of multiple types of assets have lower CV, indicating that their standard deviation and variation over time is of a smaller percentage as from the mean. This observation can be explained by the significant proportion of collateral pools being made up of stablecoins, which reduces the degree of market influence and improves the stability of reserve pool value. Meanwhile, in this comparison, the ALUSD is an outlier that takes single type of asset as collateral but has an extremely small CV. This is because ALUSD is using DAI as the only type of collateral. Given the stablecoin nature of DAI, its price is bound to have very small variations even after normalisations.
Potential issues of CV
While the normalised way of comparison using coefficient of variance gives a simple way of comparison, it is not a comprehensive way of analysing financial risk from collaterals and has some demerits that need to be noted.
Firstly, the coefficient of variation does not always give accurate descriptions of the collateral pool. In the analysis, we have only considered the top 10 types of collateral asset by value. For most protocols, this range covers about 80% of the whole collateral pool. While this number seems to be sufficient, it is still not describing the full picture. There could be small amounts of assets that contribute to reducing inter-correlation that are left out, hence the result is overly optimistic.
Also, while the coefficient of variation shows overall weighted volatility of the collateral pool, it does not account for inter-correlations between the various assets, hence is insufficient to determine the level of financial risk exposures just based on the coefficient. In order to uncover correlations, we need to use other methods, such as calculating a correlation matrix to identify the asset with highest influence on prices of others.
Another point to note is that such analysis using the coefficient of variation is fully constructed using historical data. Although the readily retrievable on-chain data makes analysis easier, the market conditions and development of each token is unlikely to replicate in the future. This results in limited usability of the analytical result, and interpretation of financial risk should only be used as a reference or estimate. It is still important and necessary to keep track of new changes, and be aware of their potential impact on risk, so we can know about risk exposures in a more detailed manner.
The coefficient of variation can be used as an useful indicator of financial risk for stablecoins backed with collaterals, as it gives information on the relative volatility of collateral value that eventually supports price of stablecoin at its target. As a single number and normalised metric, the coefficient of variation can be used for simple comparisons between different tokens. For a more detailed analysis of the collateral, we can also consider to calculate the coefficient of variation with different number of assets, use multiple timeframes and compare against other metrics like pairwise correlation between the top collateral assets by value.