Market risk and volatility assessment formulas are engineered to adjust collateralization requirements dynamically to ensure a reasonable on-boarding ratio for users who want to collateralize synthetic asset pools or loans based on the present state of the market.

Without this value being dynamic a set value creates over-collateralization, which hinders individuals from taking part in the creation of synthetic assets and taking out loans.

Community voting is a popular method by which a set collateralization value is calculated. However, the community at large is often unaware of the complexities involved in determining the best value. Therefore, collateralization will be determined algorithmically as a dynamic value and not a set value.

### Volatility Determination

Since most crypto assets move in parallel to Bitcoin we are able to determine the volatility drawdown for the crypto market using the following steps:

The formula for daily volatility is computed by finding out the square root of the variance of Bitcoin's daily price. Further, the annualized volatility formula is calculated by multiplying the daily volatility by a square root of 365.

Step 1: We first gather the daily price of Bitcoin and then determine the mean. Let us assume the daily price on an ith day as Pi and the mean price as Pav.

Step 2: Next, we compute the difference between each day’s Bitcoin price and the mean price, i.e., Pi – P.

Step 3: We then compute the square of all the deviations, i.e. (Pav – Pi)2.

Step 4: Next, find the summation of all the squared deviations:

$$\sum(Pav-Pi)^2$$

Step 5: Next, divide the summation of all the squared deviations by the number of daily Bitcoin prices, in this instance we say n. It is called the price variance of Bitcoin.

$$V=\sum(Pav-Pi)^2/n$$

Step 6: Next we compute the daily volatility or standard deviation by calculating the square root of the variance of Bitcoin.

$$DV = \sqrt{\frac{(Pav-Pi)^2}{n}}$$

DV = Daily Volatility

Step 7: We annualize the volatility. The formula is calculated by multiplying the daily volatility by the square root of 365. Here, 365 is the number of active trading days in a year (crypto markets don't close as traditional markets do).

$$AV = \sqrt{365} \frac{(Pav-Pi)^2}{n}$$

AV = Annualized Volatility

### Moving Average Computation

We take the EMA for BTC/USD and analyze the short term and long term averages to create a balance for our collateralization rate.

$$EMAt=[Vt(\frac{s}{1+d})] + EMAy[1-(\frac{s}{1+d})]$$

Where:

• EMAt = EMA today
• Vt = Value today
• EMAy = EMA yesterday
• s = Curving smoothing
• d = Number of days

We take 3 EMA data points from average cycles to cover the entire crypto landscape. Since the average cycle duration seems to be about 3 years, we have a max point to indicate the higher-end level of risk tolerance which will carry a heavier weight impact on our risk index calculation.

### MA Vs. EMA

We propose EMA as it emphasizes more on recent data points. Because of this, EMA can be considered more of a weighted average calculation.

### Weighing Importance

Sigma Risk Index output weighs every data point according to importance.