Here we use the logarithm of returns instead of price returns. The benefits of using log-returns, versus prices, is log-normality: assuming the prices are distributed log normally, the log return is conveniently normally distributed, which is handy given much of classic statistics presumes normality.
We can then divide the log-returns into 27 intervals: (-14%, -13%), (-12%, -11%), …, (12%, 13%), count the number of minute returns for each interval and we get the following histogram:
Step 2: Calculate the average and standard deviation of log returns
We can then calculate the average and standard deviation of log-returns based on the formulas:
The average (µ) of 10,080-minute log-returns turns out to be 0.001083%, and the standard deviation (?) is 0.03170.
Step 3: Calculate VaR based on confidence intervals of normal distribution
Assuming the returns are normally distributed, we can see where the worst 5% and 1% lie on the normal curve. They show traders’ desired confidence, the standard deviation and the average from the below table:
The Verdict
There are two ways to understand the VaR calculation results:
- With 95% and 99% confidence, we can expect that the worst loss will not exceed 5.23% and 7.38% respectively;
- If we invest $10,000, we are 95% and 99% confident that our worst minute-loss will not exceed $523 (=$10,000 x -5.23%) and $738 (=$10,000 x -7.38%) respectively.
VaR is useful for calculating the maximum expected loss on an investment over a given time and a specified degree of confidence. Traders can apply VaR to determine the level of risk or potential losses of their trading portfolios easily and hence take necessary measures to control the risks.
This post originally appeared on OKEx Blog. Read more.
Disclaimer: This material should not be taken as the basis for making investment decisions, nor be construed as a recommendation to engage in investment transactions. Trading digital assets involve significant risk and can result in the loss of your invested capital. You should ensure that you fully understand the risk involved and take into consideration your level of experience, investment objectives and seek independent financial advice if necessary.
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