Annualizing Crypto Portfolio Volatility and Estimating VaR
Summary
The document outlines a variance-covariance approach to estimating volatility for a portfolio of cryptocurrencies. It starts from daily price changes, forms a covariance matrix of daily returns, and scales that matrix by 365 to estimate annual variance, reflecting that crypto markets trade throughout the year. Portfolio volatility is then calculated by applying the portfolio weights to the annualized covariance matrix and taking the square root of the resulting variance. Without annualization, the same calculation describes volatility over the daily return interval rather than a year.
The answer also describes scaling volatility by a normal quantile to estimate 95% VaR, assuming zero drift and normally distributed returns. It cautions that these assumptions may be poor fits for crypto returns and that multiplying daily covariance by 365 assumes independent, identically distributed daily returns. The method is a simple estimate, not a guarantee of realized risk.
Key ideas
- Estimate daily returns from the assets’ price changes and calculate their covariance matrix.
- Scale daily covariance by 365 to annualize it for continuously traded crypto markets.
- Calculate annual portfolio volatility as the square root of the weighted covariance variance.
- A normal quantile can scale volatility into a VaR estimate under zero-drift and normality assumptions.
- Annualization by 365 assumes daily returns are independent and identically distributed.
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Full text
# beginner portfolio statistics - annualized volatility of multi-asset portfolio
# beginner portfolio statistics - annualized volatility of multi-asset portfolio
Sorry for the dumb question, but I wanted to make sure my understanding of what I read and compiled was correct! I am trying to calculate the variance-covariance matrix, and annualized volatility of a multi-crypto portfolio. My method is as follows:
- got the daily prices of the cryptos in the portfolio. Given for one of the assets, only ~120 days of prices exist, I have a sample of 120 prices.
- I compute the percent daily change
- I calculate the variance-covariance matrix on these daily changes. Then, do I have to multiply by 120, or 365 ? I am trying to get the portfolio volatility, and I read everywhere that this should be annualized. For stocks, it's by multiplying 252, but for crypto is it 365 (24/7 trading)?
- I then calculate the dot product of the variance-covariance matrix and weights, and once more the dot product of what I get by the weights The square root of this then is annualized volatility?? What happens if I don't multiply by 120 / 365? Is this a useful metric?
Lastly, if I want to get the VaR of my portfolio, I can multiply the volatility by the z value ~ 1.64?
Does this make sense, or am I completely wrong and I have to hit the books again??
Thanks!!!
Alex
EDIT: distribution of BTC returns over 2 years
## Answer by Tim Wilding (score 3, accepted)
https://quant.stackexchange.com/a/41366
Yes, it mostly makes sense. The process you are outlining would give you a VaR estimate using the assumption that the returns of the cryptos are Normally distributed, and have a zero drift value. I think those assumptions are a bit of a stretch for cryptos in practice.
I would multiply the variance matrix of the daily changes by 365. 365 would be the best choice because cryptos are traded every day of the year. This gives you an annualized variance matrix ($V$). Note that multiplying by 365 assumes that the daily returns are IID, and this may also not be true in practice.
The calculation of the annual portfolio volatility is correct: $\sigma = \sqrt{x'Vx}$. This can be converted into the 95% VaR by scaling by $z \approx 1.64$Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.