Volatility Signal-to-Noise Ratio

🙏🏻 this is VSNR: the most effective and simple volatility regime detector & automatic volatility threshold scaler that somehow no1 ever talks about.

This is simply an inverse of the coefficient of variation of absolute returns, but properly constructed taking into account temporal information, and made online via recursive math with algocomplexity O(1) both in expanding and moving windows modes.


How do the available alternatives differ (while some’re just worse)?

• Mainstream quant stat tests like Durbin-Watson, Dickey-Fuller etc: default implementations are ALL not time aware. They measure different kinds of regime, which is less (if at all) relevant for actual trading context. Mix of different math, high algocomplexity.
  
  
• The closest one is MMI by financialhacker, but his approach is also not time aware, and has a higher algocomplexity anyways. Best alternative to mine, but pls modify it to use a time-weighted median.
• Fractal dimension & its derivatives by John Ehlers: again not time aware, very low info gain, relies on bar sizes (high and lows), which don’t always exist unlike changes between datapoints. But it’s a geometric tool in essence, so this is fundamental. Let it watch your back if you already use it.
  
  
• Hurst exponent: much higher algocomplexity, mix of parametric and non-parametric math inside. An invention, not a math entity. Again, not time aware. Also measures different kinds of regime.
  

How to set it up:
Given my other tools, I choose length so that it will match the amount of data that your trading method or study uses multiplied by ~ 4-5. E.g if you use some kind of bands to trade volatility and you calculate them over moving window 64, put VSNR on 256.

However it depends mathematically on many things, so for your methods you may instead need multipliers of 1 or ~ 16.

Additionally if you wanna use all data to estimate SNR, put 0 into length input.


How to use for regime detection:
First we define:

• MR bias: mean reversion bias meaning volatility shorts would work better, fading levels would work better
  
  
• Momo bias: momentum bias meaning volatility longs would work better, trading breakouts of levels would work better.
  

The study plots 3 horizontal thresholds for VSNR, just check its location:

1. Above upper level: significant Momo bias
   
   
2. Above 1 : Momo bias
   
   
3. Below 1 : MR bias
   
   
4. Below lower level: significant MR bias
   
   

Take a look at the screenshots, 2 completely different volatility regimes are spotted by VSNR, while an ADF does not show different regime:


^^ CBOT:ZN1!


^^ INDEX:BTCUSD


How to use as automatic volatility threshold scaler
Copy the code from the script, and use VSNR as a multiplier for your volatility threshold.

E.g you use a regression channel and fade/push upper and lower thresholds which are RMSEs multiples. Inside the code, multiply RMSE by VSNR, now you’re adaptive.

^^ The same logic as when MM bots widen spreads with vola goes wild.


How it works:
Returns follow Laplace distro -> logically abs returns follow exponential distro, cuz laplace = double exponential.

Exponential distro has a natural coefficient of variation = 1 -> signal to noise ratio defined as mean/stdev = 1 as well. The same can be said for Student t distro with parameter v = 4. So 1 is our main threshold.

We can add additional thresholds by discovering SNRs of Student t with v = 3 and v = 5 (+- 1 from baseline v = 4). These have lighter & heavier tails each favoring mean reversion or momentum more. I computed the SNR values you see in the code with mpmath python module, with precision 256 decimals, so you can trust it I put it on my momma.

Then I use exponential smoothing with properly defined alphas (one matches cumulative WMA and another minimizes error with WMA in moving window mode) to estimate SNR of abs returns.

…

Lightweight huh?

∞