One of the most important lessons about optimization in quant finance is that you need to make sure you are optimizing for a close to optimal but also robust solution. A good example is with portfolio optimization where MVO can underperform OOS from you not taking into...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
account the error of the expected return or the error in volatility. Volatility is usually more robust, and correlations can be considered the most robust of all, but this is super important to consider. The same rule applies to pairs trading...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
pairs trading is just an optimization problem. Whether you are brute force checking combinations of symbols and testing for ADF (or whatever chosen metric) or even going up to many assets with VAR (box-tiao) optimizations etc it is still an optimization problem...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
the issue is that often these portfolios are not robust. I don't trade this model anymore since it has low capacity, but adding a validation period improves performance massively. Train maybe 30 pairs portfolios (but also PCA them all together then use correlation...
Don
Stat Arb
@quant_arb
as a way to reduce correlation, you can use average correlation, but PCA is far more robust). Then with your 30 portfolios you can use a robustness measure, normally I would use a mean-reversion ensemble for the first training round (portmanteau, box-tiao, proprietary ones...
9:18 PM · Dec 2, 2022
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Don

Stat Arb
@quant_arb
·
Dec 2, 2022
Replying to
@quant_arb
like Hurst which you can derive convex relaxations for) and then stationarity tests for the validation part (ADF, KPSS etc). Finally I just slap some Bollinger bands on it with a reverse exponentially weighted moving average (so large shocks/deviations didn't immediately...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
move the spread leading to something I called "lag error"). Lag error comes from 3 things:
1. wrong period of mean reversion (in the photo below we see an example of failing to specify a specific period for mean reversion and just optimizing for general unpredictability...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
if you trade the longer timeframe of mean-reversion you get loads of noise in your curve from the lower timeframe white noise, and if you try to capture the lower timeframe you get lag error from drift. Drift is what create lag error. You can remove lag error using a smart...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
model that accounts for trends/ different timeframes. I won't explain how I used to solve this problem since I'm pretty sure it still performs in equities if you have half decent fees (feel free to figure it out, I'm all crypto now)...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
The second reason was just a long-term drift stated above. 3rd reason is that deviations from the mean also move the mean. How do you determine when the long term mean has shifted. Bollinger bands are usually better than the standard method of taking the mean if you optimize...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
for mean-reversion. If you optimize for stability (which is what most people do, hence less alpha) then Bollinger bands are less appropriate. Fun to share a bit of alpha from research I did a while back. I'm pretty sure there is still like 20-30%+ returns from these...
Don
Stat Arb
@quant_arb
·
Dec 2, 2022
strategies on daily (maybe even 4h, not sure) rebalance, and likely much higher for intraday. Need good execution tech since you have so many legs frictions become important. 4-6 asset portfolios aren't practical in crypto and bivariate only has n^2 solutions...
Don