Thread by @HangukQuant

1. Quant firm I worked for pitched as "computationally intensive,modern ML methods". Asked around and the “big guy” confirmed “Linear Regression”. Thoughts? Good Sharpe and attractive fees, no harm no foul. Also they weren’t wrong.😂

Thread; Deeper look into Regression Methods

2. Skip to 12 if you don’t want the ”college recap”, a lil something for the more unique. Btw, this is more of the sort of stuff you learn in an STAT101 class rather than ML class. Anyway, LR begins before college, doing y = mx + c. This we call Simple Linear Regression.

3. Ok that is bit too simple for most practical use cases in finance. So extend that to Multiple Linear Regression, we have multiple predictors. Now the mathematics need some college level algebra and calculus, but those should be fairly accessible and I don’t want to bore you.

4. But at this stage many of the concepts that can be extended to more complex methods already surface. Take for instance, we know that our RSS/R^2 increase monotonically with number of predictors, why not keep adding? Overfitting!

5: Now if you fit a 100 predictors and your t-tests show 5 “statistically significant” variables, you would not celebrate, because that is to be expected as per noise. Now, you understand this concept well, but MANY traders do this on backtests and conclude having “alpha”

6. That is just incoherency in thought, or illogical optimism. Don’t throw shit at the wall and pick what sticks. Next, your test MSE is almost always worse than training. In the same way, your live results are likely to be the same. Your backtests are likely a “conservative”.

7. Advantage of LR in general is the interpretability of the model. You have the ability to make statistical inferences about the parameters of your estimations. (CI, PI). However, in most cases, as flexibility increases, interpretability decreases.

8. For that same reason, when you build neural networks and stuff fails, you go “shit”. Ability to diagnose assumptions and accuracy of models in production is one of the primary advantages. “Black-box” sounds cool, but Mr. Market couldn’t care less.

9. It goes without saying that one needs to be aware of concepts such as bias-var tradeoff, error correlations, heteroskedasticity, multicollinearity and how they affect statistical inferences.

10. Now before you snooze off, this is where things get more exciting. Let’s start with adding transformations. Ok lil bit more. Let’s relax additivity with synergistic effects. How about MLE estimation instead of OLS? Weighted-Least Squares? Restricted Least Squares?

11. There are many extensions, and comprehensive literature on Regression. I can go on and on, but a book would do it more justice. Enough being the poster child for Regression.

12. “Ok silly, how is college-level algebra getting me alpha?” Absolutely right, regression is a tool, and alpha is market structure. That’s like saying, this chopsticks are really delicious. If you eat lobster bisque with chopsticks, you won’t know if alpha hit you in the head.

13. So, instead of telling you abstractly that “you need to use it where it counts”, let me just give an example use case. Lil bit of an alpha leak over here. (experience tells me when you tell people there is alpha straight up nobody believes anyway😂)

14. Singapore is a country heavily reliant on import and exports for GDP. As you can imagine, FX stability relative to trading partners is a primary concern, to maintain stable prices for G&S. Their answer to that is S$NEER, Singapore’s monetary policy.

15. The SGD is managed against a basket of currencies of their partners, operating as a managed float regime. That is, the weighted currency acts as somewhat of an “index” that floats within a band. Now we know that curbing FX speculative attacks is important (cue Baht, Pound).

16. To defend against speculative attacks, they are several unknowns, e.g. constituent currencies, weights, band width, crawling gradient, midpoint, adjustments. These are not known, albeit with some guidance from the Monetary Authority of Singapore.

17. Before you start despairing that for the above reasons they cannot be estimated, let me just say, YES you can. A fantastic baseline, using Restricted Least Squares Estimation from UOB.

uobgroup.com/web-resources/…

18. Their paper isn’t written in the context of trading, but one does not require too much creativity using mean-reversionary strats. “Don’t fight The Central Banks” has a lesser known Corollary; if you predict their actions you will be rewarded.

19. This is an example of policy-driven alpha. As @therobotjames would say, understanding incentives and constraints of other players in the market are key to edges. FIN.

https://twitter.com/therobotjames/status/1442443301034938368