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This is full of gems ; and a great compendium I wish I had 10 years ago.

However, honest advise: if you actually really want to trade in this way, start with a solid course in mathematical finance. It’ll teach you how to model the space, think about arbitrage, portfolios, risk, factors and the sheer important of theory and hypothesis in real strategy.

Building a backtester is exceptionally hard to do if you include scenario analysis, slippage, event risk, lag, multi hypothesis testing, data snooping, etc. Testing is a huge source of competitive advantage.

In summary, if you’re starting out, go learn the basics like the back of your hand, and he basics are mathematical finance.

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I work in HFT, and I'll be contrary and suggest that if you want the most value from your time, focus on learning as much maths and probability as possible. Once you have a strong maths background, learning most financial maths is relatively easy. Any of the financial models you find in textbooks are probably useless because if they work, everybody else who's read the textbook has also used them so there's unlikely to be any edge left, hence it's the ideas underneath them that matter, and understanding and extending these is much easier with a strong maths background. The key skill is developing and assessing new models, and the better one's maths, the easier this is (imagine if a market behaved like a complex aerodynamic system; only somebody with enough mathematical background to model a complex aerodynamic system would be able to create a very accurate model of that market).

One of the most successful hedge funds, Renaissance Technologies, also takes this approach. Regarding its employees: "a third have PhDs, not in finance, but in fields like physics, mathematics and statistics. Renaissance has been called “the best physics and mathematics department in the world” and, according to Weatherall, “avoids hiring anyone with even the slightest whiff of Wall Street bona fides." (https://en.wikipedia.org/wiki/Renaissance_Technologies). Similarly some of the best HFT hires I've been have been people with a maths or science background.

A quote sourced to Renaissance Technologies from https://www.quora.com/What-is-the-secret-behind-Renaissance-...: "We have some Tier One mathematicians and a lot of Tier Two mathematicians. Other quants funds have mostly Tier Three mathematicians, and worse, they don’t even know that these tiers exist! Someone has to create the correlations in the markets." Aim to be one of those Tier one mathematicians!

How would you even become a 'Tier One' mathematician? What does that entail?

I suppose work hard on learning, deeply understanding and practicing as much math as possible, and trying to make novel discoveries / models. I'm certainly not a Tier One mathematician, so I'm probably not the best person to ask. Maybe it requires people to be born with some innate ability, although I'd certainly like to hope it doesn't. Regardless of whether it's actually achievable or not, however, it's definitely a worthy goal to strive towards if you want to be a good quant/trader (and a very intellectually stimulating one).

A nice post on the topic by someone who most certainly is a Tier One mathematician: https://terrytao.wordpress.com/career-advice/does-one-have-t....

Remember reading an article by an ex rentech guy who says that linear regression is about as complex as the modelling gets; that the edge is not in making things hard.

Deep neural nets approximate polynomial regression. That's probably the limit now.

The finance industry loves deep neural networks because it provides them a way to extract money from all of the naive tech engineers who took a deep learning class on Coursera and thought they could apply neural networks to trading. The general consensus is that deep learning for general trading purposes is complete bullshit because it unavoidably overfits.

There are some quality uses for NN, but price or volatility prediction is not one of them.

I'd be surprised if that's the case, as surely somebody else would have replicated it by now. https://www.quora.com/What-are-the-investment-strategies-of-... describes something that sounds much more complex than what could be achieved by linear regression alone.

Tbh I imagine their edge is more likely to be better data and a secret theory.

Then the applied part of it is simple but different: different analysis, different theory, different data, extraordinary results.

Edit: just read your article ... kind of poo poos my theory if what he says is true ; at least at the level of the mega model.

It doesnt refute your theory, it's just that your theory applies very specifically to HFT. Alpha generation in HFT is incredibly simple, and HFT analysis typically relies on very basic math: linear regression and recursive filters. HFT relies on execution far more than modeling to generate returns.

But HFT is inherently low capacity. You can't put a billion dollars on an order book and expect to make the same returns as you would with a thousand. That's the reason HFT firms are almost always proprietary trading firms...they don't need or want more capital.

A hedge fund, like Rentech, is typically on much higher timeframes because their size necessitates higher capacity strategies. This could mean holding periods of minutes for the million dollar funds to days for the billion dollar funds. As you get to higher and higher timeframes, your mathematics are going to need to be dramatically more sophisticated in order to beat the market. The math you are looking at in that quora link is about pairs trading which is where pairs of instruments mean revert over time. I would expect Rentech to be doing this type of trading over long timeframes and holding a trade for days to weeks.

I don't think you will find a generally-accepted definition of "Tier One." For this context, I would say you need to be capable of creating mathematical techniques that are significantly more powerful than what is considered state-of-the-art. That entails a high level of talent and a great deal of education in the mathematics associated with the particular problem you are solving.

I think at least caveating your advise with “learn as much applied maths as possible” may be an improvement .

From there, “learn as much relevant applied maths as possible” would be more time efficient.

And from there, “learn financial maths first” proceeds as an obvious corollary.

So I kinda feel we agree :)

I suppose it comes down to how the "financial maths" is taught. If it thoroughly covers the foundations, giving somebody the tools they need to build new models upon them, I agree. But if it's like "engineering maths", just teaching formulas and models without building a deep understanding of the foundations, then to me that's counterproductive, giving people tools they can't really use but not the ability to build better tools. Maybe I'm just biased however from seeing the results of assigning moderately maths-heavy problems to potentially unrepresentative samples of interns with finance degrees.

Do you have a recommendation for a good probability course/textbook for that matter?

https://www.amazon.com/Probability-Theory-Science-T-Jaynes/d... is pretty decent.

Thanks!

I've always wondered what an algorithmic trader actually does. Does an algorithmic trader get to write algorithms like the job title suggests?

I'd say it depends on the firm. They could write and even implement algorithms, but they might also just spend most of their time monitoring and fine-tuning existing algorithms.

That sounds interesting. Its exactly the kind problem solving I enjoy. You also gave some good advice on what prerequsites are needed to work as a HFT trader. Is HFT the same as algorithmic trading? If not what are the differences?

Algorithmic trading can just mean trying to place orders with minimal slippage, e.g. if you were a bank that only places one order per day, that's definitely not HFT, but you might still want to get the best price for that order, which you won't if you just place it all in one go.

> I work in HFT, and I'll be contrary and suggest that if you want the most value from your time, focus on learning as much maths and probability as possible.

Why not go even further and just not bother with algotrading, dumping money into index funds like VTI instead? It certainly gives a lot more value for your time.

I'm not sure what you mean here by algotrading, but HFT at least can achieve much better returns than index funds, like 2-5x more at least.

I was just going by the post title; thanks for the correction. Also, I was mostly responding to the value/time efficiency part of your comment. By putting in nearly zero effort, you would get the gains of the total market.

While we're here, though, I'm genuinely curious: how accessible is HFT to the average retail investor, let alone those who aren't investing at all? Lastly, can HFT consistently beat a total stock market index like SPTMI year-over-year?

HFT is not accessible to an average retail investor or even one who is far above average. It requires extensive technological expertise, expensive equipment, and a professional infrastructure. Yes, good automated trading systems can consistently beat any index. With that said, there are bad systems that actually look good for a long period of time until an unusual situation occurs and wipes out all past profits or even brings down an entire firm. Risk management is a key component.

Has there been any serious push to get HFT accessible to the average retail investor in the same way that Vanguard did with the S&P 500?

As for beating indexes, it goes back to the age-old question of being able to identify the great automated trading systems.

Not that I am aware of. HFT firms generally don't need outside capital, so they have no motivation to deal with the headaches of running a fund. Funds exist for capital-intensive strategies where receiving fees provides a higher risk-adjusted return than the actual strategy.

I figured HFT firms exist in their own bubble away from most people. So from the perspective of the average joe, they only indirectly exist as a tiny market force that does price discovery.

As for the funds you mentioned, are there any that have a minimum investment of less than $1,000?

The impact of HFT firms is significant, although not obvious to the average person.

Investing directly in a hedge fund requires a much higher initial investment as well as a high net worth. I would not recommend it. It is very difficult to select a portfolio of hedge funds that can outperform a simple low-cost index fund tracking the S&P 500.

Or a more tongue-in-cheek answer: if you're starting out, just pour money into ITOT, SCHB, or VTI and call it a day =P

In all seriousness, though, it's crazy that we're at a point where these hyperactive algorithms can perform price discovery fairly decently.

Do you have recommendations on good Mathematical Finance books? I have a background on maths and engineering. Thank you.

As a textbook, I suggest Investment Science by Leunberger. It's concise and has great coverage, and you can just keep referencing it over time.

As an initial focus, I suggest understanding discrete time models well. If you've got some LA and calculus then I'd suggest just hoping into Introduction to Mathematical Finance by Pliska. It's concise, zero filler, but really clear.

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