Investing Incrementally

Trying not to retire after one solitary trade is a virtuous endeavor...

If you are lucky enough to achieve your retirement goal after just one investment, you might want to take that money and run. Certainly, that's the vibe I got after reading Fooled by Randomness by Nassim Nicholas Taleb. Now that cautious approach to trading and investing is being reinforced as I read Paul Wilmott.

Today is day one of reading the much-accoladed second edition of Paul Wilmott's FAQ. This article is about the vibe I'm picking up as I poke around his "refresher in the fundamentals" of quantitative finance.

Manage risk…
Without putting capital at risk in the expectation of a profitable return you aren't investing or trading. If the return was certain, then you'd be doing something other than investing or trading. While you can't control the outcome, you can be patient and control the capital at risk. Focus on that. Focus on fundamentals.

Quantitative finance is largely over my head. At least I thought so because looking at the Black-Scholes model did nothing for dopamine levels. Even after months of trading derivatives, before today I'd rather regurgitate than sniff or poke around the theory that powers options pricing, etc. However, that's slowly starting to change thanks to very straight-shooting Wilmott and the eloquent Taleb.

I thought Taleb was a Neanderthal after reading some of his tweets. His profane response to antagonists in the cryptocurrency community always had me wondering if he was the same author of the much-hyped Black Swan.

That initial impression is evolving. The book was outstanding. It led me to Wilmott and developing an appetite.

Nibbling Around

"Trade small and trade often" - Paul Wilmott, page 322 of Frequently Asked Questions in Quantitative Finance, Second Edition

This hackneyed expression may have been lifted by Wilmott. I am not sure the attribution is correct. Long before I heard of Wilmott, Tastytrade and OptionAlpha Youtube videos taught me the virtues of nibbling small and often.

Anyway, I'm starting to enjoy nibbling on the theory. Taleb and Wilmott have whetted my appetite for quantitative finance theory because it has become more apparent that understanding the math matters if you are frequently trading derivatives.

While quantitative finance might be an acquired taste even if you are a math nerd, being a math genius doesn't translate into being a successful trader.


Emotions come into play when there's gain, honor, and praise at stake. Unfortunately for traders, the cognitive brain rolls on emotional rails. If the emotional infrastructure isn't steady, the mind will struggle to trade rationally.

In the Aṅguttara Nikāya, the Buddha warns even the most talented monks to shrink away from gain, honor, and praise. If highly disciplined monks could be undone by the allure of huge gains more capricious personalities have no chance.

That's a boon for [less mathematically inclined but more practical] traders disposed to emotional restraint. It's also the reason I've taken out the all recommended texts for a master's degree in quantitative finance from the library. Since the math isn't more important than the execution, it makes sense to not only master the execution but also try to grapple the math. The reverse seems less logical now.

Since practice trumps theory, it doesn't make sense to master quantitative mathematics and casually understand discipline.

Disciplined Trading

Trade execution requires discipline. Discipline means behaving a certain way and not deviating from it. It makes sense to emphasize removing the randomness in risk since it is less trivial to remove the randomness in reward.

How is discipline implemented practically?

Trading small.


Expected values.

The future state of the world (for example, the price of AAPL stock tomorrow) is uncertain. It is just became a three trillion dollar company. The stock price is trending upward. It's at all-time highs. The stock's price might move within a range based on recent historical price movement, but also might not.

You'll lose less risking a smaller amount in the face of that uncertainty.

Frequently Virtuous

Of course, risking smaller amounts and risking more often means making comparatively less than you could have made if you threw the kitchen sink at one successful trade like George Soros famously did.

Higher frequency trading puts the focus more on the process (knowledge, behavior and mindset) and less on the outcome.

Patience is a virtue and incremental investing is for the virtuous investor. It isn't for the impatient. Trading frequently and risking little won't make you suddenly rich. However, it certainly makes you virtuous. Diligent execution (disciplined trading) over many years is an exhibition of skillful practice.

There's more skill and less luck involved in incrementally growing a portfolio over decades.

Mastering Fundamentals

To optimize the results of risking small and risking often, the trader should possess a more rigorous understanding of the tools of the trade. That means quantitative finance theory must matter more to the incremental investor.

Consequently, I'm already looking forward to deepening my fundamental understanding of quantitative finance and day two with Wilmott tomorrow. After only a couple of hours with him today, I was able to more penetratively understand convexity, and supply and demand in options pricing.

However, those were the "dessert" understandings. The main course was figuring out that the fundamentals are within reach. Risk management and robust (not complex) mathematics are the most important aspects of this "soft" science.

Taking smaller is fundamental risk management to Wilmott. Personally, smaller risk takes the emotion out of trading. Fortunately, derivatives trades can be engineered to deliver asymmetric payoffs as reality unfolds the way you've speculated it would.

Risking smaller amounts on long calls and long puts doesn't limit the upside potential of the risk that you take. It only means making less than you could have made had you risked larger amounts.

There's no way to know that before taking the risk, so be incremental. Be patient.