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The Fundamental Equation of Trading

Updated: May 9

Welcome


Hello and welcome to our eighth article. This issue introduces a simple equation for trading which will later serve to help explain trading styles and performance metrics. All articles are saved at our Medium page.


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These articles are based on my experience from consulting and product development at The IQT. Do let us know if there are topics you would like us to cover, questions you would like to resolve, or if there are insights you would like to share from your own experience.


Last Time


In Article 7 — “Types of Single-Asset Strategy”, we discussed the main types of trading strategy possible when trading a single asset.


Overview


Our view is that the Fundamental Equation of Trading is:



The equation hinges on the expected Rate of Profit (𝜋):


E(.) denotes expected value.


This in turn depends on:

i) The Expected Change in Total Profit (Π):


N is the number of trades

ii) The Expected Return on the ith trade (R_i):



M is the number of states / possible outcomes and p_i_j are the probabilities of those outcomes


iii) The Cost of the ith trade (C_i)



K is the number of transactions in the ith trade trade


Main Points


· Different practitioners may have alternative views on what the Fundamental Equation of Trading is, or if such a term even exists. We specify a simple equation which describes a trader’s expected rate of profit, for 2 purposes which can be explained further in future articles:


i) We can use the formula to illustrate what profile of trading strategy is likely to be effective for a trader with a given personality type


ii) We can use the terms to explain some of the metrics used when assessing a strategy’s performance


· Fundamental Equation of Trading:

The Expected Rate of Profit (𝜋) is equal to the expected change in profits (ΔΠ) during a time interval (Δt) divided by the length of that interval. In symbols,


E(.) is the expectation operator


This depends on:

i) The Expected change in Total Profit (Π): this is the sum of expected returns (R_i) over all trades minus the sum of costs (C_i) over all trades.



N is the number of trades. Note that we use LaTex terminology if symbols do not render correctly in our articles, e.g. “R_i” refers to R with subscript i.


ii) The Expected Return on the ith trade (R_i): this is the mathematical expectation / probability weighted average of all possible returns possible from the ith trade.



M is the number of possible outcomes, p_i_j is the probability of the jth outcome occurring, R_i_j is the return of trade i in state j


iii) The Cost of the ith trade (C_i): the total cost of a trade is the sum of all the transaction costs incurred during the trade, e.g. a commission may be charged each time we buy or sell.



K is the number of transactions in the ith trade


· Insights: to maximise profit, traders should aim to select strategies so that:


1) They maximise N, the number of trades or minimise Δt, to maximise trading frequency. A strategy which is highly profitable once a year is less valuable than one which generates more trades and thereby a higher rate of profit per unit of time.


2) They maximise the expected returns of a trading strategy. This implies not only selecting strategies with high upside returns (i.e. high R_i in favourable states of the world) but also those with high probabilities (p_i_j) of favourable outcomes.


3) They minimise transaction costs if possible, especially via K, the number of transactions per trade.



Further Reading


We will discuss how “The Fundamental Equation of Trading” may relate to “Trader Personality Types” and how that may inform your trading in the next article.


Thanks and happy trading!

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