**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 *i*th 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 *i*th trade (*C_i*)

*K* is the number of transactions in the *i*th 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 (Δ*t*) 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 *i*th trade (*R_i*): this is the mathematical expectation / probability weighted average of all possible returns possible from the *i*th trade.

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

iii) The Cost of the *i*th 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 *i*th trade

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

1) They maximise *N*, the number of trades or minimise Δ*t*, 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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