# How math can help discretionary traders

## The Basics

1. Reduce the number of instruments you trade

If you are doing discretionary trading you don’t want to trade on too many different instruments. It needs tremendous focus to concentrate on the flow of each tick. Choose a single instrument which has enough liquidity but is not among the most traded. Dangers of scalping say SPY or QQQQ or USDEUR is that they are traded by far too many traders and thus behavior is erratic.

It comes without saying that in fast paced trading you don’t want to be dynamically changing Position Size. Based on your trading capital, appetite for risks, leverage and instrument’s volatility pre-determine how many ticks you can afford to lose, how many ticks you want to make and how long do you want to hold. These should be written in stone and adhered too.

3. Analyse and Audit

At the end of the day, do an audit of all the trades. See if all the trades were executed as it was planned, all intended Buys were Buys and not vice versa, Position size were what was planned to be. Plot and Graph the entries and exits, see if your mathematical knowledge could be exploited to make sense of what happened in the day.

## The Intermediates

1. Multi-time frame Analysis

When you watch the instrument, use different time frames. From ‘tick-plot’s, 1 sec, 5 sec, 15 sec, 30 sec, 1 min, 5 min and 10 min. Apart from these if your trading setup has multiple screens then it is not a bad idea to have longer time-frame charts, like 1 hr, 4 hr and 1-day and 3-day charts open for the longer term perspective. I must  apprise you of the caveat though, Multiple Time frame analysis will add more questions than answers, will probably make you skeptical of the current flow and direction as different time frames will be in discord among themselves. How you use it is your personal opinion, it all again boils down to two main different styles of trading viz. Trend following vs Mean Reversion. There is no scope here for the discussion on this subject, may be some other time. Interesting discussion on the same is here.

2. The ‘hunch’/’feel’ by logic and math

Even with the risk of being ridiculed I am going to attempt to quantify and standardize what it means to be ‘in-the-zone‘. For those of who are unaware of the trading faux pas which I am going to commit, it is that ‘the-zone’ is considered to be the sacrosanct in the trading world. It is graciously accepted that with enough trading experience you will get there. As they say in redundant tautological statement – “you will get there when you will get there”.

Conjecture : If you can distinguish your instrument from any other instrument with non-negligible accuracy, you are in the zone

For my mathematical friends, it can be written as :

$\exists\imath:\forall\jmath\neq\imath Pr[Q(i)=Q(j)]\leq\frac{1}{\varepsilon}$

where, $Q(.)$ is the function of predicting the given instrument’s time series and $\varepsilon$ is the non-negligible factor (in the order of 10^-5)

So if by enough practice on any given day you can successfully break “The financial Turing test” (see this for general read, and this for the actual paper) then you have gained the ‘hunch‘ or ‘the feel‘.

1. Quantification to achieve ‘the feel’

Here are some of my mathematical tools you should be adept with to get ‘the feel’.

a) Volatility pattern of the instrument.

b) De-trended Chart of the same. (if instrument is Agri-product, remember to remove seasonal cycle influence too)

c) Co-integration of the instrument with its peers, as in similar comatrix representation (read Ganapathy on Pair Trading)

d) Correlation with all the influential instruments.

I find that novice traders read the correlation correctly but assimilate it incorrectly. Correlation doesn’t imply working “Pairs” (for that you need Augumented Dickey Fuller Test) and also correlation doesn’t guarantee cointegration and certainly doesn’t signify causation*. Correlation can (with enough reliability) only be used to determine the list of influential instruments.

*There may be some causation which implies correlation but assume otherwise until you know it to be true.