# Maximal Strategy questions

- Posted in: Trading strategies

Hi Steve,

Firstly thanks very much for your very thought provoking article.

I’d always thought I might be placing my stops too close but how close is too close? How far is too far? I think your article gives a possible answer. I like to understand the maths behind the reasoning before putting it into practice hence the questions.

Anyway here’s what I think is happening, let me know if I’m off track, which will probably be soon…

1) Compute the volatility, sigma (pips). This is the std dev of the difference between high and low for each bar (eg. M5), for a time period eg. 24Hrs. The period length is somewhat arbitrary…

2) If we assume no drift for the distribution of the random walk, mu (mean) = 0

3) Std dev, of the random walk at time t (num bars), = sigma * sqrt(t)

3) At time t, convert price to a Z score, where n=num pips gained, z=n/(sigma * sqrt(t)).

eg. Probability of price>+40pips, at time t, P[Z>+40pips] = 40 / (sigma * sqrt(t))

While P[Z>0] = 0.5 and P[Z>(some negative value)] > 0.5, I guess my question is how P[Z>(some positve value)] could be 82%, eg. P(TP)=82%, or is that not what that actually signifies/implies?

I realise that the above does not take into account the possibility of the num of pips gained/lost prior to time t, which could hit TP or SL, but simply P[Z>n], only at time t. But I thought that you dealt with that later ( P(SL only hit), P(TP only hit), etc.) and not at this point. If so, or not so, how do you derive P(TP) for your maximal curves?

Thanks!

Yes I agree it’s better to understand the background, using these methods without that is very risky.

If you are interested I recommend taking a look at some of the papers at Duke (e.g. this one) – they have a lot of resources there on this subject.

Hi Steve,

This are the probabilities I get for random walk with no trend, for various hours and 40pips TP. But I got this by using ~15bp 5minute volatility, the article says the 5min vol is ~10bp. I was wondering if you could confirm the exact volatility you used for the curves?

hr P(S>TP)

1 0.2898402

2 0.4541886

4 0.5966454

6 0.6656599

12 0.7599524

18 0.8029973

24 0.8289543

Thanks

Your numbers do look reasonable. Did you generate these for a whole series of curves or just this one TP value? If you can upload an excel chart here please with all curves that would help.

As for the example in the article, I would need to dig into the spreadsheets and figure out exactly the vol that was used to produce those curves. But you can also use our spreadsheet to match and compare your figures.

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