## Robust optimization for profit/risk/day

Discussions about the testing and simulation of mechanical trading systems using historical data and other methods. Trading Blox Customers should post Trading Blox specific questions in the Customer Support forum.
explorer
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### Robust optimization for profit/risk/day

Hi,

I am aware of this post (see below), but that was written before c.f. created more robust measurement methods.

viewtopic.php?t=17&postdays=0&postorder ... on&start=0

If I would like to find a more robust measurement to optimize for profit/risk/day, would you recommend to use the score of rCubed * #trades (instead of ExpectationRatio * #trades) as a Measure of Goodness and optimize for it to find the mathematically optimum strategy?

By the way:
What is Expectation? What is Risk/Reward Ratio? Are the two the same? If not, what is the difference i.e., what are the formulas behind the â€œexpectationRatioâ€
sluggo
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The Trading Blox calculated result named "Expectation" is discussed here: viewtopic.php?p=24064&highlight=expectation#24064

More generally, expectation is a term used in math books about probability. The expectation of a probability event X is the sum over all possible outcomes X, of (the probability of outcome X occurring) times (the result value of outcome X).

If you and I play a card game where I pay you 6X your bet if you draw a diamond, and you pay me 1X your bet if you draw a non-diamond, then the expectation of this probability event (this game) is

(prob(diamond) * +6.0) + (prob(non-diamond) * -1.0)

= (0.25 * +6) + (0.75 * -1)

= +1.5 + -0.75

It is a "positive expectation" game for you (and a negative expectation game for me). If we were to play this game many times, and if you were to employ excellent betsizing, you would win a lot of money from me.

Math books quickly generalize this to the continuous case where there are an infinite number of possible outcomes, thus discrete sums are replaced by continuous integrals, and you are now in the land of calculus. It's a university course that lasts twelve or fifteen weeks and marches through a 200 page textbook.

(Incidentally, it is reputed that "card counting at 8-deck Blackjack in Las Vegas casinos" has a positive expectation of approximately +0.009. For each \$100 you bet over the very long term, you can expect to make \$0.90 in net profits. Over the very long term. But the variance is extremely high AND you have to avoid getting thrown out of the casino.)

The gambling probability book that Cutris Faith noticed on William Eckhardt's shelf, is (this one). It's very comprehensive, but it does assume you've made it through a university course in probability and now wish to apply that pure mathematics, to specific practical situations called Gambling.
explorer
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Location: Bay Area, CA
Thanks Sluggo,

Based on your explanation if I understand:

Expectation Ratio = expected profit per dollar risked = avg trade outcome / avg trade risk = (avg win â€“ avg loss) / avg loss = ((Probability of Win * Avg. Win Size) - (Probability of Loss * Avg. Loss Size)) / (Probability of Loss * Avg. Loss Size)

Here is when things get fuzzy:

So in effect the Expectation Ratio is a Risk/Reward ratio (for each 1 unit risk we expect to make x unit profit, if all goes per plan)

In c.f. book, when he improves the robustness of the Risk/Reward ratio, he develops the R-Cubes as his most robust Risk/Reward ratio.

Risk/Reward ratio = profit per dollar risked = R-Cubes

Is the only difference that one is â€œexpectedâ€
sluggo
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Joined: Fri Jun 11, 2004 2:50 pm
c.f. created the R-Cubed measure of goodness; I think if you find his book's explanation of R-Cubed (p.188) confusing or unclear, he is the one to ask for further amplification. I also think he may be the one to ask whether or not R-Cubed is supposed to be numerically equal to the Expectation number printed by Blox.

(A thought: If R3 is supposed to be equal to Expectation, why did he bother to invent a new way to calculate the same number?)
explorer
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Joined: Thu Jun 07, 2007 8:45 pm
Location: Bay Area, CA
Thanks Sluggo,

I don't feel that bad now that even your brilliant mind couldn't clarify it.

I have c.f.' book, and I reasonably understand how he calculated it. (Reasonable means, I have yet to recreate the calculation in Excel.)

Since it supposed to be a risk / reward calculation, and although it is done differently then the Expectation ratio, I expected the two ratios to be somewhat close. But 22c profit per \$1 risked or \$1.69 per \$1 risked in the same system are very different numbers from each other.

So the mystery for me I guess will remain until c.f. himself straighten this out, that I would very welcome.

Thanks for your help, and let hope that I will be lucky and c.f. has the time to clarify it.

Thanks,