How to maximize the "compound-interest-effect" in the stockmarket?

The above of course ignores trading costs.

Thank you for your comment:
But as I wrote: I know the probability (thats why I wrote that it might not be a "real" stockmarket situation)

To clarify:
At the time of buying the stock I do know the probabilty (or at least a very close estimation) to win a certain amount at the time (which is fixed)  of selling.

Why not invest everything in the "best" stock: to spread the risk and use the "compound-interest-effect" which is needed since the winning per buy-sell-cycle are rather small.

Please ignore trading cost!

Annagret

If you know the probability distribution of the "gain" at the time of selling then, you can calculate the expected gain of the stock. Integrate g.P(g) where g is the gain. The expected return is the gain/share price. Now this is the metric by which you calculate the best stock.

Every time you have fresh probability data you recalculate the best stock and move all your money there. That is the optimal strategy to maximize the expected value of your eventual return.

A cautionary note: this is maximizing the expected return, there is no awareness of risk. If you wish to factor in risk then you would have to balance risk against potential return in a more complicated calculation.
I dont know if you are after such detail.

As far as the compound interest, again I don't see how compound interest applies here. I can see that the recalculation of the best stock and rebalancing of your portfolio may seem analogous to compounding interest, but that term is generally reserved for fixed or at least predictable interest compounded at a given period.

Hi,

Thanks again!
The term "compound-interest" might not be perfect, but it gets the idea across I hope.

I'm looking for a hint how you might solve the described problem or  an (part of) algorithm (with the given variables/facts).
I'm NOT looking for general investment advice or something similar!

Best Regards,

Annegret

Look at the attached picture with an additional example:

Image you are at the "now"-point:
You have invested a part of your money in stock 1and you know that stocks 2-5 might be a good investment each.
Eventhough stock 2 might be the best, remember you might lose everything (for example all stocks are derivatives where you can lose everything) ! This is why you need/should spread you investemnt over several stocks
The question is: what is the best allocation (which stocks gets how much money)?

Just splitting the money evenly between Stock 2 and 3 might be bad, because stock 3 pays out earlier so that you can reinvest your money in stock 4 and so on (under the assumption that stock 2 and 3 are equally "good").

Assuming you have the probability of all possible gains for each stock. i.e. P(+$1.00)=p1 P(+$1.50)=p2 etc.
Then for each stock the expected Gain is either the sum or the integral (discrete or continous) of " Gain * P(Gain)".

Now you need to maximise your return/profit. You therefore want to be fully invested in the stock that has the best ratio of (Expected Gain/ Stock price) at the moment. Statistically this strategy will give you the best expected result. That is over an infinite number of trials this is the best strategy.

As an analogy this is looking at the average (expected return) without considering the standard deviation (a measure of risk).