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Suppose by some magic, I know all stock price of several stocks (Apple, Netflix, Boeing ... for instance) from tomorrow until the end of next year.

So basically I have a list of vectors X1, X2, X3, ... with X1 is the daily closing price of Apple every day from tomorrow, X2 is the daily price of Netflix etc.

Suppose that I can sell and buy stock with no fee.

Suppose that I have now 1 million dollars.

How can I maximize my total amount of money in the last day, i.e. what stocks I should buy and shell at what day to maximize my cash in the end?

I have no knowledge in finance. I was reading some blogs about porfolio optimization such as https://towardsdatascience.com/efficient-frontier-optimize-portfolio-with-scipy-57456428323e but they mention Modern Portfolio Theory that calculate the optimized return given the risk, but in my case I don't think there is any risk because all the prices are provided beforehand?

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  • $\begingroup$ buy as much as possible on each local minimum and sell as much as possible on each local maximum $\endgroup$
    – shimao
    Commented Jun 21, 2019 at 4:56
  • $\begingroup$ It might work for a univariate setting, but in multivariate settings how should I allocate to different stocks? $\endgroup$
    – mommomonthewind
    Commented Jun 21, 2019 at 6:02

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You are looking to maximize your return. Assuming you don't have the option to short, you can allocate money to the stocks you have information on or keep it as cash(that is not buy anything).

At the start of each trading time-period, you choose the stock with the highest return in the next time-period, and if that's positive, invest all your money into that stock. Else, you keep your money as cash.

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  • $\begingroup$ It is not guaranteed for the maximum return, right? For instance if we look to a period of 3 days we might miss the chance that the price changes dramatically in day 4 $\endgroup$
    – mommomonthewind
    Commented Jun 21, 2019 at 7:28
  • $\begingroup$ I take your point. The response to this is twofold: 1. The trading time-period in practice is instantaneous. 2. And if you had the restriction to trade every 3 days, then we can't use the fact that a stock's return can be increased by holding it for only a part of the period. $\endgroup$
    – StatsML
    Commented Jun 21, 2019 at 16:29

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