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Suppose me and my friend invest in the same stock but he has 10% more than me. I want to have the same amount as him, but I have no money to buy 10% more, so I'm gonna leverage my position to profit more % than him and reach him. My question is: how do I calculate the minimum profit required to achieve it given a specific level of leveraging?

For example, if I have 100 shares at 1 dollar each, my friend has 110 shares. I leverage at 2,1x, so I borrow 110 dollars from the broker and operate at 210. If the stock grows 10%, I'll profit 21 dollars (10% of 210) and my friend will profit 11 (10% of 110). Now I pay the 110 of the broker and take my 21 profit and buy more 10 shares at 1,1. So, for a given leveraging (2,1x) I need 10% of profit to reach my friend. But what if I leverage at 2x, 3x, 1,5x etc?

Eduardo M
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    This is not clear. Are you ascribing some cost to the leverage? If so, how much? If not...well, if you have $2x$ shares and your friend has $1.1x$ then your profit will always exceed his (assuming there is some profit). – lulu Feb 21 '21 at 15:55
  • @lulu, yes. If I have 100 and he has 110, I must profit more than him to neutralize his 10% advantage. Suppose I leverage 2,1x, so if it grows 10%, he's gonna have 121 and I'm gonna have 121 too (I'm operating 2,1x which is 210). – Eduardo M Feb 21 '21 at 16:04
  • I don't understand. Stock prices may climb, but the number of shares you have don't (unless you buy more). – lulu Feb 21 '21 at 16:07
  • The way leverage works: Suppose the stock currently trades at $$1$ a share and you own $100$ shares. You want to buy more, so you use those shares as collateral for a loan. Say your broker will loan you $$50$ against those shares. You could then buy another $50$ shares in which case you would own $150$ shares but would still need to pay interest on that $$50$ loan. Your friend owns $110$ but has no loan to pay off. If you meant something other than this you should edit your post to clarify. – lulu Feb 21 '21 at 16:09
  • @lulu, I'm gonna buy more shares with the profit. With 2,1x leveraging I'm gonna profit 21, and then I will have money to buy those 10% more shares and reach my friend. – Eduardo M Feb 21 '21 at 16:09
  • @lulu, I'm gonna borrow 110 and operate with 210. With 10% of profit it will turn 221. So I pay the 110 of the broker and take my 21. Buy more 21 shares and now I'm 1-1 with my friend. – Eduardo M Feb 21 '21 at 16:13
  • Just edited my question. Hope it is a bit clearer now. – Eduardo M Feb 21 '21 at 16:58

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