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7846599 No.7846599 [Reply] [Original]

I have math/statics problem I hope someone can give me some pointers on.

Let's assume the following (extreme) scenario:
I invest with 90% probability that I win 150% of my investment, and 10% that I will loose 50%.

I also have the option to leverage my holdings. Meaning that I can, for example borrow 10x my initial holdings. But when my investment drops 10% I will loose everything.

Now given those parameters, how do I go about computing an optimal leverage size?

>> No.7846622

Oh and I should mention that I can make this investment multiple times.

The 'obvious' answer might be to do a maximum leverage. But the problem is that as the number of trials goes to infinity, the chance of getting liquidated also goes to 100%. Or no?

>> No.7846653

>>7846599
On average, you lose 5%, so optimal leverage size would be 20x I suppose?

Btw don't trade on margin please, that shit is very dangerous. At least keep it small, maybe 2x. Don't want you to get fucked anon.

>> No.7846669

>>7846599
>I invest with 90% probability that I win 150% of my investment, and 10% that I will lose 50%.
that's not possible anon, because you would be literally printing money, just by putting let's say 10% of your holdings each time to minimize the risk

>> No.7846672

Optimal leverage is 2x here since you can still lose your 50% but not get liquidated and still double your already doubled money

>> No.7846704

>>7846653

Ah that seems like a solid solution, I'll do some simulations to see how it works out, thanks.

>Don't want you to get fucked anon.

Yeah I know, I just do it for shits and giggles with a small part of my stash.

>> No.7846743

>>7846622
It depends on your personal risk/reward profile.

To maximize your *expected* return over N trials, go ahead and leverage.
But if you can just keep doing this over and over again and don't want to lose everything, just don't leverage. Or leverage a small amount.

The other fact is that once your gains become huge, you won't be able to make the same bets. Finding an investment for $1000 with 90% chance of 150% increase is not the same as betting $1M with 90% of 150% increase. So if you can make multiple bets, then not leveraging looks really good, since you're much more likely to grow to your limit.

>> No.7846772

>>7846669

Like I said, they are extreme figures. It just makes the math easier to understand for me personally.

>>7846672
Let's say I have 100 dollars. I leverage 2x, I have 200 dollars. I loose, thus I loose 50% of 200 dollars, so now I have lost 100 dollars. Which means I get liquidated.