I want to invest in a certain stock portfolio using long down-and-out barrier options. But I am not sure in what ratio to buy the barrier options to retain the same exposure to the volatility of the underlying stocks. Suppose that an XYZ stock portfolio contains 20% company X, 30% company Y and 50% company Z. The aim is to retain the diversification effect of the portfolio, yet leverage the investment. In what ratio should I buy the barrier options to preserve the diversification effect of the underlying stock portfolio? The barrier options do not expire unless the stop-loss barrier is hit.

My reasoning is as follows, but I am not sure if this is correct. Let:

p = Option price

S = Stock price

F = Financing level. So that:

p = S - F

As a result, when buying the option you own the following fraction of the underlying stock:

own = p / S

So my sense is that the investment would be as follows:

investment = (weight / own) * p

This means I would end up with the following numbers. I not sure whether this is correct though. Any suggestions?

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  • Your guess is as good as anyone's. There is absolutely no answer to such questions. There are buildings full of PhD analysts who work on this sort of question, and in 100% of cases for 100 years, they consistently, always, every time, without fail - there has never been an exception - lose money like niagra loses water.
    – Fattie
    Jul 9 '20 at 12:10
  • Why is this such a complicated question? I did not realise ... Can you explain the complexity?
    – twhale
    Jul 9 '20 at 14:01

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