Consider an investment that pays off $800 or $1,400 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happend to the expected value and standard deviation of the investment if you borrowred and additional $1,000 and invested a total of $2,000? What if borrowed $2,000 to invest a total of $3,000?
Investments made in risky assets with borrowed money is generally not a wise thing for most people to do. But if you are employed in a company that runs a hedge fund, a mutual fund or even in a company not involved in financial products there are many instances when borrowed funds are used. And this can be beneficial if done in a proper manner.
In your question you say that $1000 invested can become $800 or $1,400 with an equal probability. The expected value of an investment of $1000 is equal to $1100. The standard deviation is 424.26. For $2000, the expected value is $2200, with a standard deviation of 848.52. As the amount borrowed and invested increases, the expected return and standard deviation for every $1000 remains the same but the total loss increases. For example, if you invested $1000, the maximum you could lose is $200, for $2000 it increases to $400 and for $3000 it is even higher at $600. Whether you should make this investment with borrowed money depends on your risk appetite and what you think is the appropriate increase in potential profits to justify the extra risk that is being taken.
I can only echo the warnings other editors have made above. It is incredibly risky to borrow in order to fund an investment, because in a sense you are risking two lots of money instead of just one. There are no guarantees that your investment will bring you the returns that you are looking for, and if this is the case, you may find that you default on the loan that you made to borrow money for the investment in the first place.
I agree with the previous answer. Borrowing in order to invest does not seem a very wise idea, especially because the returns on very few investments are guaranteed. Perhaps there is a sense, however, in which taking out a mortgage involves borrowing with the expectation that the value of one's investment will increase, so, maybe such borrowing is more common than I would have thought when I first read your question.
This is not a good idea. First of all, just because an investment is expected to pay off does not mean that it will. You could lose everything, and end up owing more than you invested in the first place.