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I recently started learning about finance and we talked about Markowitz Portfolio Theory. I understand that a portfolio consists of different assets, each of them with a certain weight. So, for example, I could have a portfolio with 50% Exxon Mobil and 50% IBM.

However, we then mentioned that if we are allowed to short IBM, for example, we could end up with a portfolio of "weights" 120% Exxon Mobil and -20% IBM. Then, the expected return calculation would yield 1.2 * (Expected return of Exxon) - 0.2 * (Expected return of IBM).

I am a little confused how this calculation makes sense. How could I have more than 1.0 for a weight of a portfolio. My professor mentioned something about using the short to "lever up" investment in Exxon, but I'm not quite sure how to make senes of that.

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The total is still 100% - the 20% short offsets the "extra" 20% long you are.

In your example, it means that you start with 100% Exxon stock, short 20% of that value in IBM stock (which nets you cash but you owe someone stock), and use the proceeds to buy another 20% of Exxon stock.

Here's what your professor means by "leveraging" (we'll skip efficient frontier and other portfolio theories). Suppose you really think that Exxon stock will go up but only have $10,000 to invest. You can borrow $10,000 ("short" cash) and buy $20,000 in Exxon stock. You have "200%" in Exxon stock and -100% in cash. If Exxon goes up 10% to $22,000, your gain is $2,000 which is a 20% return on your $10,000 investment. Your return has been multiplied by a factor of 2. Leverage works both ways, though - if the stock goes down 10%, you'll lose 20%, so you can lose all of your investment if the stock goes down just 50% (the other 50% will need to be sold to pay back the loan).

  • Oh that makes sense. I always thought that the broker would hold onto the money you get from the short as collateral so you wouldn't be able to use it to long Exxon - is that true? – Vasting Jun 20 at 20:38
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    @Vasting that would be the case if you don't have a margin account - but if you do have a margin account, depending on the margin value, you can use those funds to buy other assets. – Chait Jun 20 at 20:41
  • @Vasting To explain Chaithanya's comment further, if you have a margin account, you can use money in that account to buy stocks, and those stocks will then be in your margin account. You then have to keep them in the margin account so that they can be collateral for your other trades. – Acccumulation Jun 20 at 21:03
  • The mathematical version of this answer is 120% + -20% = 100%. – RonJohn Jun 20 at 21:21
  • @Chaithanya - You can't short without a margin account so it's all moot and there's no holding of the money by the broker. – Bob Baerker Jun 20 at 22:04

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