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Sorry in advance if this question is either too basic or really dumb, but I've been researching this and am a bit confused. I'm trying to help my niece with a question she has and the gist of it is she has the following portfolio:

Name     Shares    Price a        50        50 b        85        20 c        10        -30 Total Value = $3900 

I might be missing something obvious but I tried to take each value and divide it from the total, which gives me:

a 50 * 50 = 0.641% b 85 * 20 = 0.436% c 10 * -30 = -0.077% 

Which equals 100% but is not correct because of the negative weight(I also tried to make the negative number positive but it didn't seem right). I understand the negative value is causing the weight to be negative but somehow I need to account for the 10 shares(I also want to account for it based on the value and not number of shares). How can I use this information and create a weight that doesn't have a negative value?

I don't really need the answer, just the logic(or what kind of math I need to learn to solve this).

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Usually you can abandon an asset that has a negative value, so you can ignore c and just consider a and b. The sense is that the weighting gives you and idea how sensitive your portfolio is to changes in the value of the asset. If you are stuck with c (say it is your house and you won't walk away) you could take the absolute value-in a sense a 5% change in the value of c will be properly reflected that way.

Then you need to normalize. The fractions of the portfolio need to add to 100%, so divide by the sum of the percentages. Then a=25/45, b=17/45, c=3/45.

This is the impact on your portfolio of a change in the value of one asset, but it ignores that the various assets could have much different volatilities. Suppose a is cash, deposited in a bank account, while b is shares in Facebook. The value of your portfolio is much more sensitive to Facebook than cash as the value will change much more.

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    Thanks Ross. I am trying to figure out how to do it while maintaining the same structure. I am starting to suspect it may not be possible to maintain a similar structure and convert it for the same results. I'll play around a bit and think about this and might ask if I have a different question. Thank you so much for your help, and I'll accept your answer(and upvote). Thank you!2012-03-20
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I understand that this answer is late but I just see it. A short answer to your question is yes. Let me explain this. Suppose that you buy today stocks (a) 50*$30, (b) 85*$15 (c) 10*$45. The market value of this portfolio is $3225. Three months later you could have the next values (a) 50*$50, (b) 85*$20 (c) 10*-$30, with a market value of $3900. In the real world negative dollars do not exist, in the accounting and financial world it means losses. Thus, you have from the first portfolio value ($3225) the next weights:46.5%, 39.5%, 14%. From your second portfolio value ($3900), 64.1%, 43,6%, -7.7%. Then your gain/loss in 3 months is: gain of 17.6% from stock a, gain 4.1% from stock b, and losses 21.7%(-7.7-14) from stock c.