# Is it possible to calculate weights of a portfolio with negative values?

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). - ## 2 Answers 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. - Thank you so much for taking the time to help, Ross. I'm still a bit confused. I thought about the way you normalized the number(in fact I tried that before by using absolute numbers) but isn't the problem that the value of the portfolio is now$4500 using those numbers? Also doing a (.50 * 50)/39 + (.85 * 20)/39 + (.10 * 30)/39 equals 115%. I might be missing something, sorry. – Error_404 Mar 20 '12 at 5:06
@learningJava: yes, the assets are worth 4500 this way. The point is that reductions of the negative one are worth as much as improvements in the positive ones. But if the negative one improves \$100 it is as good as a positive one improving by the same \$100. And you are right, the denominator should be 45 as 25+17+3=45. Fixed. – Ross Millikan Mar 20 '12 at 5:11
Thank you for explaining it more clear. I do see your logic, but I'm not sure if it fits my problem. You see, I know the value is $3900 and although setting it to$4500 seems to solve my problem, I'm not sure if it reflects the correct valuation. I think its the interday performance evolution of a fund, so overall it can never be negative but if you look at one days performance, then negative values happen. I get your logic but if your bank account says your portfolio is worth $3900, I'm not sure if its accurate to change that. – Error_404 Mar 20 '12 at 5:26 okay, I think I need to think about this logic more..but I think I took my eye off the prize and lost track of what your were saying. The more I think about it, am I correct in your not saying to value the portfolio at$4500, but use it to figure the weights? So in the overall portfolio I own 6.67% of C? Basically if I want to recreate the above portfolio($3900) without any negative weights would it look like this: a= 55.5%, b= 37.7% and c= 6.67%? Is that correct? – Error_404 Mar 20 '12 at 6:00 Yes, that is what I was getting at. It gives you a flavor of how much each will contribute if it improves by 10% of its value. For the negative one, an improvement is a reduction in the absolute value, but it still indicates how important it is. – Ross Millikan Mar 20 '12 at 12:47 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.

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