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Hello People at Stackexchange :)

First of all: Thank you so much for taking the time to answer my question!

I need to calculate weights of a time series which I planned to do by calculating the average or the arithmetic mean and weighting each return proportionally. As my time series contains negative numbers, however, the "typical" formula is not appropriate: Typical Formula

My problem:

I want to overweight stocks with higher return and underweight stocks with lower return.

Stock 1: 5%
Stock 2: 3%
Stock 3: 1%
Sum: 9%

The weights would then be:

Stock 1: 5 / 9
Stock 2: 3 / 9
Stock 3: 1 / 9

In my data, however, I have negative values:

Stock 1: 0,1 %
Stock 2: -2,5 %
Stock 3: -0,3
Stock 4: 0,4

Applying the same strategy would result in non-sense results.
The highest returns have a negative weight, while negative returns have a postive weight:

Stock 1: 0,1 / -2,3
Stock 2: -2,5 / -2,3
Stock 3: -0,3 / -2,3
Stock 4: 0,4 / -2,3

Some other posts suggested the Root Mean Squared but in my case it did not result in any logical solution. The lowest (negative) returns still have the highest weights and vice versa: Root mean squared

Thank you so much for any help on how to calculate the weighting including negative values!
It is highly appreciated!

Best regards, Anni

Anni
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    You could add an offset value to all of the returns, where the offset is just enough to bring the most negative number up to zero. Then use your typical formula. – Narlin Jun 28 '18 at 16:20
  • Hey Narlin! Thank you so much for your answer! So, you would add an "absolute" number? I was wondering whether this is allowed as the ratio between the stock's return changes.

    Example: Stock 1: -4 %
    Stock 2: -1 % Stock 3: 5 %

    If I add an offset value - let's say 5% to all of them - the ratio changes, doesn't it? The new values: Stock 1: 1 %
    Stock 2: 4 % Stock 3: 10 %

    In the example before adding the 3%, Stock 1 performed 100% worse than Stock 2. After adding the 3%,

     – Anni Jun 28 '18 at 17:33
  • It might be that change in percentages is misleading and that you may want to rethink what what the final result is supposed to explain. Perhaps translating everything to shares and dollars instead of percent could be more enlightening. – Narlin Jun 28 '18 at 22:35

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