Percentage Change with negative and positive values

[Giovanni DellErba]

Dear all
I am faced with the following problem on Stata: I have to calculate the daily % change for a variable that can take both negative and positive values. If you want more information, I am using PVS "Price of Volatile Stocks" and proxies for market-wide risk perceptions. It is defined as PVS(t) = Avg. B/M( low vol,t) − Avg. B/M (high vol,t). I aim to calculate the daily % change of the PVS that ranges from -0.93 to 0.53 over 50 years of daily data. When calculating the % change from negative to positive values and vice versa, % changes are biased and inaccurate. I was wondering the best way to approach this on Stata and ensure I have the best estimation for the changes.
This is my first post here, so please let me know if I am missing something that could be useful for you.

Thank you so much in advance for your answers,
Kind regards,
Giovanni Dell'Erba

[Tiago Pereira]

Giovanni, hi.

Let A and B define the before and after values. You can compute the relative change via:

gene relative_change = (B-A)/abs(A)

The tricky part is the interpretation. A stock that changes from -0.1 to 0 has a larger relative change (100% increase) compared to a stock that changes from 0.20 to 0.35 (40% increase).

[Nick Cox]

I don't see that you have a soluble problem except in terms of seeing that % change is here a useless measure. The problem is not one of bias or interpretation as reported prices are presumably to be considered as exact within conventional resolution -- so there isn't e.g. an issue of measurement error -- and 0.02 / 0.01 say still has an interpretation as 200% change. Taking @Tiago Pereira's example just one step further if a change from -0.1 to 0.0 is feasible then so is one from 0.0 to -0.1 and then you have the elementary but fundamental problem of division by zero.

I don't deal with this kind of data and there is presumably a literature on what to do, but on the face of it this is a dead end.

[Giovanni DellErba]

Dear Mr. Pereira & Cox, I am sorry for the late response. Thank you so much for both answers. I have applied the absolute values method and done a thorough screening of the dataset to pay attention to the interpretation. Also, switching from negative to positive occurs less frequently than from positive to positive and negative.

[Nick Cox]

For the avoidance of doubt, my advice was not to do that. Positively, llooking at changes themselves seems perfectly defensible mathematically and may help substantively.

As you have done it, what I recommend is that you plot your chosen measure against

first value

second value

mean of first and second value

and that you check for missing values whenever abs(first value) is reported as zero.

[Tiago Pereira]

I agree with Nick. If the values can change to 0 or near zero, then this approach would not be suitable.