# Can you apply percentage calculations when the changing value crosses the zero point?

Recently oil prices went negative, changing from about +20\$/barrel to -27\$/barrel (citing from memory, the exact numbers are not relevant here), to then become positive again the next day. And I read somewhere that the prices had fallen by 357% one day and then risen 258% the next day (also from memory, but it struck me how precise the news wanted to appear). So I am asking if this calculation makes sense at all. What if I divide the fall into two tranches: from +20\$/barrel to zero, and from zero to -27\$/barrel. The first tranch has fallen 100%. How would the fall from zero to whatever negative number be calculated, how much would that be? And by how much would it rise from -27\$/barrel to zero, and from zero to whatever positive value it attains afterwards? It makes no sense to me, but perhaps there is a way to calculate it properly and I just have not thought of it. Any ideas?

Percent change is usually spoken of as difference divided by start times 100. If it goes from 10 to 4 it’s down (-6/10)*100= -60%
I don’t see how crossing the zero line necessarily makes a difference in this calculation. It was \$10, now it’s -\$6, so -160%

The only time this does not make sense is when the zero is arbitrary, like temperature. A percent change is a quantity change. Temperature going from 10° to 4° did not drop -60%, because the quantity - 10 or 4 - is meaningless. (C or F)
The only time it might make sense is in absolute/Kelvin degrees.

I would say 20/bbl or -27bbl is a meaninful quantity compared to \$0/bbl.

I agree with what md2000 said, but he didn’t fully address is when the starting price is negative, when things become a little less clear to me. How would you describe a change from -20 to -25? If you use the same approach, that would be (-5/-20)*100=+25%. In the oil market context, I think you’d need to reverse the sign after taking the ratio to accord with intuition, and call that -25%. But I’m not sure I always have that clear an intuition about what was meant if someone started quoting percentage changes from negative baseline values.

If you owed \$20 and now owed \$25 your debt has gone up 25%. Your net worth has gone down by 25%.

But you are right, the denominator probably should be “absolute value” unless terminology (i.e. “debt”) is clear about the sign.

Why is 0/bbl not meaningful? The price equals zero, looks as sensible to me as minus 27. Imagine the price falls to zero one day, the loss is 100%. No problem. Then it falls to minus 27 the next day. How much did it then fall in percentage? Infinite, according to your formula: (-27/0)*100. So the result is different if you stop on the way from 20 to -27 at zero or if you go from one to the other in one go. And it is not a small difference: it is infinite.
And back up? Same difficulty. I don’t get it.

I think it’s mostly that percentage calculations aren’t very meaningful when you start near zero.

As you point out, 0 to something else is an infinite percentage change. But anything starting close to zero is going to be a very large percentage change which is rarely interesting unless you’re specifically talking about something where the percentage mattered.

If you invested in oil futures at \$0.0001, then a 52345% increase matters for you. If you did not, then the percentage change is mostly meaningless.

Because zero is unique.

I wasn’t saying \$0/bbl was meaningless so much as it was meaningful compared to 0°F. Arbitrary zero means nothing. 10° to 5° the temperature did not fall by half, unless that’s Kelvin.

But this is the flaw. If the price is \$1 and goes to \$27, it went up 2700%. From 10 cents to \$27 it went up 27000%. From 1 cent to \$27 it went up 270000%. the problem isn’t the price would be zero, the problem is when comparing to zero expressing the change on percent or “it went up X times the original price” is a meaningless thing to compare.

you are correct, percent changes when the starting point is close to zero simply give exaggerated numbers.

That kind of percentage change would only really make sense if you were buying a stock at \$0.0001, where the \$0.0001 would represent your investment outlay and your maximum possible loss.

You don’t have an “investment outlay” for a futures contract, you put up margin to cover your potential risk of loss. So when buying or selling a futures contract, especially one
that can go negative, it can be more natural to think in terms of number of contracts rather than investment outlay. In that case, rather than thinking in percentage of investment outlay, you’d think of your p&l as number of contracts (barrels) x price change.

Having said that, something like S&P futures that represents stocks can’t go negative, so thinking it percentage terms as though it were a physical stock is quite reasonable.

I suspect the denominator they used in the rise was the original price so something like this

Start \$50
Next day -\$20
Next next day \$35

First percent of change -70/50 = -140%
Second percent of change +55/50 = +110%

But typically, the starting price/value/number is used. It dropped 50% means the price went to half the original amount. It rose by 300% means the price tripled. If the price tripled, you don’t say “the price changed 66%” unless you’re a New Age Accountant.

Yes, these numbers can be problematic when dealing with numbers crossing the zero point. This is where absolute numbers make more sense - dollar change, not percent, for example.

Actually the price quadruples when it rises by 300%. It ends up 4 times a large.

And all of this perfectly illustrates why so many of us find percentages confusing, and why advertisers use them to deliberately confuse us.

If we talk about a percentage of a whole number, then there is no problem. 60% of 200 is 120. The problems arise when we talk about percentage increases and reductions. If I want to make a dramatic point, I might say that there has been a 50% increase in the number of COVID19 deaths in my locality. Or, I could be more honest and say that there were 2 yesterday and 4 today. A store near me is offering clothes in a sale, saying that "they will pay the VAT (VAT = sales tax = 20%). The sign says that this is a 20% reduction. Of course, this would not fool anyone here, but I tried to explain to a friend that it was actually a 16½% reduction. (or did I get that wrong?)

Doh!!

Very true. Political ads, for example, might say “XXX raised the sales tax by 25%” when they mean (s)he took it from 3% to 4%. 50% more doctors recommend X" when it means 4% recommend the competing brand and 6% recommend X. Percentage changes are probably most meaningful when the actual proportion of change is small, since “it changed by 13%” (or, 13/100 higher than originally) is more meaningful to the average person than “price went up to 1.13 times what it was.”

Are you all kidding me now?

If there were 2 cases yesterday and 4 today, the increase is 100%.

And if the political rival rises a tax from 3% to 4%, the rise I claim (s)he perpetrated will be 33 1/3%, not just 25%. (25% would be if (s)he took the tax from 4% to 5%.) It would take a 25% reduction to bring it back to where it started (20% in my second case), as percentages are not symmetrical when going up or down.
But that is another difficulty with percentages; my question was what happens when we cross the zero point and I am not sure it has been answered and if it has, if I understood the point.

3% to 4% is an increase of a lot more than 25%…

Anyway, I don’t mind correct use of percentages, like a product for sale at 20% off. It’s complete bullshit statistics of which we should be wary, and framing such in terms of percentages or promilles or some other way does not make much difference.

Anyway I would assume veteran derivatives traders understand price fluctuations, including negative prices, and have their own jargon for it.

It seems like an unusual situation: plenty of contracts end up worthless, but it seems atypical to deal with one where the value is negative. I would want to see some actual traders’ handbook or folklore that it is dealt with in terms of percentages at all.

I didn’t claim they did it right. I just claim that I suspect that’s how they did it. It’s a technique I have to unteach some of my math students.

I feel the urge here to point out that Kelvins are not degrees. 99.44% of the time I have this urge it’s pointless pedantry, but in this particular case it’s the whole point: it’s the meaningful distinction between the units that you just referred to. It’s because Kelvins are not degrees but are instead directly related to a physical property that percentage changes have meaning.