The Problem with Percentages

On my drive home last week, I was listening to a radio show.  The host guy was talking about the stock market.  He said that the stock market lost 5% the day before, but it gained 5.5% this day, so that’s a net gain of 1/2 a percent.  As soon as I heard that, I knew I had to write this post.  Some people are percentages illiterate, and perhaps I can help them.

Percentages do not add nicely, if you’re talking about one number going up and down.  If he had been talking about points, such as the Dow Jones Industrial Average, he would have been fine.  If it is down 500 one day and then up 550 the next, then that’s a net gain of 50 points.  But percents do not work that way.  Down 5% and then up 5.5% is a net gain of only 2.25%. You need a gain of 5.79% to come out 0.5% ahead after a 5% loss.

Another example: a stock worth $100.  If it loses 50% one day, it will be worth $50.  If the next day, it gains 50%, then it is only $75, not $100, because you’re taking the percentage of the new, smaller value.

Similarly, if the stock were to gain 50% first, it would be worth $150.  Then if it lost 50%, it would be worth $75.  You always need a larger percentage gain than a loss in order to come out even because the gain is calculated on the smaller value and the loss is calculated from the larger value.

“Divide your portion to seven, or even to eight, for you do not know what misfortune may occur on the earth.”
– Ecclesiastes 11:2

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This little article thingy was written by Some Guy sometime around 8:19 am and has been carefully placed in the Finance category.

4 Responses to “The Problem with Percentages”

  1. Burrill Says:

    Could you also deal with the problem with photo print sizes and the necessity of cropping prints that aren’t in a 2×3 ratio? It’s always fun to hear people say “Hey! My 8×10 was cropped! What’s going on?”

  2. js Says:

    And 2×4 aren’t really 2×4. I learned that the hard way. It’s not exactly the same problem as the percentage one, I guess.

  3. Some Guy Says:

    2x4s have the same problem as the so-called quarter-pound hamburgers: size before cooking. 2x4s are really 1.5×3.5s after drying, and quarter-pound hamburgers weigh who-knows after cooking.

  4. Some Blog Site » Blog Archive » The Problem with Percentages, Part 2 Says:

    […] previous post mentioned how some people have problems with percentages. Now there should be fewer problems with […]

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