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Friday, January 16, 2015

On Percentage Changes

Sometimes people get the impression, from the way percentages are calculated, that to get back to even a stock has to go up much more than it dropped.  Here is a simple example:  suppose we buy a stock at $2/share and it drops to $1/share.  By the conventional way of calculating percentages, this represents a decrease of (1-2)/2 = 50%. The formula is:  (ending value - beginning value)/beginning value.

To get back to where we started, it will need to go from $1/share to $2/share which equals a percentage gain of (2-1)/1 =100%!  Yikes!  It has to go up twice as much!  Really?  Actually, as you can see, it just needs to rise by the same $1 it dropped.

To look at this another way, check to see if you are really ahead if you buy a stock that round trips from $1 to $2 and then back to $1.

As an FYI, this is one area where economists are not lazy.  In dealing with elasticities, it is necessary to calculate percentages; and the approach economists use is to take the average of the prices for the divisor.  This would make a move from $1 to $2 a percentage change of 1/1.5, or .67%.  If it goes back to $1, the change would be -.67%.


  1. I'm not sure I get your math. If my stock is $2 per share and I lose 50% my stock is now worth $1 per share. If I then gain 50% my stock is only $1.50 per share not $2. in order to go from $1 per share to $2 per share I have to gain 100% .percent.

  2. Suppose I started at $1/share and went to $2 (+100%) and then back to $1 (-50%) and then told you that +100 - 50 = +50. Would you say that's pretty good performance?