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Instantaneous Stock Percentage Calculation

A more intuitive percentage system
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Every day, millions of people check to see "how the stock market did". And, the percentage change number indubitably reigns king of all daily market indicators. However, this number can be notoriously misleading.

For example, pose the following scenario to anybody on the street (or even people in the financial Industry):

Over the past 6 months, the Dow (DJIA) has dropped 30%. By what percentage will it need to rise over the next 6 months in order to recoup our losses?

Most people will answer that the market must simply rise another 30%. However, the market would actually need to rise 43% for it to be at its previous level.

(Math: Drop of .3 means market is at .7 of its previous level. Simple algebra shows that DJIA must be multiplied by the reciprocal of .7 to be back at it's original level. [Reciprocal of .7]=1.43, so 43%)

So, what we need is a new market change indicator that meets the following conditions:

—Looks like a regular old percentage, reasonable to people accustomed to the old system

—Acts like a percentage; varying as a function of the change in value of the stock/market, but is smaller when the market is larger (accounts for the size of the market)

—A drop by a certain amount of this indicator would be offset by a gain of the same amount of this indicator.

Here is a rather obvious solution: The new percentage is calculated by taking the change in points, divided by the average of the market's open and closing values. So, for a drop of 200 points from a market that opened at 8000 points, the percentages would be calculated as:

200/8000 = old percentage = .025 = 2.50% | 200/([8000+7800]/2) = new percentage = .0253 = 2.53%

Using the new system, the market dropped 2.53% that day. The next day, if the market rose by 2.53% in the new system, the market would be right back at 8000 points.

We would need some new simple equations to use with this new system. Simple algebra shows the following to be true using this new system if P=continuous percentage, S=Market's opening value, C=Market's closing value:

P = 2(C-S)/(C+S) | S = (P+2)C/(2-P) | C = (2-P)S/(P+2)

This system would clearly be much more intuitive and lead to more accurate judgment when people make financial decisions. However, I think there is an even better solution.

NOTE: Variables followed by a "#d' mean that value will be in the decimal form. So, a 2.5% drop in value will be represented by 0.975 in these variables. You can easily find the number the other way by subtracting 1 from these decimals.

This would be: P=ln(C/S) | C=e^(P)*S |

This leads to very similar numbers as the earlier formula. For the earlier scenario, it also results in a P of 2.53%, but varies only by 0.0000014%. Although it is less obvious, the calculations are actually simpler.

Also, using this system, one can easily convert between original percentages and "continuous percentages" The "obvious" system requires a more complex formula to do this. Here is the conversion from new percentage to old using the P=ln(c/s) system:

Old Percentage#d = e^(New Percentage)

New Percentage=ln(Old Percentage#d)

Therefore, I now favor this system for calculation "continuous percentages".

Amall, Nov 30 2008

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       interesting, however i suspect rather worthless as the percent change is literally the change in dollar valuation of various issues and thus must be the actual percentage change in value. I don't think that totaling up your daily numbers for a month would give you the change for that month as the current system does.
WcW, Dec 01 2008
  

       Please elaborate?   

       As far as I can see, the current system does NOT allow you to add up the percentages with any meaning. For example, a 2% drop one day, followed by a 2% drop the next day does NOT represent a total drop of 4%. (.98^2=.9604, so a 3.96% drop actually occurred)   

       However, with the new system, a continuous percentage 2% drop followed by a continuous percentage 2% drop DOES mean that the stock dropped a total of 4%.   

       Example: ln(98.02/100)=-.02 the next day ln(96.08/98.02)=-.02. You could then say a total drop of 4% occurred, which would be accurate since 96.08*e^(.04)=100, the market's original value.   

       Similarly, you could total up the actual dollar losses for that month. In this case, that is 3.92. Then, subtract that number from the starting price of the stock/market, in this case, 100-3.92=96.07. Finally, P=ln(96.07/100), which equals -.04, so -4%.
Amall, Dec 01 2008
  

       no, but applying them sequentially as a plot on a graph would does follow the actual valuation. In your system the plot and the valuations would move apart as the price rose or fell. for example if the value of a company valued at 100$ falls to 50$ we have a 50% loss for that day under the current system. Under your system if the stock would show a 66% loss. If the stock doubled in value the next day and we applied the equation again we would be at 200% on the old ticker and 166% on your system. Now apply the fractions sequentially and we get 100$ for the old system and 109$ for the new system. Over time the exaggeration of rises over falls takes the dot tracing the market higher and higher relative to the actual valuation.
WcW, Dec 01 2008
  

       It has been known for commentators to refer to changes as a percentage of some past value (typically a peak value, but it could be any value, such as value as at year start). That does the job more simply, I think.   

       [UnaBubba], //Knowing the overall delta of the market is pointless// *unless* your exposure is to unitised investments, which may well track the overall index either by accident or design, in which case it's far from pointless. Admittedly, people tend not to get rich quick from unitised investments, but they're good if you'd rather spend your time here than researching individual stocks.
pertinax, Dec 01 2008
  

       Percentages are useful to see how a stock is doing over time only if you know the start value and the length of time is defined.   

       If you simply say "This stock has changed by 5%" then it has no reference no matter what system you use.
miasere, Dec 01 2008
  

       Don't they quote changes in the market in 'points' rather than percentages (presumably) for the very reasons described?   

       i.e. when the NYSE drops - that gets reported both as a percentage, but also more importantly, as a number of points - e.g. "There was a panic similar to many with a fall of 7.2% in value (554.26 points) on October 27" - that's why people get excited when the DOW crosses 10,000, or when the FTSE goes one side or other of the 5,000 marker.
zen_tom, Dec 01 2008
  

       its all relative. what actually matters is the change since you bought the stock. I guess i just disagree with the notion that people don't understand that a seventy five percent decrease in value would require the stocks value to quadruple to return to the previous level. If mathematics of this sort are unfamiliar to you then you should let somebody else watch your equities and turn over to the cooking network or whatnot.
WcW, Dec 01 2008
  

       You've forgotten about discount rates. This would effect your math.
williamsmatt, Dec 03 2008
  
      
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