For example,

$FB is $180 today.

If it were to lose 50% of it's value it would be worth $90.

If it was to then gain 50% back it would be worth $135.

So the percentage change was the same but the dollar change was different.

I suppose this presumes that bad news affects the percentage drop in the same way that good news affects a percentage gain, if bad news makes the stock drop less (all other things being equal) than 50% here then it might not be the case.

Does this mean that losing in the stock market is far more destructive to your portfolio than winning and that you should not lose at all costs?

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    You are assuming a 50% drop has the same likelihood as a 50% rise. That's not a valid assumption. – ChrisInEdmonton Aug 14 '19 at 20:41
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    Your comparison is a simple logical flaw. If the stock loses $90/stock, it is worth $90/stock. If it then gains $90/stock, it is worth $180/stock. When you compare with %, you skew the perception of your results, biased towards the "left-hand" value. – Ian MacDonald Aug 14 '19 at 20:55
  • Mental masturbation is engaging in intellectually stimulating conversation with little or no practical purpose. AFAIC, that's what dealing in the derivative percentage of gains and losses is. KIS: If your stock drops 2 points, you need it to rise 2 points to break even. – Bob Baerker Aug 14 '19 at 21:03
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    let's do another exercise. $FB is $180. it rallies 200% so now it is at $540. then it falls 200%, which is impossible. There is always a hard limit of 100% of your money that you can lose, but there is no theoretical limit (I use this loosely because there are tons of limiting factors) to how much money you can gain with a stock. – rhavelka Aug 14 '19 at 21:16
  • @rhavelka You can lose more than 100% of your stake if you sell short, the stock goes up more than 100%, and you're forced to cover your short. – shoover Aug 15 '19 at 13:14

In one sense, yes, percentage losses have a greater impact than percentage gains. But while losses reduce the base from which subsequent gains can occur, they also reduce the base from which subsequent losses can occur.

Stock prices are often modeled using geometric Brownian motion, reflecting that a stock (or stock index) cannot go below zero. The process involves "drift" (average return) and "diffusion" (random ups and downs). If a stock had an equal probability of rising 50% or falling 50% in a given period, it would mean the drift (average return) is negative. This is not observed in historical stock returns. So indeed, "bad news makes the stock drop less (all other things being equal) than 50% here".

However, once you apply leverage, these safeguards go out the window. A leveraged portfolio can go below zero, and leverage can turn a portfolio with positive drift into one with negative drift. For example, if the stock had equal probabilities of falling 10% or rising 12%, that is positive (0.90 x 1.12 > 1), but if you lever it 2x so it falls 20% or rises 24%, that is negative (0.80 x 1.24 < 1).

EDIT: What I am calling "drift" here is the geometric average return, corresponding to mu - sigma^2/2 in the linked article.

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If you buy stocks "long" (as opposed to speculating on "shorts" and "options", then the most you can lose is when the share price drops to $0/share. OTOH, it can grow and grow and grow and grow.

Thus, "Does this mean that losing in the stock market is far more destructive to your portfolio than winning and that you should not lose at all costs?" is a gross misunderstanding of Jr. High fractions.

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Of course losing money is worse than making money. Investors should focus on minimizing losses and maximizing gains.

Your example is just an observation of a mathematical phenomenon related to gains and losses. A 50% loss requires a 100% gain to return to breakeven. You could also infer that losses are capped at 100% whereas gains have no theoretical cap.

Neither of these analyses are very relevant to a practical investment strategy.

Risk should be mitigated simply because it is best practice. For example, some investors cut losses at 5%. They don't do this because they know it will require a 10% gain to break even. They do it because they want to protect their portfolios.

You also should not assume that positive events and negative events have opposite but equal impacts on the stock. Positive news may push a stock 20% and negative news may pull the stock down 10% (and vice versa).

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