The Money Mustache Community
Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: kvette on November 05, 2014, 10:10:21 AM

A coworker said his dad told him never to invest in the market. His reason is this:
If a stock goes up 50%, then goes down 50% the next day, how much money do you have? (his example was $100 goes to $150, which then goes to $75.)
How would you respond to this question? I know there's a simple explanation, but am having a hard time putting my finger on it.

First of all, that is never going to happen. Except maybe with penny stocks. But you shouldn't be investing in penny stocks anyways.

Stocks aren't priced on a % of what they were yesterday or tomorrow. They are priced on valuation. Predicted earnings are 100000% more important than the stock price yesterday. Stocks don't move 50% up and 50% down. If you really want a good return % number, base it on your cost. Your cost will never change unless you buy more, sell, or your cost basis somehow changes due to accounting/dividends/etc.

Also  stocks are a longterm investment. This is a 2 day example, so even if this somehow happened, it doesn't matter over a timeframe measured in years.

His scenario is correct. However, it's only possible with an individual stock. The proper response is to tell him about index funds, have him pick any point in the history of the market, and then show him the return after 30 years. People like this are afraid of short term volatility. Show them the long term charts.

Good thing stocks have more up days than down days. Take confidence in the fact that, since the 50's, there is no decade where the S&P 500 didn't go up on more days than it went down. There were even more up days in 2008! (source (http://www.crestmontresearch.com/docs/StockYoYo.pdf))

I'd probably say something like "What if the value of the dollar went up 50% in a day, and down 50% the next day?" Then walk away.

It's also "bad math" in that you are assuming "50% increase" is essentially equivalent to "50% decrease" (and that each scenario is equally likely.)
Stocks, even index funds can increase in value some percentage and decrease in value some percentage  that's possible.
But a more equivalent scenario would be $100 invested increasing to $150 in value... and then dropping to $100 in value the next day. You've lost nothing and the real percentage decrease was 33%  realistically the equivalent to the previous 50% increase.

I think the OP is asking for an explanation of the math principle behind this effect. The link I put below asks and answers the question (I think) in some very complex equations..but I think it's relatively simple: Your base number changes after the initial increase, therefore the percentage is a larger number.
http://math.stackexchange.com/questions/205152/thinkingwhyequivalentpercentageincreaseofaanddecreaseofbisnotthe (http://math.stackexchange.com/questions/205152/thinkingwhyequivalentpercentageincreaseofaanddecreaseofbisnotthe)

His scenario is correct. However, it's only possible with an individual stock. The proper response is to tell him about index funds, have him pick any point in the history of the market, and then show him the return after 30 years. People like this are afraid of short term volatility. Show them the long term charts.
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Tell him the market has never been in negative territory over long periods of time. It's called investing. Even the Great Depression paid out 45%. If you were a Mushtacian in those days you would have been ok.

I would have to ask, "Where then should I invest my money?". I would love another investment to diversify into that would give me what the market does: growth, diversification, liquidity, minimal management. The way I look at it there are only a few true investments out there, securities, real estate, and active ownership of a business. Real estate and owning a business are more difficult to diversify and require more active management than what I dedicate to my portfolio (or significant management fees). Sure there are a few investments on the fringes, such as collectables, but they tend to suffer the same pitfalls.
They guy probably buys lotto tickets...

He's sort of looking at it wrong. He's using percentages, but he really should look at like this:
Let's say a stock is at 100/share. If it goes up 50 points, then it's at 150/share. You bought one share, with $100. You now have $150. So far, same thing.
BUT
Now it's at 150/share. He's says "What if it goes down 50%" the next day. But that's not equal to what happened the first day, anyway. If it goes down 50 points, then it's back to 100. But he's saying it drops 50%, so he's saying it drops 75 points. Basically he's saying "What happens to your money if it goes up 50 points, then it goes down 75 points." Which of course means you lost money.
But a solid stock doesn't do this kind of crazy thing anyway. And most don't invest in an individual stock anyway. All the MidCap stocks in my 401(k) are not going to do this combined.

When it goes down 50%, buy more...cause it's going to go back up 50% (or more) at some point. Duh...

When it goes down 50%, buy more...cause it's going to go back up 50% (or more) at some point. Duh...
if he knew enough about this sharre to make it worth buying at 100 a share then he'll be delighted that its on sale at 75.
If he's not then he shouldn;t be buying individual companies.

If that's his reason not to invest in the market just tell him to change the word "stock" in the question to something he does think is worth investing in...
the answer is obviously the same due the the math linked above so his point is moot.

I'd say "ah, you mean Jensen's inequality".
Stocks don't follow a zero return random walk. They do, on average, go up in value.
His statement is true. But, the probability of that occurring, and repeatedly is nil. Like saying "if a tsunami hits Nebraska, then a lot of damage will occur". True, but a tsunami won't hit Nebraska. Sort of a false premise.
If I fly in a plane and it crashes, then I will likely die. Should I not fly in planes?
Another viewpoint is that the stock market would not attract $$ if there were better expected alternatives. People accept the risk in stocks because there is an "expected" reward. As one poster notes, by using index funds, you can lower volatility around the expected return.

For a real world perspective Robert Shiller (Yale professor and Nobel Prize winner) has a great explanation of this in his Economics class  check out this video starting near the end, at 1:02:45  visual should say "Histogram of daily stock price changes since 1928"
https://www.youtube.com/watch?v=QbosMr2JVrc
Risk comes from lack of diversity. He explains in episode 4: https://www.youtube.com/watch?v=_B_24GUWdSM
(the whole course is a bit dry and very technical, but it's totally worth it for the few nuggets of great info each class)

Your coworker's question has a hidden assumption. Namely, it assumes that his proposed sequence of returns is characteristic of the stock market.
Would you take me seriously if I asked the following questions?
What if a $100 index fund goes up 5% and then down 99% how much money do you have?
What if a $100 index fund goes down 10% then up 25% then down 50% how much money do you have?
What if a $100 index fund goes up 500% and then down 100% how much money do you have?
None of these hypothetical questions has any bearing on the question if stocks are good investments. They're just 5th grade math problems.
A better question is are positive returns more likely than negative returns. The best way we have of answering that question is looking at historical data. Here is a well done histogram of market returns over since the 1800s
http://amarginofsafety.com/wpcontent/uploads/2014/01/ReturnHistogramThrough2013.jpg
Notice that positive returns are much more likely than negative returns. There are 10 years in the data set with a >40% return and only 1 year with a <40% return.
If you run the math all the way through, you find that stocks return about 67% (real return) over long periods of time.

retired?  Thank you for someone noting Jensen's inequality theorem!
I think the correct response is that his father's observation is really about how percentages (or geometric progressions, if you prefer) work. His issue is with math, not the stock market.
MathNinja

This is true of literally anything you could invest in (stocks, bonds, houses, pork bellies)  if the price of anything (including a dollar) follows the path you stated, you'll get the same outcome.

I vote for a punch to the face.