Idiot World - Why I don't look at the market

Idiot Activites:

But that was ten in a row!

Quick, what's the odds of getting heads 10 times in a row? It's 1/1024 to be precise, or about 1/1000. Obviously, if you flip enough times, you'll see ten straight heads, or even twenty straight heads. In fact, if you flip around 1000 times, on average, there will be a string of 10 heads. You can in fact prove, with high probability, for any strings of k heads, there exists some c which corresponds to the desire confidence that some constant times 2^k will exist.

Okay, the math-ish mumbo jumbo out of the way, what does that mean for us? Let's say you look at your results every day. In 3 years (more than 1000 days), there will be a string of "hot streak" of 10 days which can directly explained away with. Luck might matter more than you think!

Or put another way, you have a thousand people. At the end of ten days, on average there will be one person that will have gotten 10 straight good days. Is this guy good or lucky?

But wait a minute, you say, people don't flip coins!

Or do they?

Let's shift gears a little bit, and we'll be right back, don't worry.

Let's say you have a chance to play two games. The first game cost a dollar to play, and one out of two times, you will make two dollars. The second game also cost a dollar to play, but one out of a thousand times, you will make a thousand dollars.

It's easy to see both games are fair and even, and pointless, except for maybe it's fun to see if luck is on your side. And since you break even on both, it's easy to say that the games are pretty much equivalent. So which one would you rather play?

Of course, they aren't quite the same. The risktakers might aim for the latter, and hope they get lucky once early and be done with. The more conservative of us might aim for the former, hoping that we'll get a string of ones, and then quit while we're ahead. And the even more conservative of us might just not play - it is rather pointless, and it's a risk.

So what's different between the two games? The volatility.

You can probably skip ahead a little bit if you know what volatility is, but to put simply, volatility is the mathematical term defining the likelihood to jump around. High volatility means it's all over the place, while a low volatility means it's pretty stable and doesn't move around much.

The savings account is an example of something that has low volatility - you can pretty much be sure that it'll be there tomorrow. The odds of the bank going bankrupt, and that the FDIC can't help is pretty low. Something that's more volatile is the stock market, as in, it jumps around a lot.

Now, volatility refers to the standard deviation of change, which implies that it follows the normal distribution. The normal distribution is probably the most important probability distributions, and pops up all over the place, and most of the time models the stock markets pretty well. Fat tails exists, and I'm going to handwave it away, but you can read about kurtosis if you really need to know about it.

We'll make the assumption that normal distribution is how life works, and in summary, 68% of the time data will be within 1 standard deviation from the mean. This means if the average is say, 20, and the standard deviation is 10, then it will be between 10 and 30 68% of the time. About 95% and 99.7% for 2 standard deviations and 3 standard deviations, respectively.

Why the need for volatility? It's simple. You can find how much risk you're taking. A 20% average annualized return with 0% volatility is better for the heart than a 20% average annualized return with 10% volatility. In the former, it means to have 20% every year literally. In the latter, it jumps around, say 30% one year, then 0% the one after, and 5% the one after that, etc.

Is it that bad for my heart?

People varies on what they consider a good return, so I'm going to do a few different models.

By most means, 20% a year is a pretty good return. Let's just say we have 10% volatility on that return. This is pretty good, since we'll make 10% on a down year..

So why is this bad for my heart? And why I don't pay attention?

Using the Z-Score Calculator, we see that we will make a gain 97.725% of the time! Yay!

Okay, since no one checks their balance once a year (except for the laziness or apathetic of us), what happens if we check it twice a year, and to make it simple, at half-year intervals?

That 20% annualized calculates to about 9.54% per half year. (It's not 10% each because it's compounded.) The 10% annualized volatility is now 7.07% volatility per half year. (With the usual handwaving)

What are the odds of a good half-year? 91.146%. And you can easily do the math and know that the probability of having two good half-years is 83.0759%.

And just as easily, we can generate a table:
A year - 97.725%
A half-year - 91.146%
A quarter - 82.451%
A month - 70.21%
Daily (252 days) - 54.573%
Hourly (252 days times 9 hours) - 51.527%
Minutes (Hourly times 60) - 50.1972%
Seconds - 50.0255%

Seconds might be a little too much, though I know some crazy addicts. Minutes is reasonable if it's your day job, and I can see some of us hooked hourly.

It's completely reasonable to check how you did every day. Unforunately, in a year of 252 days (holidays and all) you will have about 138 good days, and 114 bad days. That's a difference of 24 days over a year, or noticeable if you really pay attention. It's like watching baseball. You can watch every game and not be able to tell who's a .300 hitter and who's a .250 hitter (difference of about 30 hits a season, or a little more than a hit a week.)

Now, the more sensical thing is probably to check every month - they usually send you with a statement anyhow. Now that's much better, over a year, you'll have 8 good months and 4 bad months, and you can literally see the difference. And if you only check once a year, you'll have 39 good years to come with one bad year. Now that's a good performance!

The 20%, 10% is very good, and even then you can't really tell unless you look at the whole picture.

It gets blurrier even, when volatility is higher, and our expected return isn't likely to be 20% a year. (If you know one, let me know!) For a 15%, 10% portfolio, it's even worse:

Period	15%,10%	10%,10%
Yearly	93.3191%	84.1345%
Bi-yearly	84.6991%	75.4985%
Quarterly	76.1508%	68.5194%
Monthly	65.7561%	60.8815%
Daily	53.5088%	52.3943%
Hourly	51.1707%	50.7984%
Minutes	50.1511%	50.1031%
Seconds	50.0195%	50.0133%

And you can easily say that both have performance you would love to have.

Are we doing better than merely lucky (flip a coin enough times..)?

For that, we look at the beta of the portfolio, but that's really not the point of this article.

Since there's really no need to make myself feel bad about it, and that even if I can see what happened, it's not likely I can actually spot the difference. So, I just let things be, and not look at the market so much. It's better for the heart that way.

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