An Argument for Statistics (Part 3)

Posted by Mark on December 18, 2015 at 06:16 | Last modified: March 31, 2016 06:27

I left off with a general description of the statistical hypothesis testing process.

Once the assumptions behind a sample or experimental design are identified, the next step is to choose an appropriate statistical test to run on the data.

Select a level of significance (greek letter alpha: α), which is a probability threshold below which the null hypothesis will be rejected. Common values used are 0.05 or 0.01. By definition, status quo is likely to maintain. α states “if the chance of the sample being status quo is less than one in 20 (or 100, respectively), then I believe it is not status quo (i.e. reject H₀) but rather something different (i.e. accept H_A).”

Perform the statistical test, which will output a p-value. The p-value gives the probability of the groups being from the same population (e.g. no difference, or H₀ is true). If the p-value < α then reject H₀ and accept H_A.

Hypothesis testing is not perfect. A type I error occurs by rejecting H₀ when H₀ is in fact true. This is also known as a “false positive” and the probability of making this mistake is equal to α. On the flip side, a type II error occurs by not rejecting H₀ when H₀ is in fact false. This is a “false negative.”

People spend so much time backtesting trading strategies but I believe without statistics, essential context is missing to make sense of it. As an example, here is some data I saw recently:

With regard to average trade, groups A and D look best but we need something more to conclusively determine. An average trade PnL of $15 for groups A and B is 50% more than groups B and C! Is that a real difference or is it likely to have occurred by chance? Sample sizes would affect our evaluation of this question as would variance within/between the groups. Inferential statistics wrap all these factors together into context we can definitively understand. Without the inferential statistics we really can’t know much at all.

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An Argument for Statistics (Part 2)

Posted by Mark on December 17, 2015 at 07:48 | Last modified: November 6, 2015 08:50

Most people who know anything about statistics understand descriptive ones: numbers used to summarize and describe data. I feel strongly that as traders, we need to understand inferential statistics too.

Inferential statistics are used to reach conclusions that extend beyond the immediate data alone. These might be used to infer from a sample characteristics about the whole population.

Inferential statistics are also used to determine whether an observed difference between groups is dependable or simply a chance occurrence. This is called hypothesis testing.

I said one could lie with descriptive statistics by including certain things and excluding others.

Inferential statistics may also mislead by including/excluding certain differences/similarities in experimental design. Even before hypothesis testing begins, validation of experimental design is essential albeit beyond the scope of today’s post.

Hypothesis testing begins by defining the hypotheses. The null hypothesis (H_o) generally states that both (all) groups are the same. The value of a group is often given in terms of an average (e.g. arithmetic mean) and standard deviation. The null hypothesis represents the status quo. The alternative hypothesis (H_A) generally states the groups are not equal. H_A may or may not go one step farther and state which group is thought to be greater than the other.

The next step is to consider the statistical assumptions being made about the sample(s) involved. For example, a given statistical test may require the samples be independent (e.g. not affecting each other) or that the distribution (shape) of a sample be “normal” (bell curve, which has a specific mathematical definition), etc. If the assumptions for a statistical test are not met then the test should not be used or the caveats/limitations should be discussed to put reasonable context around any conclusions.

I will continue next time.

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An Argument for Statistics (Part 1)

Posted by Mark on December 15, 2015 at 07:21 | Last modified: November 6, 2015 05:55

I could go on with incriminating quotes throughout history about statistics:

     “There are three types of lies — lies, damn lies, and statistics.”
     –Benjamin Disraeli

     “Facts are stubborn things, but statistics are pliable.”
     –Mark Twain

     “If your experiment needs a statistician, you need a better experiment.”
     –Ernest Rutherford

     “All statistics have outliers.”
     –Nenia Campbell, Terrorscape

     “There are two kinds of statistics, the kind you look up and the kind you make up.”
     –Rex Stout, Death of a Doxy

During my undergrad years I saw a number of students develop an antipathy toward statistics because it was a subject that either clicked or totally did not. I think much of the negative press statistics gets is partially a result of the fact that many people simply do not understand it.

I have a decent familiarity of statistics. I took an advanced stats class in undergrad and I used statistics in my published manuscript as well as my Pharm.D. research project. That education has made me statistically-minded, which is probably one reason option trading feels comfortable. I constantly think in terms of sample sizes and the relevance of conclusions. I believe these are things anyone on the path to trader success should understand.

I agree with some of the negativity reflected in the quotes above. Just because you have a statistic does not mean it’s a valid one. Scrutiny must be applied to see if the experimental design makes sense and was conducted properly.

Most people only know about descriptive statistics: numbers used to summarize and describe data. These are your averages, standard deviations, and ranges. These are found everywhere when talking about sports. Descriptive statistics can certainly be skewed to include certain things and to exclude others, which is where much of the lying comes from.

I believe another branch is equally, if not more important than descriptive statistics. I will talk about that next time.

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Wasting Time

Posted by Mark on November 21, 2015 at 07:38 | Last modified: November 20, 2015 13:33

Not too long ago, I wrote about a disappointing trader Meetup where little discussed was truly actionable with regard to profitable trading. This past week I heard something very similar.

The trader in question was asked for her opinion on where the market is headed. She replied:

          “I feel that we’re caught in a range. There’s no impetus to         [1]
          do anything. People are scratching their heads over what the
          Fed may or may do. We had a muted reaction to the terrorist     [3]
          attack in France, which didn’t surprise me since we were so
          oversold at the time. We have the seasonality thing kicking       [5]
          in here. I was looking back last year wondering when the
          Santa Claus rally was going to come. I know the week of           [7]
          Thanksgiving tends to be very bullish and then we did get a
          pretty good selloff the first week of December followed by         [9]
          the Santa Claus rally. So this just tells me we’re going to
          chop around here for the rest of the year.”                               [11]

Aside from seeming like a run-of-the-mill, absolutely mundane/typical opinion about the market, one thing that did jump out at me was just how tremendously useless it is. Did you notice all the clichés?

1. “…which didn’t surprise me since we were so oversold at the time.”
   
2. “We have the seasonality thing kicking in…”
   
3. “…when the Santa Claus rally was going to come.”
   
4. “…the week of Thanksgiving tends to be very bullish…”
   

Urban legend anyone? If you think not then show me the data.

Why even talk about this sort of thing? Nobody will hold us accountable if we’re wrong. It’s also not the sort of content that could help anyone make money even if we’re right because prognostications are not intended to be financial advice (unless it’s premium content, which savvy traders know exists just to make the services/newsletters money, anyway).

Maybe it’s intended as small talk meant for entertainment but I think discussions like this occur because people don’t realize what we really should be talking about and what we should be working on. We could try a scientific approach to some of the above-listed clichés but doing so is probably something most people never even consider.

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Understanding Dividends (Part 3)

Posted by Mark on November 6, 2015 at 05:11 | Last modified: October 29, 2015 09:11

Let’s go back to the theory that capital appreciation and dividend income are two sides of the same coin.

Were this theory found to be true, something would strike me as very wrong because the financial industry significantly emphasizes a difference between these investment objectives.

Even in this case, I did think of one marketable difference in favor of dividends. I could, in effect, make a non-dividend stock into a dividend-paying stock by periodically selling shares for cash. I would have to pay a commission with each stock sale, though. The commissions amount to money lost and I don’t see a clear way around it. I wrote earlier about synthetic equivalents in Finance. Equivalents are truly identical whereas the commissions make this different. I could try to argue “companies incur significant administrative fees when paying dividends to all those shareholders on a periodic basis and these fees cut into their cash on hand, make the company worth less, etc.,” but: 1) as a total percentage of cash on hand, this is probably minuscule; 2) to suggest the decreased cash commands a lower stock price is another theoretical concept and one I doubt could even be tested (too small to detect).

So for someone who does need money periodically to pay the bills, even in the hypothetical case that dividends are nothing more than future capital appreciation realized right away, I do see benefits to that dividend check. Is this worth the significant growth/income difference affirmed by the industry with regard to the suitability standard? I think that is highly debatable but I would be much more enraged about the construct if I could come up with no difference at all.

And because I no longer believe dividend income and capital appreciation to be the same anyway, once again “FAHGETTABOUDIT!” is in order.

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Understanding Dividends (Part 2)

Posted by Mark on November 5, 2015 at 07:56 | Last modified: October 28, 2015 10:35

I now believe dividends are bona fide income that may or may not come at the cost of capital appreciation.

Hypothetically speaking, suppose I did the study and found dividends are future capital appreciation realized now. I cannot emphasize enough [to myself] that this is not necessarily the case.

Nevertheless, I think understanding whether investors realize a decrease in stock price offsets the dividend would be very important for determining whether it’s a bunch of financial hocus-pocus.

I asked a former director of a NYSE-listed utility company. He said yes: most savvy investors know this.

He continued on: “sometimes the stock price falls some but sometimes it doesn’t. The stock usually falls less than 1%. Investors like the stability. They get the dividend checks in the mail and they feel good about that.”

I corrected him by saying the stock falls by exactly the amount of the dividend and that is cumulative over all dividend payments (a claim I now know to be theoretical). I said total return is equal whether or not a dividend would be paid.

He said, “most investors don’t know the term ‘total return.’ People want their dividend and their cash now and that’s it.”

I argued, “we could do a study to determine whether dividend payers are more stable than non-dividend payers. It’s a hypothetical claim that we don’t know the answer to.”

He said, “stock splits are the same way and stock splits are just like dividends. Companies with stocks that split are more healthy than those that don’t. Stock splits and dividends are both signs of corporate health.”

At the very least, I came away from this discussion thinking dividends are a marketing tactic by corporate boards of directors to make a stock more appealing to a particular segment of investors. Stock splits are the same way: neither change the total value of the investment. What a crock, then, for the industry to emphasize so strongly the illusory difference between capital appreciation vs. income!

Since the conclusion is based on a hypothetical premise, though, an enthusiastic “FAHGETTABOUDIT!” is in order.

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Understanding Dividends (Part 1)

Posted by Mark on November 2, 2015 at 07:06 | Last modified: October 28, 2015 10:04

I can imagine someone reading the first few posts of this mini-series and saying “okay I can see why you say there’s something misleading about dividend payments but you can’t argue that it’s income.”

A proponent of dividends might take issue with my claim that capital appreciation and income are two sides of the same coin. According to my brokerage (customer support), on the ex-dividend date the exchange lowers the price of the stock on the ex-dividend date. Were the dividends not paid, I claimed the stock would be higher by the amount of the total dividends paid. As logical as that seems, it is only hypothetical. The devil’s advocate could argue “because dividend payments are usually much lower than the average daily volatility of the stock, the impact of the dividend probably comes out in the wash.”

Designing a study to substantiate my claim would be very difficult. I would have to get intraday data and study stock price changes just after the price is reset. I would also have to use something other than an adjusted price series because when dividends are paid, all previous prices in an adjusted series are adjusted downward by the amount of the dividend. Determining a valid control group might be difficult, too. I could use non-dividend payers or any stock not paying a dividend on that day. I could probably ramp up the sample size large enough for statistical significance but would it be financially significant? Maybe not.

I can’t think of an easy way to do this study and I certainly don’t have access to the data to do it myself. I therefore must drop the claim that dividend payment comes directly at the cost of capital appreciation.

The only thing I know for sure is that the “[income] check is in the mail.” While I know for sure that the stock price is decreased, I do not know whether I will even see the difference. That gives it significantly less impact than a periodic dividend payment, which may be cashed in at the local bank.

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Are Dividends Income? (Part 2)

Posted by Mark on October 21, 2015 at 06:43 | Last modified: October 26, 2015 11:46

Since it’s 3-0, I’m not categorizing this as optionScam.com anymore. Nevertheless, I still have a problem with the dividend concept so I’m going to approach this debate from a different angle.

The financial industry is focused heavily on “the suitability standard.” When I pay someone for financial advice, the investment professional must make recommendations tailored to my personal situation. This is a Rule (2111) of the Financial Industry Regulatory Authority. For this reason, advisers compile an investment profile that includes:

• Client age
  
• Other investments
  
• Financial situation and needs, which includes questions about annual income and net worth
  
• Investment objectives (e.g. generating income, preserving wealth, or market speculation)
  
• Investment experience
  
• Investment time horizon
  
• Liquidity needs (i.e. withdrawal of cash to fund living expenses without incurring significant loss)
  
• Risk tolerance (discussed here)
  

Investment objectives may include growth and/or income.

Growth means capital appreciation, which according to Investopedia is:

      > A rise in the value of an asset based on a rise in market price.

In other words, the positive difference between current stock price and the price of the stock when I bought it. Reading on:

      > Capital appreciation is one of the two main sources of investment
      > returns, with the other being dividend or interest income.

The kicker to all this is what happens to the share price when a dividend is paid.

Do you know? This is not a secret but I suspect it is not common knowledge especially to the layperson. I went to a presentation on dividends the other night and it was not even mentioned until I asked about it.

When a dividend is paid, the price of the stock decreases by the dividend amount.

From an accounting standpoint this makes complete sense. If stock XYZ pays out $100M as a dividend then it would make no sense for the market capitalization to be unchanged. The number of outstanding shares does not change so the loss is reflected in a lower share price.

Sleep on this for a night or two because I’m going to come with this pretty hard in the next installment.

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Friday Night Secrets (Part 2)

Posted by Mark on October 15, 2015 at 06:20 | Last modified: October 26, 2015 11:44

I’ve been reviewing an article by Michaely et. al that suggests Friday evenings are used to hide bad news.

The authors conclude:

      > Additional results show that Friday evening announcements are also
      > more likely to be followed by a delisting event or merger completion,
      > suggesting that managers may announce on Friday evening to avoid
      > market scrutiny.

More specifically, they found Friday night announcers were five times more likely to be dropped from an exchange or liquidated. They were more than twice as likely to be delisted due to merger completion within 120 days of the announcement.

      > Friday evening announcements are rare (only 1.08% of earnings
      > announcements), which implies that most firms do not engage in
      > opportunistic announcement timing. Nevertheless, this small portion
      > of announcements provides rather robust evidence that the market
      > is inefficient with respect to certain aspects, such as the
      > response to the timing of news releases.

I found this study very interesting.

Is there really any trading edge here? That would be a different study but this gives at least some reason to think so. Liquidity is important and I would want to get a better profile for what kind of companies make Friday night announcements. Certainly we don’t see an AAPL or GE announcing earnings on Friday night.

I don’t often read full texts of financial manuscripts. I will come back to this in a future blog post to detail some of their good science and give implications for other trading strategy analysis.

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