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I apologize for the length of this post but hopefully those who read it will find it worthwhile. In summary, I attempt to evaluate the individual steps of the F4 variations and determine if the logic of the step is a valid argument for the premise of the theory. I specifically discuss terms of logic and not analysis. So, there are no numbers but its just as boring.

For those who don't want to read this but want to know if you should be mad, just respond angrily if you are; someone who invests by faith, someone who created a version of the F4, someone who believes in the F4 no matter what anyone else says, someone that requires no evidence whatsoever to invest in the F4, someone who believes TMF because they write books, someone who uses faulty logic to support their claims or someone who views the critique of arguments as useless nitpicking . . . oh yeah and anyone who doesn't like Qwerty or thinks Datasnooper's arguments aren't applicable.
</Disclaimer>

I was reading an old article by Ann Coleman and in it I saw this statement: “Just like truth is the best defense against claims of libel, the defense for strategies 'discovered' by data mining is that they have a valid rationale.” http://www.fool.com/DDow/1999/DDow990510.htm Hopefully, those of you who have spent time reading the posts on this board know that this statement is incorrect. But specifically, the reason this statement is incorrect is because it uses faulty logic. The implication of the message is that successful strategies that are irrational are datamined therefore successful strategies that are not irrational are not datamined. In the world of critical thinking and logic this is known as a fallacy of denying the antecedent and it has this invalid structure:

A = B, therefore since not A, then not B.

Translating that into English for this case would mean, if a successful theory is irrational (A) it must be datamined (B) so if a successful theory is not irrational (Not A), then the theory must not be datamined (Not B). This is an improper argument in that it is possible for rational theories to be datamined. As such this argument doesn't help support the premise that the F4 isn't datamined. So, I started thinking about the logic of the steps of the F4. I'm not talking about the “common sense” of it but rather the base logic of the arguments put forth. KirkWeber recently wrote: The idea (not even calling it a theory) of a good company (big name) stock that once paid a high dividend (sign of doing well) that is now on the "outs" and might make a comeback still appeals to me. This is an excellent example of why I wanted to analyze the logic of the F4. I agree with Kirk that the premise is appealing, but that appeal goes away IF the steps taken in translating the premise to a strategy aren't logically sound arguments that fit the premise. If that were to occur, then the performance of the resulting strategy would be completely unrelated to what you attempted to do in the first place. The result is that the strategy wouldn't fulfill the premise. That is my take on the F4. Almost all of the steps of the F4 do no use sound logical arguments. They use fallacies of false logic or as Soui might say, logic filled with “bogosity”.

Below, I have outlined the F4 steps and point out where (IMHO) there is no logic to support the premise. I will NOT be addressing the validity of the “common sense” (whole 'nother issue) but rather the support of the premise by the use of proper logic. This will be an exercise is critical thinking not in statistical analysis. Ready? (deep breath) . . .

Here is the F4 premise as I see it: Develop a common sense market-beating strategy that is simple to follow, quick and easy to implement and selects a group of beaten-down stocks from strong companies to hold for one year, playing a likely turnaround.

F4.0

THE TMF VIEW: “First, 30 stocks is a manageable number. After all, the system is supposed to be easy. But, more importantly, those 30 stocks usually represent financially sound companies with enormous resources behind them.” http://www.fool.com/ddow/2000/ddow000929.htm

THE LOGICAL VIEW: 30 stocks are more manageable than many other indices and help make for an easy strategy. The companies should be sound companies with good financial strength or they wouldn't be part of the DOW. It's an easy index to use as a benchmark. This argument fits the premise well.

Step 2: Rank by yield highest to lowest.

THE TMF VIEW: “A high yield (high relative to other stocks of the Dow) means that the price is low relative to the dividend. The dividend is "on sale." http://www.fool.com/DDow/1998/DDow981130.htm

THE LOGICAL VIEW: Ignoring recent splits then yes, the dividend is “on sale” relative to other stocks of the DOW, but that is not the same thing as the future stock price being on sale, which is the premise of the theory. Are you buying a dividend or are you buying a turn-around stock!? This F4 argument is a false hypothetical conditional syllogism. Huh?! In English that means, you can't say:

A=B, therefore A=C

Or in this case high yield = cheap dividend therefore high yield =cheap stock price. This step only works if you assume that cheap dividend equals cheap stock price (B=C) otherwise the argument does not support the premise. Any introductory finance class teaches that stock price is the present value of expected future cash flows, not past cash flows. Perhaps the implication of the F4 is that current dividends predict future dividends, which predict future stock price. However, there is no known correlation (and none even proposed) between current dividends and future stock price. Which means this step doesn't support the premise of picking “beaten down” companies at all.

Step 3: Pick the 5 lowest priced stocks from the previous step.

THE TMF VIEW: “Robert Sheard expands a bit on this in The Unemotional Investor [pp. 88-90, 95], arguing that (a) lower price is indeed associated with greater volatility, and (b) greater volatility magnifies returns -- either profits or losses. Since high-yield stocks should more often produce profits than losses (that is the point of all DDA strategies, right?), it therefore follows that picking the lowest-priced members of the high-yield list will improve your returns.” (from a Dave Goldman post http://boards.fool.com/Message.asp?mid=10403176&sort=postdate )

THE LOGICAL VIEW: At the outset this argument is a fallacy of confirming the antecedent, which has this invalid structure:

If A then B, therefore since B then A.

In normal-speak, this step assumes that for a stock to recover (B) it will have to have high volatility (A), which isn't necessarily true. But regardless, IF high volatility (A) causes a recovery (B) then the premise is still supported. Although you won't identify all stocks that recover, those that you do identify, will recover. Two problems develop though.

First of all, the assumption that A=B is based solely upon the data set used. Why should DOW stocks recover? Because they did in the data set used. That's not an explanation, it is an observation. This is circular reasoning, which is known as petitio principii or “begging the question” and it is the essence of the datamine (the data forces a theory and so the theory makes sense because it fits the data). This type of argument merely restates an assertion. It is like saying, “The reason the stock's return was so good was because market factors caused the price to go up.” This logic does not add any support to the argument and it does not help to translate the premise. For the premise of the theory to be translated accurately, the logic must stand on its own or in other words, an argument can not be defined by the result it is trying to predict. The assumption that A (high volatility) = B (high future price) is a false premise because it based upon the informal fallacy of begging the question and therefore it is a flawed argument. It's the classic argument of “there is nowhere to go but up”. Well, except down.

Secondly, the argument is completely irrelevant to the F4. The effect was not for Dow stocks but ALL stocks, when you remove penny stocks from the equation, the volatility effect goes away and since the Dow isn't comprised of penny stocks, this argument does not apply. From a logical point of view, the argument that A=B doesn't apply because you are starting with “Not A”. So this is not only a flawed premise but also an irrelevant hypothetical syllogism.

There is no logical argument presented to support that price alone will separate the company that will recover from the company that won't. In addition, IMO this is double weighting of price (once in the yield and once here), which means if price is irrelevant (more on that in the next step), then it is doubly irrelevant (whatever that means) here.

Step 4: Drop the lowest price stock from your list and double up on the second lowest priced stock.

TMF VIEW: “In BTD, O'Higgins mentioned in passing that the second-highest-ranked stock was the "Penultimate Profit Prospect." It had both a high yield and a low price, and tended to do better than the others. He explained that the lowest-priced stock, which you would think would be the best performer, tended to be a company in real financial trouble . . . With the rationale that too low a price could mean a stock was not just having a bad stretch, that it was really in trouble, we felt comfortable dropping the highest-ranked stock. But, never entirely comfortable.” http://www.fool.com/ddow/2000/ddow000901.htm

THE LOGICAL VIEW: Again, this is a fallacy of begging the question (the step makes sense because it works in the data set). It does not argue why the lowest price is a signal of trouble and the second lowest is a signal of a great turn-around, it merely claims that it happened in the data. Suppose that, indeed, low price meant trouble, then why would one stock at \$25 be obviously ready to go under but another stock at \$25.01 be in such great shape that you need to own twice as much? How does price in isolation determine the ability to rebound (if indeed it is beaten down in the first place). No explanation of this is provided other than that it fit. So, while this step may fit the data set used, it doesn't fit the premise of the theory.

Actually, it is worse than that because it contains contradictory arguments. In the same article, Ann Coleman later wrote, “In fact, the average performance of all number one stocks was about the same as that of the other Foolish Four stocks. So, why didn't we include it? With almost 40 years of monthly data, one fact stood out. That first stock was highly volatile.” Well that directly contradicts with the previous step's argument that claimed high volatility for DOW stocks is good.

So, in summary the steps 2 through 4 of the F4.0 strategy don't use proper (or sometimes any) logic to support the premise. Of course there have been many modifications since then, but I think you will see that all of the modifications have no logical foundation either. So, let's look at the most popular, the F4.1 and F4.2.

F4.1
Steps 1-3: Same as above, so steps 2 & 3 are not valid arguments.
Step 4: Drop the lowest priced stock from step 3 unless the lowest priced stock isn't both the highest yielding stock and lowest priced stock in which case you drop the #5 stock.

TMF VIEW: “It's really just common sense. Dropping the number one stock essentially means you are substituting the fifth-ranked stock. Historically, their returns are about the same, but number five's returns are far more consistent. So, why not use it and save yourself the possible grief that comes from the occasional stock in real trouble?” http://www.fool.com/ddow/2000/ddow000901.htm

THE LOGICAL VIEW: (prolonged silence with glazed stare at screen) . . . Sorry, Déjà vu. Same reasons here as step 4 in the F4.0 (begging the question). This the most blatant use of datamining and circular reasoning so far. TMF does not even attempt to propose any argument at all but directly references the results of the data set (It works because it does). In addition, this describes that the #5 stock is less volatile than the #1 stock and therefore preferable. Of course this contradicts with the previous step that attempted to maximize volatility.

This step is merely an observation of performance with no explanation as to how it separates beaten down stocks from those that are “too beaten down”. Unless the lowest priced stock isn't both the highest yielding stock and lowest priced then it is in trouble, if it is the lowest priced stock and the highest yielding stock then it is not in trouble. Huh!? Why? The F4 never addresses the question why this matters at all but rather states that it fits the data.

THE F4.2
Step 1: Same as F4.0 and F4.1. No problems here.
Step2: Rank the 30 DJI stocks according to the following equation (highest value first): RP ranking = Yield x Yield / Price. (This is the same as yield divided by square root of price or D^2/P^3.)

TMF VIEW: This method selects stocks with a high yield and low price, but by using the square root of price it selects stocks with higher beta. (Beta, a measure of stock volatility, correlates inversely with price but more closely with the square root of price. Inverse correlation means low price = high beta.) http://www.fool.com/School/DowInvesting/FoolFourEvo/FoolFourEvolvesVer42.htm

THE LOGICAL VIEW: (Déjà vu)^2. In an article last year Ann Coleman wrote, “I have seen the claim from academic studies that volatility correlates with the square root of price made, and, while I accepted it at face value at first, I later learned that another study had found that the correlation disappeared when penny stocks were excluded.” http://www.fool.com/ddow/1999/ddow990722.htm So same problems as Step 3 of the F4.0 and F4.1 above (false premise, irrelevant syllogism). Again, there is no explanation as to why low price should matter but rather assuming that it does and tweaking the numbers to find the optimal performance from data. No logic here at all, just curve-fitting.

Step 3: Throw out the top ranked stock, and pick the next 2 or 4 stocks.

TMF VIEW: “Sometimes being #1 is too much of a good thing -- in the past, stocks with both the highest yield and lowest price (lowest price of the 10 high yield stocks, not the entire Dow) have usually turned out to be in serious trouble. You are better off just dropping it in favor of the #5 stock, although technically, as long as the stock with the highest RP ratio isn't both the highest yielder and lowest priced, you could pick it instead of #5.” http://www.fool.com/school/dowinvesting/dowinvesting.htm

“. . . the yield/sqrt price formula was close enough to the high yield/low price method that it often ranked the same stock at the top of the list. Elan took the underperformance to mean that the same phenomenon was at work without spelling it out.” http://boards.fool.com/Message.asp?mid=13235527&sort=collapsed.

THE LOGICAL VIEW: (Déjà vu)^3 or is that (Déjà vu)^2/ (Presqué vu)^3. Same problems here as with Step 4 with F4.0 and F4.1 (begging the question). Elan wrote in a post, “I also looked at variations of the number of stocks to include - the top 5, four stocks without the top ranked stock (2,3,4,5), or 2,3,4. The choice of 2,3 came out best. The next best is picking 2,3,4,5. The top ranked stock should be avoided, as we do with the Foolish Four.” http://boards.fool.com/Message.asp?mid=10054789&sort=username

This is an argument with a false premise. It is obvious from Elan's statement that the F4.2 made no attempt to explain why the #1 stock should be sometimes dropped and sometimes kept, but rather accepted this step as valid because it fit the data and fit with the logic of the F4.0. But, since the logic of the F4.0 was flawed (begging the question), the same mistake is being made a second time. Ann Coleman writes, “If irrational conclusions are indeed being drawn, then drawing further conclusions based on them would be dumb.” http://www.fool.com/ddow/1999/ddow990511.htm I agree.

Ann correctly states, “the yield/sqrt price formula was close enough to the high yield/low price method that it often ranked the same stock at the top of the list”. In other words, it shouldn't be surprising that D/P^2 will get you close to the same results as D^2/P^3 because they are highly correlated. A relatively low price is going to provide a relatively high ratio in either formula. Therefore Elan's formula is not, the “same phenomenon” at work, rather it is a repetition of the same faulty logic. There is no corroborated effect, there is merely the same flawed “test” applied twice.

In summary, the original F4 used flawed arguments or NO arguments when creating the steps of the strategy. The revisions since then have provided no arguments whatsoever but are merely tweaking factors to try and improve the returns of the original flawed strategy. I will close this post with another quote from Ann (my bold added).

Remember, "data mining" is not finding a correlation between two factors -- it is looking through a large number of factors and picking the one that correlates most highly with what you are looking for or adding factors that improve results but that have no logical reason for doing so. http://www.fool.com/ddow/1999/ddow990511.htm

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