Strategy for the Bogleheads contest
Strategy for the Bogleheads contest
The opening statement of the Bogleheads Contest:
"Welcome to the 2019 Boglehead Contest designed to demonstrate how difficult it is to forecast future stock prices."
demonstrates how difficult it is to understand certain games. Entering the best forecast of the SP500 will not optimize your chances of winning. The way to optimize your winnings is to find the highest probability gap in the other guesses. This is best done very close to midnight just before entries are closed. To estimate the best gap, you need to estimate the distribution of closing prices. One way to do that is to use a normal distribution with the base rate mean and s.d. That would be about 8% growth and about 19% s.d. I think.
Optimal play is cutthroat because it will have you betting .01 above or below a competing player. You will be maximally taking the gap from another player.
But if you play this way you are arguably breaking the rules of the contest because the rules say "Forecast the closing price of the S&P 500 Index on December 31, 2019" but you will not be forecasting the close, you will be estimating a gap which is typically far away from a legitimate optimal forecast.
In a book on the strategy of another game, the author said that it was a "game about a game" and many confused the game itself with the game it was about. The Boglehead contest is also a game about a game of sorts (the stock market) and the game has its own strategy independent of the stock market.
"Welcome to the 2019 Boglehead Contest designed to demonstrate how difficult it is to forecast future stock prices."
demonstrates how difficult it is to understand certain games. Entering the best forecast of the SP500 will not optimize your chances of winning. The way to optimize your winnings is to find the highest probability gap in the other guesses. This is best done very close to midnight just before entries are closed. To estimate the best gap, you need to estimate the distribution of closing prices. One way to do that is to use a normal distribution with the base rate mean and s.d. That would be about 8% growth and about 19% s.d. I think.
Optimal play is cutthroat because it will have you betting .01 above or below a competing player. You will be maximally taking the gap from another player.
But if you play this way you are arguably breaking the rules of the contest because the rules say "Forecast the closing price of the S&P 500 Index on December 31, 2019" but you will not be forecasting the close, you will be estimating a gap which is typically far away from a legitimate optimal forecast.
In a book on the strategy of another game, the author said that it was a "game about a game" and many confused the game itself with the game it was about. The Boglehead contest is also a game about a game of sorts (the stock market) and the game has its own strategy independent of the stock market.
Re: Strategy for the Bogleheads contest
I have noticed this for a long time, but I've also seen "cute" or "why not" guesses that likely aren't meant to be the closing price, like 2222.22 or 2345.67. Since noone knows what will happen, all you have to do is make a guess (reasonable or not) to enter.
Those who don't enter won't even have a chance of winning.
Those who don't enter won't even have a chance of winning.
Re: Strategy for the Bogleheads contest
“Eighty percent of life is showing up.”celia wrote: ↑Fri Jan 04, 2019 1:18 pmI have noticed this for a long time, but I've also seen "cute" or "why not" guesses that likely aren't meant to be the closing price, like 2222.22 or 2345.67. Since noone knows what will happen, all you have to do is make a guess (reasonable or not) to enter.
Those who don't enter won't even have a chance of winning.

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Re: Strategy for the Bogleheads contest
Given how lowstakes and wildly unpredictable this contest is, I'd venture to say anybody betting .01 over another person intentionally is just being mean. Choose another random number. This ain't the Price Is Right!
Re: Strategy for the Bogleheads contest
One year I went to the trouble to try to estimate an optimal bet, but I did not bet the optimal 0.01 above an opponent. I gave them some room. This did not greatly reduce my estimated win probability and it avoided the mean cutthroat thing.lukestuckenhymer wrote: ↑Fri Jan 04, 2019 1:32 pmGiven how lowstakes and wildly unpredictable this contest is, I'd venture to say anybody betting .01 over another person intentionally is just being mean.
This year, there was a 2500.01 bet just above a 2500.00 bet that came very close to winning. But I don't know if that involved any meanness.
It is lowstakes. Adding 1% to your win probability is maybe worth 20 cents in expected value.
Re: Strategy for the Bogleheads contest
I conjecture that less than 20% of one's win probability in this contest is showing up, more than 80% is finding a good gap.columbia wrote: ↑Fri Jan 04, 2019 1:24 pm“Eighty percent of life is showing up.”celia wrote: ↑Fri Jan 04, 2019 1:18 pmI have noticed this for a long time, but I've also seen "cute" or "why not" guesses that likely aren't meant to be the closing price, like 2222.22 or 2345.67. Since noone knows what will happen, all you have to do is make a guess (reasonable or not) to enter.
Those who don't enter won't even have a chance of winning.
It has to do with the fact that people, even Bogleheads, just don't have a good grasp of the implications of the mean and standard deviation of the stock market.
The open this year is about 2500, so the base rate estimated close is 2700. Two standard deviations above 2700 is about that is 3727. Therefore, 2.5% of the win probability is above 3727 according to the base rates and the normality assumption. Not a lot of players cover that range, there tend to be some good gaps up there.

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Re: Strategy for the Bogleheads contest
The contest is only for like a free book or two  correct? And with dozens of pages of entries I'd say the odds are low.
You are way over thinking it.
I did enter a decimal place for mine but only because I was slow to enter and the rules stated you couldn't guess the same as someone else. I apologize if I entered a decimal place above someone else (I didn't do a .01)  wasn't trying to be mean and if someone thinks I was, I will gladly donate the prize (to the person I am 0.01 above) and just maintain the bragging rights.
You are way over thinking it.
I did enter a decimal place for mine but only because I was slow to enter and the rules stated you couldn't guess the same as someone else. I apologize if I entered a decimal place above someone else (I didn't do a .01)  wasn't trying to be mean and if someone thinks I was, I will gladly donate the prize (to the person I am 0.01 above) and just maintain the bragging rights.
Re: Strategy for the Bogleheads contest
I read thetadamsmar wrote: ↑Fri Jan 04, 2019 2:41 pmI conjecture that less than 20% of one's win probability in this contest is showing up, more than 80% is finding a good gap.columbia wrote: ↑Fri Jan 04, 2019 1:24 pm“Eighty percent of life is showing up.”celia wrote: ↑Fri Jan 04, 2019 1:18 pmI have noticed this for a long time, but I've also seen "cute" or "why not" guesses that likely aren't meant to be the closing price, like 2222.22 or 2345.67. Since noone knows what will happen, all you have to do is make a guess (reasonable or not) to enter.
Those who don't enter won't even have a chance of winning.
differently than you. I took that to mean that those who don't participate won't have a chance at winning. (The numbers weren't meant to be literal, in my opinion.) In other words, you need to participate to win, not be a wallflower.“Eighty percent of life is showing up.”
Re: Strategy for the Bogleheads contest
In 2018 479 showed up. Showing up got you a .002 probability of winning on average.columbia wrote: ↑Fri Jan 04, 2019 1:24 pm“Eighty percent of life is showing up.”celia wrote: ↑Fri Jan 04, 2019 1:18 pmI have noticed this for a long time, but I've also seen "cute" or "why not" guesses that likely aren't meant to be the closing price, like 2222.22 or 2345.67. Since noone knows what will happen, all you have to do is make a guess (reasonable or not) to enter.
Those who don't enter won't even have a chance of winning.
It is pretty easy to find a gap that will boost that by 500% so that more than 80% of your win probability comes from finding a gap.
Therefore, that maxim does not apply to this contest.
Re: Strategy for the Bogleheads contest
Well, no chance is 0%. Showing up is 0.2%. Finding a gap can be 1%.celia wrote: ↑Fri Jan 04, 2019 2:54 pmI read thetadamsmar wrote: ↑Fri Jan 04, 2019 2:41 pmI conjecture that less than 20% of one's win probability in this contest is showing up, more than 80% is finding a good gap.columbia wrote: ↑Fri Jan 04, 2019 1:24 pm“Eighty percent of life is showing up.”celia wrote: ↑Fri Jan 04, 2019 1:18 pmI have noticed this for a long time, but I've also seen "cute" or "why not" guesses that likely aren't meant to be the closing price, like 2222.22 or 2345.67. Since noone knows what will happen, all you have to do is make a guess (reasonable or not) to enter.
Those who don't enter won't even have a chance of winning.differently than you. I took that to mean that those who don't participate won't have a chance at winning. (The numbers weren't meant to be literal, in my opinion.) In other words, you need to participate to win, not be a wallflower.“Eighty percent of life is showing up.”
One can do more than take it literally, one can take it mathematically.
Perhaps you mean you are taking it nonpecuniarily? It's just for fun.
I think is worth thinking about mathematically just to better grasp the uncertainty of the stock market.

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Re: Strategy for the Bogleheads contest
Similar to the stock market, you are not the only person who knows this strategy. How does that change things?
Re: Strategy for the Bogleheads contest
If everyone played an optimal strategy then the game would reach financial equilibrium. Everyone would wait till the last few seconds before the deadline to bet. No one would have information on the bets of others. The optimal equilibrium strategy would be a mixed strategy where each player would pick a random sample from the normal distribution with mean 8% and s.d. 19%.MotoTrojan wrote: ↑Sat Jan 05, 2019 1:09 amSimilar to the stock market, you are not the only person who knows this strategy. How does that change things?
In the current situation, the Nash equilibrium calculation indicates that players are getting about a twentycent nonpecuniary payoff. Calling it a "nonpecuniary payoff" assumes that the players are making a rational financial choice. It's more properly called an unexplained gap that could be explained in a number of ways. We tend to not pro forma assume the rational choice theory these days. But I don't think Nash ever used the term "nonpecuniary payoff". He was not an economist and I think he generally avoided putting an interpretation on his mathematical equilibrium unless he had to. It could be explained as a behavioral anomaly or just by the fact that time is money ("it's not worth the effort").

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Re: Strategy for the Bogleheads contest
I've seen this happen with my guesses more than a few times over the past few years, a later poster will bet either below or above my choice by a mere .02 or less. I get a real chuckle out of it, especially when I intentionally play to "lose".lukestuckenhymer wrote: ↑Fri Jan 04, 2019 1:32 pmGiven how lowstakes and wildly unpredictable this contest is, I'd venture to say anybody betting .01 over another person intentionally is just being mean. Choose another random number. This ain't the Price Is Right!
"One should invest based on their need, ability and willingness to take risk  Larry Swedroe" Asking Portfolio Questions
Re: Strategy for the Bogleheads contest
I had no idea people were taking it this seriously!
My guess was pretty random. I sure hope I didn't guess .01 above or below someone.
Actually, my guess was the ROUGH average of the first however many guesses I looked at (putting some faith in the collective Bogleheads wisdom). I didn't even have any idea where the S&P was the day I made the guess. This took me about 5 minutes.
Of course, people had been pretty equally bullish or bearish to that point, so I pretty much guessed the current level without noticing (oops!). I'm pretty sure any random guess  within reason  has about as good a chance of success as any other (disregarding the .01 gamesmanship approach).
Some people's elaborate strategies make me wonder: How many of the last 5 or 10 winners used one of these careful strategies, and how many were random guesses? It seems to me that winners often talk about their guess being a rough stab in the dark.
If most winners spent less than 10 minutes on their guess, it would seem to me that a random guess is a lot more efficient use of one's time.
Best of luck to everyone, whether your guess took 5 seconds or 5 days!
My guess was pretty random. I sure hope I didn't guess .01 above or below someone.
Actually, my guess was the ROUGH average of the first however many guesses I looked at (putting some faith in the collective Bogleheads wisdom). I didn't even have any idea where the S&P was the day I made the guess. This took me about 5 minutes.
Of course, people had been pretty equally bullish or bearish to that point, so I pretty much guessed the current level without noticing (oops!). I'm pretty sure any random guess  within reason  has about as good a chance of success as any other (disregarding the .01 gamesmanship approach).
Some people's elaborate strategies make me wonder: How many of the last 5 or 10 winners used one of these careful strategies, and how many were random guesses? It seems to me that winners often talk about their guess being a rough stab in the dark.
If most winners spent less than 10 minutes on their guess, it would seem to me that a random guess is a lot more efficient use of one's time.
Best of luck to everyone, whether your guess took 5 seconds or 5 days!
Re: Strategy for the Bogleheads contest
I don't think that would tell you much since you don't know how many guesses were careful vs random overall, the winners might be random guesses because most are random guesses.
Also, I know that at least one player is careful bet an s.d. or two away from the mean, but they don't bother to wait late and ensure that they get a big gap.
Re: Strategy for the Bogleheads contest
That's a fair point from a statistical standpoint. Still, if no one's winning with the intensive approach, that's a pretty rough track record for all the effort that goes into it.
That said, as long as people are having fun putting that effort in, to each their own. My original point was that I didn't be realize that people were putting so much into it.
Re: Strategy for the Bogleheads contest
I think I have already shown with an analytic approach that the effort is worth only about 20 cents, maybe 50 cents for a twobook prize. Certainly not more than a dollar.develop wrote: ↑Sun Jan 06, 2019 2:59 pmThat's a fair point from a statistical standpoint. Still, if no one's winning with the intensive approach, that's a pretty rough track record for all the effort that goes into it.
You are suggesting an empirical approach. A direct empirical approach of looking at the winners would take maybe a 1000 years of data. If you win only once in 100 years you are about 5 times better than just a random guess, but it takes a lot of data to confirm a 1% win rate.
Right now, the effort is pretty large because Ralph Averson has not loaded the contest page, so its hard to tabulate the gap information. Maybe he will not load the page till after betting is closed. If the data can be easily tabulated in a spreadsheet you can just eyeball it or do a bit up analysis with the normal distribution to find a good gap.
Re: Strategy for the Bogleheads contest
Sounds like fun! I wish you the best of luck!tadamsmar wrote: ↑Sun Jan 06, 2019 3:36 pmI think I have already shown with an analytic approach that the effort is worth only about 20 cents, maybe 50 cents for a twobook prize. Certainly not more than a dollar.develop wrote: ↑Sun Jan 06, 2019 2:59 pmThat's a fair point from a statistical standpoint. Still, if no one's winning with the intensive approach, that's a pretty rough track record for all the effort that goes into it.
You are suggesting an empirical approach. A direct empirical approach of looking at the winners would take maybe a 1000 years of data. If you win only once in 100 years you are about 5 times better than just a random guess, but it takes a lot of data to confirm a 1% win rate.
Right now, the effort is pretty large because Ralph Averson has not loaded the contest page, so its hard to tabulate the gap information. Maybe he will not load the page till after betting is closed. If the data can be easily tabulated in a spreadsheet you can just eyeball it or do a bit up analysis with the normal distribution to find a good gap.
Re: Strategy for the Bogleheads contest
Being $0.01 above or below a competing player may work only if you have a single competitor. With 500 competitors, the optimal play is to bet inside the widest gap in the competitors' bets.
Victoria
WINNER of the 2015 Boglehead Contest. 
Every joke has a bit of a joke. ... The rest is the truth. (Marat F)
Re: Strategy for the Bogleheads contest
Do you think many players are really strategizing like this? I figure during the first day or two you could easily pick a number and you owned it. Once the thread grew, there was a greater chance that someone else had already selected the same number, so you would need to tweak your original guess. Whether you tweak it by .01 or 1.01 or 10.01, may just depend on how devoted you are to your original guess.
Re: Strategy for the Bogleheads contest
It has to do with the shape of the normal distribution (bell curve). The gap in question is a probabilityweighted slice of the bell curve. The section labeled "B range" is an example of a gap. The two verticle sides of this section would the locations of the two competing bets. In order to optimize, you want to get as much of the light blue area as possible, because that area is the probabilityweighted slice of the gap. Your section will always be 1/2 of the horizontal width of the blue section. In order the optimize the size of your section of the light blue section, you will bet .01 above the leftmost side of the light blue section, .01 above a competitor's bet.
But, of course, the yellow section of the best one to bet and the optimal bet would not be on the edge for the yellow section. But, In the Bogleheads contest bets are crowded around the mean, so the section at the mean of the bell curve (which is also the highest point) is not going to be the location of the optimal bet. (It could be, but I am conjecturing that it is very unlikely to be the location of the optimal bet). Therefore, the optimal gap will be like the blue section and the optimal bet will be a "cutthroat" bet.
However, it is true that betting a bit above the optimal bet does not hurt your win probability much. The optimal bet in the Bogleheads Contest tends to be farther out in the tail where the gradient is flatter, so you can be relatively nice to your opponent without losing too much probability.
Re: Strategy for the Bogleheads contest
If you bet as late as possible, then you can analyze all the other bets and pick the biggest gap. Perhaps not worth the effort, but can be done and does optimize your chances of winning.GerryL wrote: ↑Mon Jan 07, 2019 1:34 pmDo you think many players are really strategizing like this? I figure during the first day or two you could easily pick a number and you owned it. Once the thread grew, there was a greater chance that someone else had already selected the same number, so you would need to tweak your original guess. Whether you tweak it by .01 or 1.01 or 10.01, may just depend on how devoted you are to your original guess.
I did this 2 or 3 years in the past, but I bet .01 above a competitor in only one of those years. Someone noticed probably because I also had a thread on the strategy that year, but, of course, I was not breaking the rules. In other years I used a nicer and somewhat less optimal bet and left my competitor with an above average chance of winning.
Last edited by tadamsmar on Mon Jan 07, 2019 8:53 pm, edited 1 time in total.

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Re: Strategy for the Bogleheads contest
Except for the minor detail that the normal distribution may not be a good model for the distribution of the S&P500 index.It has to do with the shape of the normal distribution (bell curve).
Taking a break from Bogleheads.
Re: Strategy for the Bogleheads contest
The logic (that the optimal bet is a cutthroat bet) would hold for all probability density functions that fall off monotonically from the mean, including fattailed distributions. That would probably be the set of all plausible closing price distributions.

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Re: Strategy for the Bogleheads contest
It's not obvious to me that monotonicity holds in the left tail for that set.tadamsmar wrote: ↑Mon Jan 07, 2019 9:09 pmThe logic (that the optimal bet is a cutthroat bet) would hold for all probability density functions that fall off monotonically from the mean, including fattailed distributions. That would probably be the set of all plausible closing price distributions.
Re: Strategy for the Bogleheads contest
My previously supersecret method posted for all to see:
+10% over the previous year's close.
Unless the previous year had a very low gain, or loss, in which case add 5% (+15%)
Modify the resulting number to look nice. This year 3033.33 had a nice ring to it. "From the glasslined tanks at Old Latrobe." Lucky.
This is the year. I guarantee that this method is equally valid compared to all other methods.
I have entered twice and not won once, which is well within the range of expected values.
+10% over the previous year's close.
Unless the previous year had a very low gain, or loss, in which case add 5% (+15%)
Modify the resulting number to look nice. This year 3033.33 had a nice ring to it. "From the glasslined tanks at Old Latrobe." Lucky.
This is the year. I guarantee that this method is equally valid compared to all other methods.
I have entered twice and not won once, which is well within the range of expected values.
The discovery of America, and that of a passage to the East Indies by the Cape of Good Hope, are the two greatest and most important events recorded in the history of mankind.  Adam Smith, 1776
Re: Strategy for the Bogleheads contest
But the widest gap is probably between outliers, such as 20,000 and 10,000. Would you then pick 15,000 even though the S&P index is more likely to be closer to 2,500? So what if your guess covers a large range (12,50017,500 in this case), since the odds are very low it would be anywhere near there.
Re: Strategy for the Bogleheads contest
So, you thinks it's plausible that a price far away from the mean would have a higher probability than a value closer to the mean? Possible, but I don't find it plausible.desafinado wrote: ↑Mon Jan 07, 2019 9:15 pmIt's not obvious to me that monotonicity holds in the left tail for that set.tadamsmar wrote: ↑Mon Jan 07, 2019 9:09 pmThe logic (that the optimal bet is a cutthroat bet) would hold for all probability density functions that fall off monotonically from the mean, including fattailed distributions. That would probably be the set of all plausible closing price distributions.

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Re: Strategy for the Bogleheads contest
I don’t know the answer, but it is not unreasonable that there could be some very low probability middle ground between “well behaved” outcomes and outcomes resulting from events of great duress or crisis.
Taking a break from Bogleheads.
Re: Strategy for the Bogleheads contest
I suppose the distribution of returns could, in principle, become bimodal. It seems that color distribution of the world population of actual swans may be bimodal with a big population of black swans in Australia. Let's hope that stock market black swans don't become common enough to produce a bimodal distribution.
I think fat tails and black swans could be largely independent phenomena. Fat tails could be somewhat due to just different mean returns in different years.

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Re: Strategy for the Bogleheads contest
In any case, The Boglehead contest should be conducted where people submit their guesses without being able to see other guesses, simulating them all being submitted as a single, atomic action.
Taking a break from Bogleheads.
Re: Strategy for the Bogleheads contest
I regularly make the strategic decision to forecast a bear market, because the contest has more bulls than bears. If the market happens to drop, I might win. This year, I was in second place on December 27, but the market went up on the last two days rather than going flat.
Re: Strategy for the Bogleheads contest
Going for a bear market win is an interesting strategy, particularly this year.grabiner wrote: ↑Wed Jan 09, 2019 8:59 pmI regularly make the strategic decision to forecast a bear market, because the contest has more bulls than bears. If the market happens to drop, I might win. This year, I was in second place on December 27, but the market went up on the last two days rather than going flat.
I have assumed the historical base rate mean of 8%. That seems to favor a bet for a bull market (based on my very limited analysis).
But with the CAPE high, maybe a 0% mean (along with an appropriate s.d. estimate) would be a better estimate. This very interesting study (Figure 5) seems to indicate returns near 0 when the CAPE is 28:
https://www.brandes.com/docs/defaultso ... timing.pdf
Admittedly, the fit is statistically insignificant. The paper attributes the lack of significant association to momentum, but we don't have a positive momentum situation this year because 2018 was a bear. We have a high CAPE and no momentum or maybe even negative momentum.
So, going bear might be a good strategy this year.
But you did not seek a large gap. Your 2018 gap was less than 3 points. If you just added 2 points to your guess then you would have been in a 11+ point gap that would have more than doubled your projected win probability.
I think 1900 may be a relatively good bet, but I have not eyeballed all the other bets to confirm it.
Last edited by tadamsmar on Thu Jan 10, 2019 8:32 am, edited 1 time in total.

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Re: Strategy for the Bogleheads contest
OP, you assume that the market is random. What if you know what the final number is going to be? Then you should guess it.
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Re: Strategy for the Bogleheads contest
Bogleheads:
Whatever your strategy, today (until midnight) is the last day to post in this year's contest.
Best wishes.
Taylor
Whatever your strategy, today (until midnight) is the last day to post in this year's contest.
Best wishes.
Taylor
"Simplicity is the master key to financial success."  Jack Bogle
Re: Strategy for the Bogleheads contest
Or your bedtime, whichever comes first.Taylor Larimore wrote: ↑Thu Jan 10, 2019 10:38 amBogleheads:
Whatever your strategy, today (until midnight) is the last day to post in this year's contest.
Best wishes.
Taylor
Re: Strategy for the Bogleheads contest
I did a backtest of the strategy of looking for a relatively large gap based on the assumption of 8% return with a 19% standard deviation. Here are the gap percentiles of the 16 past winners:
88% of past winners were in the top 60% where the gap had more than a 0.14% of winning.
75% of past winners were in the top 80% where the gap had more than a 0.24% of winning.
63% of past winners were in the top 90% where the gap had more than a 0.34% of winning.
50% of past winners were in the top 95% where the gap had more than a 0.45% of winning.
This is based on 2019 percentiles.
Only 5% of the guesses account for 50% of the past winners. This is the 5% with the highest gaps.
88% of past winners were in the top 60% where the gap had more than a 0.14% of winning.
75% of past winners were in the top 80% where the gap had more than a 0.24% of winning.
63% of past winners were in the top 90% where the gap had more than a 0.34% of winning.
50% of past winners were in the top 95% where the gap had more than a 0.45% of winning.
This is based on 2019 percentiles.
Only 5% of the guesses account for 50% of the past winners. This is the 5% with the highest gaps.