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Monday, September 17, 2007

Another Bet?

Apparently flush with confidence from his successful bet last year with Duck regarding the price of oil, Oroborous is interested in seeing if he can extend his winnings. Oroborous has made a number of dire predictions for the economy and the markets. For example, in a comment to his post "Morons" he wrote:
"However, buying stocks [on the rally on August 29, 2007] because they're "bargains", with the Dow a mere 6% down from the nominal all-time high, with the economy's warning lights all in the red and flashing, and with the "recession klaxon" sounding, is either speculation of the most egregious kind or simply moronic."
A second example is his comment from "Mountains, Molehills and the Government":
"Rather, the problem is just getting started, and the worst is yet to come."
My response was that the only significant problem facing the economy and/or financial markets was the potentially precipating panic due to the rising subprime mortgage rate of defaults and that the potential for panic seemed to be dissipating. Oroborous replied as follows:
"Would you like to make a small wager on that ?"
I wondered what exactly we might bet on and Oroborous replied:
"You'd have to come up with a description of what you'd be willing to wager won't happen.

"We could use GDP stats, employment figures, foreclosure stats, declines in home prices...

"Whatever you like."
Whatever I like? Excellent! I bet the stock market doesn't go down 100% in the next month!

Actually, being the fair guy that I am, let me propose something more sporting. What I think the fundamental claim that Oroborous is making is that something unusually bad is in store for the markets and the economy. For example, people who are investing right now (or at least on August 29th) are moronic for not seeing a train wreck coming.

I'm claiming that nothing out of the ordinary is likely to occur and that there's no readily available knowledge that makes the current moment a particularly bad (or good) time to invest.

So what's ordinary? One thing that ordinarily occurs is that the Dow Jones Industrial Average chops around an upward trendline of about 6% per year. The standard deviation of the movement about that trendline for any given period can be approximately predicted from lognormal standard deviations of the daily returns. If the lognormal standard deviation of the daily returns is S, the lognormal standard deviation for a period of N trading days is S * (N 0.5). The lognormal standard deviation of the daily returns for the DJIA from August 1st to September 14th is 1.27%. The quarterly, 1/2 yearly, and yearly derived standard deviations to the downside would be approximately 10%, 13%, and 19% respectively.

To have statistical confidence (to the 95% confidence level) that something out of the ordinary has occurred, we would need to see a drop of at least 1.96 standard deviations below the expected trend line. Since my prediction is simply that we don't observe anything out of the ordinary (with statistical confidence), I thus predict (and am willing to bet) that the DJIA doesn't drop more than 17% in the next 90 days, 22% in the next 180 days, or 29% in the next year. (Note that all these calculations are done in the lognormal domain which is why the don't "add" up).

Since the DJIA is more or less as good a measure as any regarding the future health of all aspects of the economy, if Oroborous isn't willing to take one of the above bets, then we have to assume that he and I are in concurrence that nothing unusual and measurable with statistical confidence is likely to occur to the downside during the above periods due to the subprime markets, the housing market, or anything else.


erp said...

That's a safe bet.

Oroborous said...

So are you saying that if the DJIA drops only 28% over the next twelve months, that would confirm that "the only problem was the potential for panic", and that it had "dissipated" ?!?

Oroborous said...

After reviewing the history of the DJIA, it seems to me that you're offering to wager than nothing of historic note will occur in the market, since drops of those magnitudes have all been named.

My impression was that you feel that fears about the imploding housing bubble, recession, and a bear market are overblown and alarmist.

If not, then we are in general agreement, we've just been disagreeing over semantics.

How about this: We'll wager that the DJIA will close above 12,000 sometime in Sep. '08. You take the over and I'll take the under.

Oroborous said...

Or, since you've written that "nothing unusual is likely to occur to the downside" with regard to the subprime markets or the housing market, we could bet on home sales figures, or house prices.

Bret said...


I'm saying two things.

Natural market and economic behavior involves fluctuations and those fluctuations over shorter time frames are generally random and unpredictable.

In particular, all fluctuations within the ranges I've specified are completely ordinary and could be completely explained by random chance and wouldn't prove anything regarding how dire (or not) the current situation is.

If the DJIA drops more than 28% we can have high confidence that you're correct that things currently are dire. If it drops less than that, you might still be right, but random chance might well explain the price fluctuations, and I would also be right in that statisically, there is no evidence of unusual perfomance and that the prices could be explained by random chance.

Again, you are proven correct and I am proven wrong if it drops more than 28% in the next 12 months. Otherwise, there's no useful information regarding our predictions.

I'm willing to take a bet that I'm not proven wrong.

Bret said...

Oops, I'm several comments behind. The previous comments was a response to the 12:33 comment.

Oroborous said...

[If the DJIA drops less than 28% in a given year, random chance might well explain the price fluctuations. Statistically, there would be no evidence of unusual perfomance.]

Sure, if such a drop occurred anomalously.

However, if there were to be a recession, and employment, consumer spending, and corporate earnings dropped, but the DJIA retreated by only 20%, who in their right minds would attempt to argue that these corresponding factors had no influence on the market, and that the drop was purely a matter of random fluctuation ?

A declining market might move in ways that could be attributed to random flux, i.e., that are within the parameters explainable by chance alone, but that merely means that there is considerable overlap between the sets of results obtainable by chance, and those for which a cause can be reasonably determined.

Bret said...

Okay, now on to the 12:59 comment.

oroborous wrote: "How about this: We'll wager that the DJIA will close above 12,000 sometime in Sep. '08. You take the over and I'll take the under."

I did a quick simulation based on nothing but the current price, recent daily returns, and expected yearly return (6%), and it shows a 78% chance of closing over 12,000 and a 22% chance of closing under.

I guess what you're saying is that since you're confident that things are more dire than what is currently reflected in the price, you're willing to spot me what would normally be a 3:1 odds advantage.

While that doesn't really tell us much about why the price ends up wherever it does in Sep. 2008, given that the odds are solidly in my favor (based on nominal data) and for the entertainment of post-Judd alliance readers, I'm probably willing to take such a bet, depending on what we would be betting.

What do you have in mind?

Oroborous said...

A book, or DVDs or CDs. Under $ 50.

But, unless you don't want to spend any more time on this, perhaps we should agree on two or more conditions that have to be met, to decrease the likelihood of the outcome being random.

How about also total nonfarm payrolls, not seasonally adjusted, of under 138MM for Aug. '08 ?

That would be net zero employment growth for the next year.

Or, I'm open to suggestions.

Bret said...

So, let's see if I understand what you're proposing:


(a) DJIA does NOT close over 12,000 during September 2008


(b) total nonfarm payroll, not seasonally adjusted, is under 138MM for August 2008


You win!


If (a) OR (b) are false,

I win!

How did you and Duck chose the book?

Oroborous said...

The winner gets to choose. In that case, I chose well after winning.

But nothing prevents choosing ahead of time, or making that choice public.

So, let's see if I understand what you're proposing:

Yes, as far as you've written.
But an important point is that the conditions must be such that you feel comfortable that meeting them falls within your 95% confidence level that there was readily available knowledge that made the current moment a particularly bad time to go long real estate or equities.

If this set of conditions won't do it, then we can add something else.

Bret said...

oroborous wrote: "But an important point is that the conditions must be such that you feel comfortable that meeting them falls within your 95% confidence level that there was readily available knowledge that made the current moment a particularly bad time to go long real estate or equities."

No, this bet doesn't show that.

First, I agree that right now isn't a particularly great time to get into real-estate, at least here in San Diego, though we probably disagree as to the magnitude of the problem.

Second, the only thing that will show with statistical confidence that there was readily available knowledge that made the current moment a particularly bad time to go long equitites is if they drop 17%, 22%, or 29% in the next 90, 180, or 365 days respectively.

Anything short of that can be explained by random chance. Much of that chance may relate to potential events that are already foreseen and even partially incorporated in the price.

For example, there's some chance of a war with Iran, and let's say that would be detrimental to the stock market. Let's say the probability of war with Iran is 10% (to use a round number). Then approximately 10% of the impact of war is incorporated in the current prices. If war actually breaks out in the next year, the negative impact on prices will be 10 times as great as currently expected. That doesn't mean we're wrong now. It just means that the information available is limited and unpredictable future events will affect prices in ways that can't be totally foreseen.

Multiply that effect by numerous events that may or may not happen and are only partially reflected in stock prices based on the probabilities of them happening and you get a huge variance in the possible price next September.

Only once we get beyond a 29% drop can we have confidence that the prices moved so far that currently available information was overlooked by a significant number of traders.

Even there, it'll be a little tough to assign blame. For example, if war broke out with Iran and the stock market dropped 29%, how would we know that the war didn't completely explain the drop and that the current subprime mortgage problems caused a significant part of the drop?

The analysis is the same for virtually every other economic indicator, even real-estate prices. If a dirty bomb goes off in Phoenix and real-estate drops, what would that tell us? It might be because Phoenix was overbought, it might be because of the radioactivity. Who would know and how?

Oroborous said...

...approximately 10% of the impact of war is incorporated in the current prices.

Yeah, that's the theory. But as it turns out, humans in reality don't always play the role of homo sapiens computus.

If they did, then the housing bubble in SoCal would have deflated four years ago.

People there were getting mortgages that they KNEW that they wouldn't be able to make the regular payments on, once their interest rates reset from the teaser rate.
They were essentially betting that home prices would never go down, and that they'd always be able to roll the debt over.

Is that rational? Will you argue that some people did forsee that home prices might drop, and that therefore the insane '06 prices were actually LOWER than they might have been, if nobody appreciated that there was risk involved?

Further, let us examine the behavior of the S&P 500 and DJIA during the recession of Jul. '81 - Nov. '82, the longest post-WW II recessionary period according to my analysis of data from the National Bureau of Economic Research,* and a period when the Fed Funds Target Rate averaged over 9%, which would have retarded market growth.

During the early 80s, the S&P 500 fell only 27%, peak to trough, and the DJIA dropped a mere 24%.

Should we then conclude that we have no definitive means of assessing whether the prolonged recession and high interest rates affected the markets ?!

* The recession of Nov. '73 - Mar. '75 was officially of equal length, but the recession of '81 - '82 followed right on the heels of the brief '80 recession.

If a dirty bomb goes off in Phoenix and real-estate drops, what would that tell us? It might be because Phoenix was overbought, it might be because of the radioactivity. Who would know and how?


That's a classic example of "book-smart but foolish".

Anyhow, I have two thoughts about betting on market outcomes: One, the 29% drop doesn't account for inflation, which has officially been running at an average of 3% over the past four years, and two, the markets themselves are a SECONDARY reflection of reality, and one with global inputs.

Betting on market movements is betting on the market, not directly on the U.S. economy.

Finally, if you do want to bet on a market, calculate what a statistically-significant drop would be for the S&P 500 over the next 12 months, less 3% for inflation, and I'll take the under, IF you'll give me 2 - 1 odds.

Bret said...

S&P500 is actually a bit more volatile than DJIA, so it would require a larger drop for statistical confidence in readily available current information being ignore.

However, its close enough, so we'll take the 29%, subtract out the 3% per your request (note that 6% was already subtracted out for the average gain over that period). So that'd be a 26% drop.

Yesterday, S&P500 closed at 1529. The statistically confident threshold (26% drop) is 1131. The S&P500 is down a bit today (as I write this) so you're making headway already!

Also, the market only needs to close below that any time before the end of september next year for you to win. That's the statistical definition of what I'm looking at and that should move the odds in your favor a bit. In other words, if the S&P500 closes below 1131 before September 2008 you still win even if it's over that price during September 2008.

Lastly, I'll give you 2 to 1 odds as requested ($100 of books for you if you win versus $50 of books for me if I win).

Let me know if that works for you.

What I don't understand is why you're interested in this bet with me when you can get much better odds with the market for not all that much money. With a futures account you could buy an in the money PUT for DEC S&P500 futures for very little margin and if you're on your way to winning your bet with me, you'll make ten times your bet.

Oroborous said...

Works for me.

My interest in betting with you is simply to add a small real-world outcome to what is otherwise a purely academic disagreement.

If I make money in the market, nobody cares but me. The counterparty is anonymous.

Bret said...

Okay, we're on.

Oroborous said...

What happens if an S&P 500 company goes bankrupt, and gets replaced in the index ?

Obviously, I think that we should track the performance of the S&P as it's now composed, even if that's a little divergent from the index as of Sep. '08, as my contention is that some of those companies are in predictable danger of failing - for instance, Countrywide Financial Corp.

Bret said...

"Obviously, I think that we should track the performance of the S&P as it's now composed..."

Obviously? I think not.

As it's composed today? Or as of October 5th (they're adding Nobel Energy and deleting Archstone-Smith due to a merger)? How are you gonna calculate the Oro500 (or Oro4NN) with weighting and modifications for dividends, etc.? I certainly have no interest in calculating the Oro4NN or checking your results. In addition, your example of Countrywide represents less than one-tenth of one percent if deleted.

The bet is on the S&P500, not some random index.