A thought on probability

I was at my in-laws yesterday and my father-in-law and I were watching some football. As the games were winding down, some channel surfing landed us on the movie, "Once Upon a Crime."

There's a scene where Marilyn Schwary (Cybill Shepherd) is playing roulette. She places her bet on 13 - and wins - on her first spin. On her next spin, she again places her entire bet (including her winnings from the previous spin) on 13.

My father-in-law asked, rhetorically, "what are the chances it will be 13 twice in a row?" I knew what he meant, but it got me thinking... The chances 13 would come up twice in a row is exactly the same as any other two numbers coming in sequence. The probability of that specific sequence occurring may be small, but low-probability events occur frequently.

What lowers the probability in this case is specification. To restate my father-in-law's question including the specification he probably intended, "what are the chances she will bet on 13 - and win - twice in a row?" That dramatically lowers the probability of the event occurring. In fact, if she were to bet on 13 and win 3-4 times in a row, everyone would start to be incredibly suspicious the game was rigged.

She wouldn't even have to bet on 13 each time. The specific sequence of numbers does not matter, since each sequence of 3-4 numbers has equal probability of occurring. What matters is that she correctly chooses the sequence of numbers ex ante.

Too Little, Too Late

According to a CNN Money article, the Fed is expected to propose rules to crack down on mortgage lending tomorrow. Some examples of the rules being considered are (emphasis mine):

• barring lenders from penalizing subprime borrowers - those with spotty credit or low incomes - who pay their loans off early.
• forcing lenders to make sure that borrowers, especially subprime borrowers, set aside money to pay for taxes and insurance.
• restricting loans that do not require proof of a borrower's income.
• examining lenders' failure, in some cases, to consider a borrower's ability to repay a home loan.
• improving financial disclosure so people better understand the terms and conditions of their mortgages and get this information when it is most useful.
• curtailing abuses in mortgage advertising.

All of these were obviously needed years ago, especially the point in bold. Probably most stated-income loans made in the past couple years should have never been originated. I say 'most' because these loans are legitimate for some borrowers, e.g. the self-employed.

It is beyond me why the Fed did not address this practice until now. How could they not know these loans were being mis-used, when it's their job to regulate the financial system?

Not only are these rules too little, too late - the market is currently addressing some of them. To ask a rhetorical question, how many lenders are currently originating sub-prime or stated-income loans?

While these rules are necessary, they will do nothing to help the current mortgage-induced liquidity crisis.

Source:
Fed to crack down on shady lenders
WASHINGTON (AP), 12/15/2007 12:08 PM ET

All in One Day

The following post is courtesy of Ryan, my good friend and fellow market-watcher. We regularly discuss the stock market. Below he provides his unique insights on today's (yesterday's) market action. So, without further ado...

I've been in banking for 7 years. I spent the first 4 years picking stocks for mutual funds, and worked on a trade desk the first 2 of those years. Those were really fun days in 2001 and 2002. Amongst other things, I witnessed the dot-com bubble burst, the first surprise rate cut by the Fed (a non-meeting 50bps cut), and Sept 11 - all from a unique perspective.

The last 3 years I've worked on the mortgage side, with the last year and half with Josh in capital markets. I have continued to follow the stock market the entire time. What is so amazing about today is that I can't remember a day quite like it. I remember many days when the market opened high, stayed high all day, and then gave back everything in the last hour... but that's nothing like today.

To put it into perspective (I'm going to use the Wilshire 5000 to represent the total market, though I'm sure you can pick any index and get a similar story):

Open: 14,923.64
9:15 AM: 15,256.52
3:15 PM: 14,820.01
3:45 PM: 14,999.82
Close: 14,994.54

The market deflated like a tire with a slow leak between 9:15 and 3:15. I can't remember such a slow, steady, uneventful decline after a strong opening during one trading day. It was really amazing to watch.

For those keeping count, the first 15 minutes returned 2.23%, or approx. 0.15% a minute. For the next 5 hours of trading, the market gradually worked its way to a -0.69% return on the day (the market's low point). The amazing thing is that anybody who bought the market at 9:15 AM had lost 2.86% in 5 hours (or -0.0095% a minute). So, they were giving away 1 minute of gains from the morning's rally every 15 minutes and 30 seconds that passed after that peak.

But the market wasn't done; then it rallied for another gain of 1.21% at the peak around 3:45 PM. That's a gain of of 0.04% a minute. The VIX showed this as the period with the greatest amount of volatility. The market finally closed with a gain 0.47% on the day.

To summarize: you have a gain of 2.23%, loss of 2.86%, gain of 1.21%... IN ONE DAY!!! If you told me these were market returns, I would tell you that was 3 separate days of activity. But nope, it happened in one day.

Today's market behavior underscores investors' ignorance of the depth and magnitude of the credit crunch. Five of the largest central banks were effectively forced to work together, and that's something to cheer about? Ironically, not long after the central banks' announcement, Wachovia and Bank Of America both issued additional warnings on their exposure. Its like the market was cheering "Yeah, they're going to get us out this mess," and then screaming "OH NO!!! THE MESS!!!".

As I write this, the Nikkei is down 1.51% (its lunch time over there right now). I guess they don't think much of the worlds' central banks' coordinated efforts either.

Non-Farm Payrolls: 12-07-2007

To quickly recapitulate the press release:

• The unemployment rate remained unchanged at 4.7%
• Employment increased 94,000 to 138,467
• Hourly earnings rose $0.08 to $17.63
  

Judging from the economic calendar on CNN Money (please advise if there's a better calendar) and the reaction of S&P 500 futures, the unemployment rate - which was expected to increase - and employment were better than expectations.

However, average hourly earnings came in quite a bit above expectations (0.46% MOM versus an expected 0.30%). That doesn't bode well for inflation expectations...

Will today's stronger-than-expected employment situation change market expectations of Tuesday's Fed action? I'll update with the information from the Cleveland Fed after the market closes.

UPDATE:
Estimates of a 50 bps reduction in the Fed Funds Rate declined using either December of January options. Expectations of a 25 bps cut now stand near 60% and 70% for December and January options, respectively (in each case the remainder represents the probability of a 50 bps cut).

The USD and EU Inflation

Jim Jubak wrote a great piece on the woes of the USD this past Tuesday. The article focuses on inflation in the European Union affecting the USD. The entire article is worth reading, but I highlight a very significant portion below.

I'll admit I don't know what the two banks will decide Thursday and Dec. 11. But I do know what will happen if the interest-rate gap between the two currencies shrinks further:

• The U.S. dollar will fall, and the euro will climb.

• The price of oil, which trades in U.S. dollars, will go up again, as oil producers adjust prices so that they at least break even on the dollar's decline.

• Gold prices will climb as investors seek an alternative to the U.S. dollar as well as safety from uncertainty about the global economy and a likely bump in U.S. inflation.

• U.S. equities will rally in the days after a Federal Reserve rate cut but then give much of the gains back as overseas investors pull money out of the U.S. financial markets in response to the dollar's weakness.

Today the ECB held their target rate at 4.0% instead of raising it, as Jim anticipated. The overnight interest rate spread between the US and EU remains 50 bps (instead of falling to 25 bps if the ECB had raised their rate). That may give the Fed a bit more breathing room to cut by 50 bps instead of 25.

As of today, the Fed Funds Futures market expects a 60% probability of a 25 bps cut and a 30% chance of a 50 bps reduction using January options (click for image). Using December options, the expectation is about 50% for both 25 and 50 bps reductions. You read that correctly, nearly a 100% expected probability of a rate cut.

Source:
The dollar's perfect storm worsens
Jim Jubak
Jubak's Journal, 12/4/2007 12:01 AM ET
http://articles.moneycentral.msn.com/Investing/JubaksJournal/TheDollarsPerfectStormWorsens.aspx

Two-for-two!

Markets rallied today for the second day in a row, with very broad and large price gains. But what do these two days mean? Today's volume was higher than yesterday's on both the NYSE and NASDAQ, but they're both near their average volumes during the past few weeks of selling. In short, volume wasn't terribly impressive.

Looking at the table below, we see that market internals are not particularly strong.

	11/27/2007			11/28/2007
	NYSE	AMEX	NASDAQ	NYSE	AMEX	NASDAQ
% Adv Issues	66.0	43.1	54.1	84.8	67.0	76.0
% Dec Issues	31.9	49.7	42.1	13.6	27.5	20.8
% Adv Volume	71.8	72.6	79.0	94.8	87.0	88.1
% Dec Volume	27.2	26.6	20.1	5.0	12.5	11.7
New Highs/Lows	0.08	0.20	0.15	0.45	0.33	0.41

Advancing issues and volume were strong today, but advancing issues were weak yesterday. Probably the most troublesome is the ratio of new highs to new lows. Both yesterday and today new lows outnumbered new highs by at least a 2-to-1 margin! For what it's worth, today saw half as many new lows as yesterday. I expect some selling into this 'rally' later this week.

Freddie Mac : 2007Q3

Freddie Mac reported much worse than expected results this morning. Here are the highlights from the press release:

• Third quarter loss of $2.0 billion reflects a higher provision for credit losses and losses on mark-to-market items.
• Provision for credit losses of $1.2 billion reflects the significant deterioration of mortgage credit as a result of continued weakness in the housing market.
• Total GAAP mark-to-market losses of $3.6 billion primarily include $1.5 billion in interest-rate related items and $2.3 billion in credit-related items.
• Fair value, before capital transactions, decreased by approximately $8.1 billion primarily due to widening of net mortgage-to-debt option-adjusted spreads and valuation losses on credit-related items.
• Increase in management and guarantee income reflects continued guarantee portfolio growth.

When this 'liquidity crunch' started in July/August, investors would only buy pools securitized by Fannie and Freddie. Prior to that, it was questioned if those two GSEs were needed. Will investors be as willing to buy from Freddie now that their pools are worse than expected?

UPDATE: Some excellent answers to the above questions in Calculated Risk's comments (excerpts are below; follow the links for entire comment).

Tanta said,
The whole idea of having the GSEs continue to buy loans in this market is that they will actually bid when no one else does. That is, they are supposed to be out there saying that there is, actually, a difference between 51 bps and 450 bps and they will bid accordingly.

gse doom said,
...their [Fannie Mae and Freddie Mac] securities are "understandable" and the payment of both principal and interest is guaranteed. The loans in their securities are underwritten to more conservative and standardized guidelines, and the securities themselves are more easily analyzed and modeled. Fannie Mae and Freddie Mac guarantee to the bond holder the timely payment of both principal and interest.

October Inflation Reports

Both PPI and CPI inflation reports were released last week. PPI came in below expectations, while CPI was in line with the consensus estimate.

The chart below shows both headline and core PPI near the top of their range since 2000. Further, PPI inflation has been increasing since mid-2006. This doesn't bode well for moderating CPI inflation, if PPI leads CPI.


As expected, there was a sharp increase in YOY headline CPI inflation in October, while CPI inflation ex food and energy remained near 2.5%. In this week's Thoughts From the Frontline, John Mauldin shows YOY headline CPI inflation will remain high for the rest of 2007, due to last year's low index levels. He also describes the changes made to the CPI index in the early 1990's (substitution and hedonics).

The chart below shows two lesser-known 'core' measures of CPI inflation created by the Cleveland Fed. Both the median and trimmed-mean CPI show an increase in October. Further, Mauldin's analysis suggests we should expect these two core measure to increase in the next two months.


While the Fed doesn't have explicit inflation targets, it's believed 1-2.5% is in their comfort range for core PCE inflation. All three measures of core CPI inflation shown above are at or near 2.5%. As many have noted, this doesn't leave the Fed much room to cut thier target rate if the economy begins to slow substantially.

Dunkin' Donuts Coffee

I have an affinity for Dunkin' Donuts hazelnut coffee. But the closest Dunkin' Donuts to me, by geography, is in Champagne-Urbana IL; the closest by time is Chicago O'Hare airport.

I was excited when they announced that they would start selling their coffee in grocery stores. However, it costs $7.99 per 12 oz bag ($10.67/lb.)! I decided to see how much it cost on their website. Here's the breakdown:

Pounds	Price	S&H	Total Price/lb.
1	$5.49	$7.00	$12.49
10	$54.90	$11.55	$6.65
20	$109.80	$19.02	$6.44
50	$274.50	$40.81	$6.31
500	$2,745.00	$352.35	$6.20
1000	$5,490.00	$700.89	$6.19

Clearly, buying 1000lbs at a time is the best deal. Seriously, why can you even do this on their website? Anyone feel like ordering even 50 pounds to see what happens?

Big Rally, Small Volume

Today's rally was staggering - with the Dow, S&P, and NASDAQ up 2.5%, 2.9%, and 3.5% respectively. But how much participation was in the move? Is this simply a relief rally from the past four sessions of selling, or the beginnings of a new advance?

100 million fewer shares traded on the NASDAQ compared to yesterday, but volume was close to its average over the past few weeks. Today was also a 9-to-1 up day on the NYSE and NASDAQ, where 90+ percent of the total volume traded was attributed to advancing issues. However, the number of issues making new 52-week lows outnumbered those making new highs by a wide margin on both exchanges.

The 9-to-1 up day is encouraging but hasn't been a reliable indicator of a new uptrend by itself. However, the lack of total volume and the number of issues making new lows is cause for concern. Time will tell, but this appears to be a relief rally...

CRB Core Inflation? Hardly.

Barry Ritholtz uses the CRB "excluding food and energy" in a post today to show how high 'core' inflation is. I found the data in the post's chart at www.economagic.com. A bit of investigation into the data revealed the "ex food & energy" series to be the CRB Raw Industrials Index.

The Raw Industrials Index is composed of hides, tallow, copper scrap, lead scrap, steel scrap, zinc, tin, burlap, cotton, print cloth, wool tops, rosin, and rubber. All but hides, tallow, rosin, and rubber are contained in two other sub-groups:

1. The "metals" sub-index (40% of the 'core' index) contains copper scrap, lead scrap, steel scrap, tin, and zinc.
2. The "textiles and fibers" sub-index (30% of the 'core' index) is comprised of burlap, cotton, print cloth, and wool tops.

Therefore, this 'core' index is mainly composed of 5 metals and 4 textiles. Further, if you decompose the rise in the raw industrials index into its two main components - metals and textiles - you can see that the recent rise in metals prices is the main cause of the rise in its parent index (see chart - click to enlarge).

Barry has presented some good arguments against the use of core inflation in monetary policy. This is not one of them, however.

UPDATE: I should have guessed, Barry intended to be a bit over-the-top in his post...


For those interested, the R code used to create the chart is below.

require(fImport)

rawInd <- economagicImport("crb/crb12", freq="monthly")@data[-(1:7),]
rawInd$DATE <- as.Date(rawInd$DATE)
textiles <- economagicImport("crb/crb13", freq="monthly")@data[-(1:7),]
textiles$DATE <- as.Date(textiles$DATE)
metals <- economagicImport("crb/crb14", freq="monthly")@data[-(1:7),]
metals$DATE <- as.Date(metals$DATE)

plot( rawInd$DATE, rawInd$VALUE, type="l",
ylim = range( c( rawInd$VALUE, textiles$VALUE, metals$VALUE ) ),
main = "Selected CRB Indicies",
xlab = "Date", ylab = "Index Value",
lwd = 2 )
lines( textiles$DATE, textiles$VALUE, col="red" , lwd = 2 )
lines( metals$DATE, metals$VALUE, col="blue", lwd = 2 )
legend( "topleft",
legend = c("Raw Industrials","Textiles Sub Index","Metals Sub Index"),
col = c( "black", "red", "blue" ),
lty = c( 1, 1, 1 ),
lwd = c( 2, 2, 2 ),
bty = "n", inset = 0.05 )

savePlot( "Select_CRB_Indicies", type="png" )

Inconsistent Market Response to Inflation

The PPI released this morning showed headline inflation much below forecast, due to falling energy prices; but core PPI was higher than forecast. Stock futures markets rallied on the news. This is completely inconsistent with prior month's releases, when the markets rallied on relatively high headline readings because core inflation was at or below expectations.

It would seem that greater than expected PPI inflation, which also remains above the Fed's supposed comfort range of 1-2% year-over-year, would lessen the probability of the 50 bps rate cut the market's been hoping for.

UPDATE: It appears that some or all of the futures rally could be attributed to Lehman's earnings report. Even so, the PPI report didn't evoke any negative reaction.

Explaining the CPI-U

This Monday's Outside the Box E-Letter by John Mauldin features a great publication from the Congressional Budget Office. To whet your appetitie, here's the introduction:

This week in Outside the Box we look at a Congressional Budget Office publication that dives us the details on how the consumer price index for all urban consumers (CPI-U) is created. This is, as the CBO posits, the best-known official measure of inflation.

The brief that follows will venture to explain the methods used to construct the CPI-U, and how and why the index's estimates of inflation might differ from a consumer's perceptions of price changes. Though I think this article may be somewhat akin to discovering what components comprise the makeup of sausages (knowledge that is usually best left undiscovered), it is useful to understand just how the inflation data is constructed. Some of the points they make are controversial, especially when it comes to "hedonic" pricing, which they refer to as "shifts in the quality of goods and services over time." This does allow for some quite subjective influence in the inflation numbers. While I will visit this topic in a later letter, it is good to know what is and is not being measured.

Bernanke Speech : 07-10-2007

This Tuesday, Ben Bernanke spoke to the NBER-sponsored Summer Institute regarding inflation expectations and inflation forecasting. On inflation expectations, Bernanke summarized recent literature focusing on defining and measuring inflation expectations, and how to use that information to forecast and control inflation.

The more interesting part of the speech concerned how the Federal Reserve Board forecasts inflation. Rather than recapitulating the most intriguing portion, I've included it below:

The Board staff employs a variety of formal models, both structural and purely statistical, in its forecasting efforts. However, the forecasts of inflation (and of other key macroeconomic variables) that are provided to the Federal Open Market Committee are developed through an eclectic process that combines model-based projections, anecdotal and other "extra-model" information, and professional judgment. In short, for all the advances that have been made in modeling and statistical analysis, practical forecasting continues to involve art as well as science.

The forecasting procedures used depend importantly on the forecast horizon. For near-term inflation forecasting--say, for the current quarter and the next--the staff relies most heavily on a disaggregated, bottom-up approach that focuses on estimating and forecasting price behavior for the various categories of goods and services that make up the aggregate price index in question. ... In making very near-term price forecasts, the staff also uses diverse information from a variety of sources, such as surveys of prices of gasoline and other important items, news reports about price-change announcements, and anecdotal information from our business contacts. Conceptually, one might think of this effort to distinguish transitory from persistent price changes as a more nuanced way of estimating the underlying inflation trend, analogous to the trend measures provided by more mechanical indicators such as trimmed-mean or weighted-median inflation rates.

An accurate forecast of very near-term inflation is important not only for its own sake but also because it provides a better "jumping-off point" for the longer-term forecast. Because inflation continues to exhibit some inertia, improved near-term forecasts translate into more-accurate longer-term projections as well.

For forecasting horizons beyond a quarter or two, detailed analyses of individual price components become less useful, and thus the staff's emphasis shifts to inflation's fundamental determinants. Food and energy inflation are forecasted separately from the core, using information from futures prices and other sources. However, forecasts of core inflation must take into account the extent to which food and energy costs are passed through to other prices.

In addition to the above, Bernanke notes that the Board uses a range of econometric models to forecast inflation at longer horizons. However, the models' estimates are not so robust as to permit sharp inferences, so the Board's long-term forecasts "inevitably reflect a substantial degree of expert judgment and the use of information not captured by the models." Finally, he turns to the Board's use of inflation expectations in forecasting inflation.

Worthless Headline of the Day

CNN's Money site wins today's Most Worthless Headline of the Day award with this link on their homepage: Prices up in latest inflation read. Really, you don't say? Whoever wrote that must have a firm grasp of the blatantly obvious.

To be fair, that's the link displayed on their homepage, not the actual headline of the article.

Is Inflation Moderating?

Beginning with the March, 2007 FOMC statement, the Fed has stated that its primary concern is that inflation will not moderate as expected. The FOMC statement and minutes from the May, 2007 meeting and a CNBC interview with Chicago Fed President Michael Moskow on Friday reiterate this concern.

This suggests the inflation measure(s) the FOMC consults when determining monetary policy are at the upper end of their (collective) comfort range. The two charts below (click for larger image) show headline/core CPI and PCE inflation from 2000 to the present. Contrary to traditional headline/core inflation measures, the core inflation measures created by two regional Federal Reserve Banks show that inflation has not fallen from its levels of 2005 through early 2006.



Both year-over-year CPI and PCE headline inflation have decreased significantly from their levels of 2005 through early 2006. Compared to the same historical period, both measures of PCE core inflation have barely budged, and all measures of CPI core inflation have risen.

Both the PCE less Food & Energy and the Dallas Fed's Trimmed Mean PCE inflation measures have declined slightly since their respective peaks in late 2006. The Trimmed Mean PCE has fallen slightly less, however. Also worth noting, the spread between PCE less Food & Energy and Trimmed Mean PCE seems to be a pretty steady 20-30 bps.

CPI inflation is more interesting. CPI less Food & Energy inflation has fallen from its late-2006 peak of nearly 3% to less than 2.3% in April, 2007. However, 16% trimmed mean inflation has only fallen from 2.9% to 2.75% over the same period. Further, median CPI inflation remains near its levels (3.5%) of late 2006.

Moskow said, "The last quarter, GDP growth was very low – six-tenths of a percent. That’s history now. This quarter should be much stronger and, as we move through this year into next year, I see us moving toward potential growth, or long-term trend growth, in the economy." But if productivity continues falling and wage growth continues accelerating, I'm not sure what the Fed expects will contain inflation pressures. Then again, maybe that's why the FOMC's primary concern is inflation failing to moderate as desired...

I'll provide an update when May's CPI data come out on 6/15.

Inflation and the Fed

In this morning's commentary on The Big Picture, Barry Ritholtz writes:

Of course, many pundits, traders and investors -- and a goodly part of the Federal Reserve -- have convinced themselves that there really wasn't any inflation, ...

I agree with Barry regarding the many pundits, traders, and investors that have convinced themselves that there really wasn't a reason to worry about inflation (just look at the stock market action of the past few months), but I disagree that many Federal Reserve policy-makers are not concerned about inflation.

I know I've said it before on Barry's blog, but I'll say it again here: I worked at a Federal Reserve District Bank in 2004-05 as an economic research analyst - assisting the economists with their research.

There was much discussion regarding the measurement error of core CPI beginning in early 2005. That's about the time the Cleveland Fed came out with their median CPI measure, and the Dallas Fed - whose head of research is mentioned in Barry's post - created their trimmed mean PCE measure. Furthermore, the FOMC minutes have stated for some time that the main concern of the Fed is that inflation will fail to moderate as expected (i.e. inflation - by whatever measure they're now using - is above their comfort zone).

I'm not aware of the evidence Barry has seen that suggests that a good part of the Federal Reserve have convinced themselves that there is no inflation. One could argue that - given inflation data - the Fed should raise rates, but this is what is discussed/argued in FOMC meetings.

UPDATE:
Here's an interesting excerpt from the Reuters article referenced in Barry's post:

On the other hand, Rosenblum said that because the Fed relies on a number of different measures of price pressure, there was not much risk the flaws in core inflation would translate into a policy mistake.

"The fact that core is misbehaving now because food and energy are moving in one direction instead of up and down is not all that troublesome to me because we have the good sense to look at the wide range of indicators out there," he said.

FOMC Minutes : 05-09-2007

I think the following paragraph is the largest take-away from the FOMC minutes released this afternoon (all emphasis mine).

In the Committee's discussion of monetary policy for the intermeeting period, all members favored keeping the target federal funds rate at 5-1/4 percent. Recent developments were seen as supporting the Committee's view that maintaining the current target rate was likely to foster moderate economic growth and a gradual ebbing in core inflation. Members continued to view the risks to economic activity as weighted to the downside, although with turmoil in the subprime market appearing to have remained relatively well contained and business spending indicators suggesting a more encouraging outlook, these downside risks were judged to have diminished slightly. Members agreed that considerable uncertainty attended the prospects for inflation, and the risk that inflation would fail to moderate as desired remained the Committee's predominant concern.

I'm anxious to see how Fed Funds Futures will react to this release.

Bad Timing, or Bad Reasoning?

My employer sends a small newsletter with each quarterly 401(k) statement. I skim over them, since they usually contain fairly basic information. This quarter, one of the articles was a little too basic...

The article discouraged participants from "timing" the market. I generally agree with that principle, but not for the reasons given. The article concluded that timing the market is risky because (1) if you missed the market's top-performing days, your portfolio's overall return would drop dramatically (see Chart 1), and (2) many mutual funds have rules against "market timing" (I think they really meant "rules against frequent trading").

My first thought after reading the first point was: what would have the performance been if I had missed the market's worst-performing days? When I look at Chart 2, I can't help but wish I would have missed those 10 worst days and doubled my annual average return over the period.

Granted, it's extremely improbable to be able to miss the 10 worst performing days; but I would think it equally improbable to happen to miss the 10 best performing days.

(Note: the charts above use S&P 500 returns net of dividends. Including dividends would not change the analysis in a meaningful way, since the dividends lost over 5 or 10 days would be negligible.)

As I mentioned, I would generally agree trying to time the market isn't a good idea; but it's not because you might miss those best days. Timing the market is extremely difficult and most would be better off with a well diversified portfolio.