I was listening to someone from the top level of the private wealth department of a big bank, and this person, when asked for financial rule #1, said that staying invested in the market was the crucial thing, highlighting that rule with this claim: If you missed the best ten S&P days since the March, 2009 low, you lost half the gain you would have otherwise had.

A disclaimer: This post is *not* arguing against buy and hold, or staying invested.

However, this claim is made frequently, that if you missed the best X days since such and such a date, then you missed most/half/all of the gain since. Here is an analysis of the latest version of the claim, about the S&P since March, 2009.

Using SPY daily data:

SPY % change, Close 8 March 2009 to Close 6 May 2016: +197.40%

SPY % change after removing the ten Best days (by % change) from the series: +89.72%

So the claim, on the face of it, is true: The gain is more than cut in half by removing the ten Best days. But what if we remove the ten Worst days?

SPY % change after removing the ten Worst days (by % change) from the series: +360.60%

There would definitely be an advantage in avoiding the ten Worst Days. What if we remove *both* the ten Best and Worst days?

SPY % change after removing both the ten Best and ten Worst days from the series: +193.82%.

Pretty much right back where we started. But realistically, how would one miss the Best ten days or avoid the Worst ten? Here is a graph of the distribution of those days over the indicated time period:

(also: for a larger version)

Of course, because of volatility regimes, the Best and Worst days are clustered together - you can't have one without the other. Just to count it another way: There are a total of 1804 trading days in the study, so with 20 Best and Worst days total, you might expect one to come along about every 90 trading days if they were evenly spaced out. But when we examine the dates of the Best and Worst days and measure the distance from each one to its nearest opposite-type day, we get:

Date   -    B/W - Distance to nearest opposite-type day
Aug-26-15   Best   2
Aug-24-15   Worst   2
Nov-30-11   Best   21
Nov-9-11   Worst   13
Oct-27-11   Best   13
Aug-18-11   Worst   7
Aug-11-11   Best   1
Aug-10-11   Worst   1
Aug-9-11   Best   1
Aug-8-11   Worst   1
Aug-4-11   Worst   5
Jun-4-10   Worst   25
May-20-10   Worst   10
May-10-10   Best   10
Apr-20-09   Worst   11
Apr-9-09   Best   10
Mar-30-09   Worst   7
Mar-23-09   Best   7
Mar-12-09   Best   18
Mar-10-09   Best   20

mean distance: 9.25 days

So it might make more sense to say, "Stay invested so you don't miss the next 2013." Or something like that. But the "ten Best days" claim implies a model of the market where it just sits there doing nothing and every once in a while has a great day - more like a lottery than a time series.

Coda: From March 2009 through this week, the S&P gained about 1360 points. If you look at the daily minimal path - just the absolute number of points the S&P traverses as it moves from the previous Close through the Open, High, and Low, to the next Close - then over that same time period, the S&P traversed about 58,000 points, or approximately 42.8 points traversed for every 1 point gained. Maybe that is a simple mathematical angle on "risk aversion".

Bill Rafter comments: 

A very good study and worthy of discussion.

Yes the best days and worst days cluster, implying that volatility is symmetric. Ergo, why worry about it; just stay long. Except that looking at the chart (admittedly not a good way to do research) you can see that the clustering occurs at times when the equity market probably should be avoided altogether. Of the 5 periods of clustering, 4 of those periods fit that description. The exception is March 2009, but that was THE bottom of the market, occurring after a 50+ percentage decline. So the big bank wealth management guy has a little start-date bias in that the period chosen demonstrates that buy-and-hold is profitable without worry, whereas choosing a start-date in 1997 would drop the compound annual ROR considerably and have substantial worry.

Since equity markets are volatility-averse, a volatility screener should enable the investor to be out of equities (and possibly long bonds) during the clustering. The wealth management guys will identify that as "timing" which they say pejoratively, although most financial decisions are made with some timing in mind. One may buy a home, renegotiate a mortgage, open a business or even marry based on whether the "time is right". Those bottom up decisions of everyday life filter up to the market.

I dare say the big bank wealth management guys stayed long during the 2000-2003 and 2007-2009 declines, and the buy-and-hold argument provides them with the cover they need for those flubs.

Let me posit a side question to illustrate the volatility point. Suppose you knew the stock market would be higher over the next 12 months. What stocks should you own? Logic would suggest that since the market is going up, the more volatile stocks (i.e. high beta) should go up the most. But at most times that is incorrect, as investors pay a premium for lower volatility, and those high beta stocks were yesterday's high betas, not tomorrow's. 

Ralph Vince writes: 

You don't want to miss the ten worst days, they offer opportunity (as a buyer) as the ten best days do as well (as a holder, or seller).

The days you want to miss are the ten dullest days. Or maybe the thousand dullest days of the period in question. Those are the days where the office is a prison cell, the weather out the window looks glorious. Then the guy with the thing that blows leaves and grass and all that, is rummaging around outside the window for twenty minutes, and you realise days like this simply waste your life.

No, please, give me volatility, there's money in those days.

anonymous writes: 

From 10 years ago (August 2006 SpecList):

"Mr. Cassetti wrote, "Suffice to say, many studies now show that missing the worst days is more important that participating in the best days."

I was intrigued about what this meant, and if true, what it says about the distribution of returns. To analyze this, SP500 weekly returns since 1950 were ranked, and the compound final return calculated. (weekly returns since less cumbersome than daily) Then compounded returns for an hypothetical/supernatural trader who managed to be in the market for all but the *best* and *worst* week-pairs out of all 2950 weeks. The next trader was in for all but the best 2 and worst 2, and so on, for a total of about 1477 ranked returns. (trader 1477 was only in the market for the middle-return two weeks out of 55 years, which seems implausible enough that I might try it)

Here is a chart of the compound returns found by successively eliminating [X*(top,bottom)] week pairs, neglecting transaction costs:

The pink line corresponds with a final return for B/H of about 75 (7500%). One notes that while it is true that compound return improves by removing BOTH top and bottom weeks, further successive removal actually hurts returns. After X>363, removing additional top and bottom weeks reduces return. And since only 363/1475 top+bottom week-pair eliminations improve returns over buy and hold, if (without skill) you try to eliminate such weeks, you have about a 75% chance of under-performing.

This exercise is a successive subtraction of the extreme tails from the returns distribution, and shows that unusually large down weeks are greater in magnitude than unusually large gains. In 75% of the week pairs (just over +/- 1SD), the corresponding ranked gainer weeks are larger than losers. Another curiosity is the kink in an otherwise smooth curve around (elimination of) weeks 36-54, which could result from some kind of asymmetry in the tails."

One way to reduce exposure to volatile regimes is to be in-market only when long moving averages are up, which can be done in real time.


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