Sell in May and Go Away?

Firstly, I am not a certified financial planner, and you should make your own financial decisions, keeping in mind what is best for you.  Secondly, the future is definitely in plastics.

The Market as a Tool

Chances are, you have some money in the stock market.  Over half of America does.  If you don’t, that’s cool too.  But even if you don’t, you still might have exposure to the markets.  Do you have a 401K through your work?  Stock exposure.  Retirement pension?  Stock exposure.  Work in a soup kitchen?  Stock exposure.  The point is that you should care about the stock markets.  Not the day-to-day, week-to-week, or even month-to-month fluctuations, but how you can use markets as (one of many) tools to grow wealth.  

On average (depending on how you calculate it), money in the stock market has returned about +7% per year.  If you invested today, your return could be more positive.  It could be negative.  It could be really really negative, canceling out 100% of your investment.  But if you just invest in the whole stock market (which you can do via various mutual funds or approximate with the S&P 500) over a long period of time, you should get the average return, which may or may not be 7% in the future, and that would ideally look something like this:

That blue line up there is enticing, turning $1 into $30 over 50 years (and more if you invest longer), but the real market is never that smooth.  People (myself included) are often greedy, and would rather limit their risk (smoother line), or increase their reward (steeper slopes) compared to the market alone.  To that end, there are many strategies (tricks) people espouse to get their yield.  Some of these are smart.  Some are not.  Given the month we’re in, lets tackle one of my (least) favorites.

“Sell in May and Go Away, Buy Back in St. Ledger's Day”

In the last few days I've been doing an informal poll of my friends and about 20% had heard this saying.  The idea is that the stock market does better in the winter and worse in the summer.  The hope is that you catch the good times and miss the bad times, moving your portfolio to cash or equivalents when the market isn't growing, and back to stocks when it is.  Last Wednesday was May 1st, and coincidently the stock market dropped 1% (and has since gone up 2%), which spurred a lot of articles about this.

What is St. Ledger's day?  It is basically the British Kentucky Derby, and it takes place on varying days in September or October.  (That alone might be enough to tell you about the people who made up the saying.)  The varying date thing is weird, and most traders treat Halloween as the buy-back date, giving you 6 months on (November - April) and 6 months off (May - October).

So... does it work?

Rate of the Month

Lets make a worksheet with dates (Column A) and S&P 500 values (Column B).  We can use the first value of the month as a proxy for "The Month," and the S&P 500 value on that day as a proxy for "The Market." (If you follow my work, I am adding a few empty rows at the top and putting the data [A6:B766] as increasing date with increasing row number.)

To figure out how a certain month did, make a new column dividing next month's start value by this month's (type the portion [in brackets]).

(C6) [=B7/B6]

Complete the column and you will notice the last value (C766) is 0.  This is because we don't know next month's value yet and it distorts our numerator, so just assume that the S&P will be flatish this month and put in the value of 1.  If you take the average of this column [=AVERAGE(C6:C766)] you get an average monthly increase of 0.69% which equates to a maximum annual increase of [=1.0069^12] about 8.5%.  

As a math aside (and skip this if you hate the maths) I say maximum, because it matters how close to average the months are.  Two months at 10% give you more than one at 5% and one at 15%.  Think of it like maximizing the area of a rectangle (to get a square).  You can prove it to yourself by using the two months at 10% example and trying to add and remove a percentage "x" to each month:

1.21 = 1.10 * 1.10

vs

y = (1.10 - x)(1.10 + x)

which simplifies to

y = 1.21 - x^2

For real values, y is maximized when x is zero.  Another takeaway from this is that order of the months is not important.  Your bad month (or year) can be in 2009 or in 1955, and it affects you exactly the same (percentage-wise).

A Timely Separation

Now that we have rates for every month we can separate just the ones we want to invest in (Jan, Feb, Mar, Apr, Nov, Dec) and see what their rates are.

(Cell D6) [=IF(OR(MONTH(A6)=1,MONTH(A6)=2,MONTH(A6)=3,MONTH(A6)=4,MONTH(A6)=11,MONTH(A6)=12),C6," ")]

Completing the column and taking the average [=AVERAGE(D6:D766)] shows that these months had a higher average increase of 0.94% than the collection of all months (0.69% calculated earlier).  But what does this mean?  What would happen if we actually invested a dollar?  For that, lets assume we get the monthly increase in our pre-May months, and get no increase in our post-May months because our investment is in cash.  As a comparison, we'll also do the inverse.  (Buy in May and here to stay?)

To make this easy, I assigned E5 and F5 to equal [1].

(Cell E6) [=IF(OR(MONTH(A6)=1,MONTH(A6)=2,MONTH(A6)=3,MONTH(A6)=4,MONTH(A6)=11,MONTH(A6)=12),E5*C6,E5)]

(Cell F6) [=IF(OR(MONTH(A6)=1,MONTH(A6)=2,MONTH(A6)=3,MONTH(A6)=4,MONTH(A6)=11,MONTH(A6)=12),F5,F5*C6)]

If you complete the columns and plot versus time you get a pretty striking picture:

Sometime in the mid 80's, the "Sell in May" strategy started working much better than the "Buy in May" strategy.  So does this answer our question?  Well, not really.  No one does the "Buy in May" strategy, so it isn't a good comparison.

Its time to bring out our Champion.  In the green shorts, weighing in at 700 basis points, a strategy people actually use: Buy and Hold.  New column and graph:

(Cell G5) = [1]

(Cell G6) [=G5*C6]

WOW!  Buy and hold knocks the pants off the Sell in May strategy.  How can this be?  Well, while the Buy in May strategy looked crummy, it still wasn't negative.  Over 63 years it still turned $1 into $3.56, and it didn't take any extra effort or years of investing (because the years were built in).  As an investor, your biggest asset is time, so wasting half of every year seems silly!  Myth Busted!

Right?  Is there ever a time when it would make sense to not be invested in the markets?  A time to be in cash because the market is not just slow, but down?  One way to address this is to find the average rate for each month of the year.  We'll need 12 columns:

(Cell H3) = [1], (Cell I3) = [2], (Cell J3) = [3] ... (Cell S3) = [12]

(Cell H4) = [Jan], (Cell I4) = [Feb], (Cell J4) = [Mar] ... (Cell S4) = [Dec]

(Cell H6) [=IF(MONTH($A6)=H$3,$C6," ")]

First complete the row.  It may look like nothing happened because H6 has a value and all the "False" statements (I6:S6) are blank.  Then complete the columns (which can be done all at once).  Now we have pretty data separated by month.  If you are following along, the data table looks like a series of backslashes, but if we take the average of each column [=average(H6:H766), etc] we can see that the months are indeed different:

Most of the months averaged positive (ranging from +0.2% to 1.7%), although four months averaged negative.  While for January, May, and July the result is less than -0.1%, the real standout here is August at greater than -0.5%.  You can see how the Sell in May strategy got started though, as three of the four losing months are in the proscribed cash period.

Remember Remember Buy Back in September?

Does this mean we shouldn't have money in the market in August?  We'll, lets see what would have happened in the past.  We'll make 12 more columns:

(Cell T3) = [1], (Cell U3) = [2], (Cell V3) = [3] ... (Cell AE3) = [12]

(Cell T4) = [Jan], (Cell U4) = [Feb], (Cell V4) = [Mar] ... (Cell AE4) = [Dec]

(Cell T5) = [1], (Cell U5) = [1], (Cell V5) = [1] ... (Cell AE5) = [1]

(Cell T6) [=IF(MONTH($A6)=T$3,T5,T5*$C6)]

Complete the row.  Complete the column.  Plot the individually excluded months with the Buy and Hold control and viola:

Instead of $1 turning into $92, removing a month produces a wide array of possibilities.  Many months, when removed, produced a staggering drop of ~50% in returns (marked red on the graph).  Some months, when removed, would have shifted returns a smidge up (teal) or down (orange).  Again, the one real standout is August (green), which (if removed) increased returns by ~50%.

Covering the Spread (of data)

So I'm recommending that you convert to cash in August?  NO.  What I have been glossing over in this "average growth for the month" is that there is an associated standard deviation.  For every isolated month the standard deviation [=stdev(H6:H766), etc] is WAY more than the average.  The average for August was a 0.5 % decrease, but for that same month, the standard deviation was 4.5%.  This is because much of the market is driven by single events.  August of 1974 and 2002 each had a 12% decrease, without which the August average is only a 0.1% decrease (in line with January, May and July).

Even within these single-event months there are single-event days that cause large changes.  August 1974 had three events where the market dropped by over 2% in a day.  August 2002 had two events where the market dropped by over 4% a day.  If you missed those events, you beat the market handily.  The same works in reverse, though.  If you missed the last three years, you lost out on a bunch of recovery.

Take Home Message

This all gets to the point that past performance does not guarantee future performance, and any deviation from a diversified portfolio requires some type of thesis.  While it is true that in the past May through October (and especially August) have been months with less market growth, deciding to remove diversity from your portfolio (by converting to cash) carries more risk to long term yields than doing nothing.  If we couldn't predict the series of random events that would turn our $1 to $140, maybe we should just be happy that it turned $1 into $90.  Let's not get greedy.

Of course there are many things ignored in this model, from the effects of inflation to the bonus of dividends.  The only omission I see that would help the "Sell in May" strategy would be converting to a higher yield May-October "safety" instrument (such as a 6-month CD), and I seriously doubt there is one that has returned stock-like performance.  For now "Buy and Hold" remains champion, but I'm sure we'll find another challenger ready to go toe-to-toe.

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