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Average yearly alpha around 8%

With default settings, since the early 1980es, this strategy has beaten the market

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Sell in May and go away?

Steen Jakobsen, Saxo Bank A/S’s chief economist, was recently quoted saying you should sell your stocks and take 6 months off. The timing might be incidental but this is very much in line with an investment strategy called “Sell in May and go away“.

But can really such a simple strategy work, and why would it? Although I’m not attempting to conclude on why this should work it’s still interesting to spend a little time analysing the data. Previous work has been done to conclude on the statistical significance of this phenomenon, for example by Bouman and Jacobsen (2002) showing that the effect has indeed occurred over a long period of time.

So let’s spend a little time digging into over 60 years of S&P 500 data, going back to 1950. If you want to play around with this yourself you’ll find my code and data on GitHub. Below is our first graph. It shows the S&P 500 ranging over our complete data set, based on monthly prices.

S&P 500 all price

Besides showing the obvious there’s not much we can easily tell from looking at this in relation to the strategy. Would looking at the monthly returns help out?

S&P500 all returns

No, not really. Maybe we can make out that some of the years seems to show less positive returns towards the end of some of the years, but it’s not really clear overall. We would be guessing.. Instead, let’s group each year by it’s months and look at the average returns per month over all the years:

S&P500 average monthly returns

Aha, this is starting to show something of interest. We can clearly see that returns tends to be less positive, or even negative, on average in the middle of the year (1 = January, 2 = February, .., 12 = December), and a lot more positive at the beginning or end of the year. We would be interested in protecting ourselves from negative returns, so the strategy is starting to show some promise. This could however be skewed by outliers, so let’s also have a look at the median monthly returns:

S&P 500 median monthly returns

Ok, things aren’t so clear now. Using median returns things does seem to generally drift upwards. The question then is: What do you do with your cash when it’s not invested in the stock market? Assuming we put them in high caliber (“risk-free”) interest bearing fixed income instrument they would still give us a return on our investment while we’re out of the stock market. Based on data from various historical sources I’ll stick with an average annual geometric risk-free rate of 5%. This would very much be a limiting factor in the below analysis as a time dependent historical rate would be more optimal. For the record, I’ll also skip on the transaction costs, keeping it simple.

So given that, how would our active “sell at start of May, reinvest at end of October” strategy perform? Below we compare this active to a passive buy-and-hold strategy, with a normalised price starting at 100:

Sell-in-May vs Buy-and-Hold

The active does indeed eventually end up at a higher final value that the passive buy-and-hold. This however isn’t that interesting in itself given that our beta is now intuitively around half of the overall market. Running a regression we find the beta to actually be 0.41 on the above case. Does the strategy give us any positive alpha however? Yes it does, at almost 5% when annualised (t-prob = 2.53E-7).

You can use this for whatever you feel it’s worth, either as a slap in the face of the so called efficient markets or merely as an interesting ambiguity. I would be careful in blindly following it, given the limited understanding of why it would happen, making it difficult, if not impossible, to predict if it’s going to happen this year or the year after. Build an understanding of that and it becomes very interesting.

Another question is: Why May, and why October? Would there be other time periods that have been more optimal than just those two months? Sticking to 6 months in the market and 6 months out, we can easily shift the periods, as shown below:

Time period out-of-market Alpha T-probs
January-June 0.001628891086934963 0.027563354388632444
February-July 0.0019077562657180062 0.01115352599672903
March-August 0.003657645507896297 1.479701652318255E-6
April-September 0.00479897125435165 2.140849719722837E-10
May-October 0.003864560505495917 2.533265377469007E-7
June-November 0.002391794653946798 0.0014218779680315041
July-December 0.002537775579731788 6.140698693479774E-4
August-January 0.002258910400948748 0.0026777631120809
September-February 5.090211587704075E-4 0.4997617143696407
October-March -6.323045876849712E-4 0.39668575465853984
November-April 3.0210616117079146E-4 0.6844131501587507
December-May 0.0017748720127199694 0.017749704340670025

Illustrated differently, below are the (annualised) alpha values plotted as straight lines, where the length/position of the lines indicate when we were out-of-market:

Alpha-Timeline

The vast majority of these alphas are significant at a 5% or 1% level, with the exception of the practically zero alphas when we stay out of the market during autumn/winter time. This is also very much in accordance with the initial strategy stating you should be in the market besides summer months. Applying these different strategies would give us this graph:

Different Out-of-Market periods

The yellow April-September plotline performs best, as also shown by the the alpha table. It could be interesting to see if this is the case for multiple subsets of the overall timeline. Could it be that there’s a positive feedback loop involved here, where, due to people following the “Sell in May” strategy, it did at some point become more profitable to jump ahead of the crowd?

That question, and others, like, does the risk-free rate change the outcome significantly, is subject of later blog posts.

Things back to normal

Just a quick follow up: The data issue as described in the previous post has been fixed, and processing has catched up to current latest available input. So things are back to normal again..

Garbage in, garbage out

Late October some bad input data made it into the system. This has sadly affected the systems ability to correctly produce output. As they say in Computer Science: Garbage in, garbage out.

I’ll be working on rectifying the bad data the next coming days and rerunning all needed steps in order to repost the web app data. I’ll also add a few more extra steps to ensure the quality of the data we receive, avoiding this in the future.

More to come when things have been fixed.

How bad is a big drop?

Early Saturday morning a new indicator value was published as normal. But what wasn’t normal was the massive drop this new indicator showed compared to the previous weeks value. What’s the impact of such a big drop?

We’ve all seen the news. Bad things are happening many places in the world, and various ways of incorporating this into financial markets are manifesting themselves. But is this more than just a short blip or drop in the ocean?

In this post I’ll look at the biggest drops in indicator value, and look at longer term impact of these drops in isolation. In other words, does a single big drop down bring a longer term downfall in the S&P 500 index?

First of all, how big was the indicator drop compared to other big drops over the last 30 years or so?

20 biggest drops in indicator value
Top drop rank Indicator drop Indicator value after drop Date
1 -73 10 1992-05-22
2 -72 24 1986-09-26
3 -70 4 2004-10-22
4 -66 6 2002-04-05
4 -66 16 2002-03-01
6 -57 16 2001-06-29
7 -56 9 1995-12-22
8 -51 15 1996-07-19
9 -47 43 1991-02-08
10 -45 12 1987-09-25
10 -45 20 2014-07-18
12 -44 33 2004-03-12
12 -44 43 2005-05-06
14 -43 25 1985-08-02
14 -43 37 2007-06-08
16 -41 7 1999-03-12
16 -41 21 1984-02-10
16 -41 23 2004-09-03
19 -39 19 2002-02-08
20 -36 40 2010-03-19

We can see from this that the drop on data available as of 18th on July 2014 represents a shared 10th place of biggest indicator drops ever. That is pretty huge, and we know from earlier analysis (see 1980s, 1990s, 2000s) that indicator values below 30 generally indicate reduced index returns.

But it’s still just a single value at a single point in time. Does it still indicate future decline? Below is a chart that shows the normalized change in price the next 250 trading days from when the indicator drop occurred.

Change in S&P 500 index after big indicator drop

Change in S&P 500 index after big indicator drop

We can see that for the majority of the cases, one year later, the index is above its starting value. Put differently, a single indicator value drop a year back is not a good long term predictor. Instead, what if we look at the price development of the index compared to the average indicator value during that period.

S&P 500 index vs avg indicator

This picture gives us some more information. Generally, a big single drop does not in itself imply an average low indicator value over the next one year. The average indicator value just after the big drop is 21.15, while the average among all one year average indicators is 41.59. And as we’ve seen earlier, only during continuously low indicator values can we expect lower or negative index returns. To recap a thing stated on the “Learn more” page: “The key is to react quickly when needed.”

Update: As always, see the app, but here’s the drop I’m talking about:

big-drop-2014

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