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Sell in May and go away? | AgoraOpus

Steen Jakobsen, Saxo Bank A/Ss 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 byBouman 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.

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?

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:

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:

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 sourcesI’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:

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:

The vast majority of these alphas are significant at a 5% or 1% level, with the exception of the practicallyzero 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:

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.

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