Sell in May and go away – part 2

The spring weather has been good in London the last few days, so looking at lowering the historical average risk free rates haven’t been that tempting.

But it needs to happen, as part 1 left a few loose ends.

Two things of interest will be addressed in this post:

1: How does different levels of interest affect the Sell-in-May strategy,


2: Are there differences between different time periods as to how effective the strategy has been? Or more specifically, is the summer period a consistently good period to be out-of-market?

After posting the first round I’ve been tipped off about a few other articles and views concluding differently than my first post. Well, first off: I’m not attempting to claim anything in particular. But, those other views are lacking I’d argue.

It’s easy to just focus on the final value of some strategy, but that’s not really the full picture..

I’ve used this as an example in similar situations, but I should reiterate it here: Assume you had 2x leverage and the market went up 10%. You would then make 20% (minus leverage cost, etc..). And if things go down 10%, you are down 20%. So far you’re doing nothing more than putting on more risk. The most inexperienced retail trader can do, and does do, this every day, without regard for the implications. Not that the banks have done much better, by the way..

If you however managed to time your leverage so that you, for example, were 2x exposed when things went up and 1x, 0x, or maybe even -1x when things are (potentially) going down, then you start showing some market timing abilities. In other words: There are more than just one way of applying a strategy.

So if you’re going to tell me about some other article that is showing me that the final value of some portfolio is more or less than some other portfolio, please include something more than just a single percentage value.

But I digress, because there are valid limitations to the first post, and that’s transaction cost.

You can model transaction costs in many ways, but one option in this particular case is to view it as a reduced risk free rate. So, as I’m still not going to include explicit transaction costs in my analysis, you can easily account for them..

The other aspect is either something you’d describe as positive/negative feedback loops or just intra time period randomness: Does the strategy work within different subsections of our overall period?

Questions to ask with regards to this is related to stability of optimal strategy between periods, and if this is deterministically shifting as time moves forward.

As before there is a GitHub area with code and data, updated to reflect the additions in this post. So let’s start with variable interest received while out-of-market.

S&P500 with variable risk free rate

Not surprisingly the final value of our various strategies get lower as we reduce the out-of-market risk-free rate. However, how does this affect our alpha/beta stats?

OOM risk free rate Annualised Alpha Alpha T-probs Beta
5% 4.64% 2.533E-7 0.409
4% 4.13% 4.302E-6 0.409
3% 3.63% 5.473E-5 0.410
2% 3.13% 5.189E-4 0.410
1% 2.62% 0.003656 0.411
0% 2.12% 0.019169 0.412
-1% 1.61% 0.07519 0.412

All alpha values remain positive with the majority remaining significant at a 1% level. In other words, neither the risk-free rate nor an implied transaction cost (illustrated through reduced risk-free rate) seem to impact the observations we’ve seen earlier to much extent.

Finally we are looking at how things change over time. Is the out-of-market strategy working when we divide the overall period into sub-periods?

Generally of the opinion that changing more than one variable at a time quickly generate more confusion than insight: I’m again locking the risk free rate so that all we’re looking to change between differing simulations is the time period.

Renormalised Active vs Passive S&P 500


Supplemented with alpha/beta stats below we see that alpha remains positive for all the periods. The significance level is a bit all over the place which is probably also related to only having 120 monthly observations in each period. However, if you were forced to conclude anything based on significance we could state that they have stabilised on a 5% significance level the last 30 years.

Period Annualised Alpha Alpha T-probs Beta
[1955, 1965) 3.14% 0.113185 0.448
[1965, 1975) 2.77% 0.228970 0.381
[1975, 1985) 1.41% 0.550809 0.499
[1985, 1995) 10.29% 2.857E-5 0.363
[1995, 2005) 5.26% 0.034520 0.373
[2005, 2015) 4.67% 0.047881 0.406

A lot of stuff has been covered now by this post and the previous. One final question worth digging into is dividends, and potentially something called smart beta. That will be the subject in the final round next time.

Posted in Analysis.