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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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Reviewing 2016

Another year has passed, and just like last time, I’ll summarise 2016 below.

2015 was a rather flat year, with the opportunity index hovering around 30 throughout the year. 2016 was a lot less boring, with an ever increasing opportunity index, reflected in the index value also heading north. Besides a dip below 30 around August, and some initial below 30 values at the beginning of the year, this development allowed us to stay in the market throughout most of the year, capturing whatever gain was there while avoiding negative and uncertain territory.

With default settings, this gave us a nice alpha value of about 13%, at a beta of 1.29. With an initial index value of 2052.67, the active performance ended at 2663.24 while the passive S&P 500 value ended at 2244.41. As always, feel free to click the image above to dive into the details.

PS: I’ll be stopping the stock pick publishing that has been published to Github at the end of each month. I’ve not followed up on this and believe it was prematurely made available, compared to some of the internal development progress made with regards to single stock selection.

Looking back at 2015

Happy New Year, guys!

It most definitely is time to give an update to this blog. Rest assured, I’m still here, just been rather busy working on my ranking algorithm (and I found it a bit boring to do, almost mechanical, monthly updates as I tried for a while.) I alluded to some of the direction I was going in one of my previous blog posts. We’ll see how or if that pans out publicly here or on the GitHub repository, but good progress has been made. The results might be too good to share freely.

I thought I’d summarise 2015 with regards to the opportunity index. 2015 was, well, pretty flat. It’s difficult to beat an index by being either long, short, or out of the market on that index, when things are generally flat. But there was some significant movement, a couple of times, and over all, as in 2014, we ended our portfolio value higher than the benchmark. With 2015 starting at 2071.13, it ended at 2052.67 for the S&P 500, while the active strategy managed 2124.46.


In addition to that, we also logged a positive alpha at 3.43%, still sticking to the default settings.

Other potentially interesting observations:

  • The general trend for the opportunity index has been going down throughout 2015.
  • This has towards the end manifested itself as us being out of the market for the majority the last two months.
  • We are now very close to and slightly below an indicator value of 30. Things might jump up again quickly. But generally, all of 2015 showed little sign of wanting to be too far above this level.

2016 certainly didn’t get off to the best start (if you’re long), but it will be interesting to continue to follow its development.

Sell in May and go away – part 3

So far in part 1 and part 2 we’ve established that:

  1. There has historically been lower, or negative returns, in summer months, compared to higher returns the rest of the year.
  2. This tendency has been there since the 1950s, and seems to be getting stronger/more significant.
  3. It doesn’t make much difference what the average historical risk-free rate is, used when we’re out-of-market.

So that’s all strong indicators that something is going on in the summer months. Maybe holiday and warmer weather is to blame? If so, it could be interesting to see if this is still the case for markets on the southern hemisphere.

However, we’ve yet to include dividends in our analysis. So how would dividends change the outcome? Assume we reinvest any dividends we receive; Doing that would increase our exposure to any future market changes. Does this have an impact? Well, of course, as we can see in the below graph showing returns vs total returns. For the record, you can find the original source of this dividend data from Robert Shiller’s online data page, with a handy tool for exploring it available here. Also for the record: The cost of reinvesting dividends are not included.

S&P 500 returns vs total returns

So that’s it then? No point worrying about selling stocks in May? No, as I’ve said multiple times before: Leverage in itself is not an intelligent strategy. And given that reinvesting dividends is essentially just increasing your leverage, this is not the end of the story.

In part 1 we looked at monthly average and median returns. Let’s repeat that and compare monthly average/median returns with/without dividend reinvestment.

Average monthly returns vs total returns

Median monthly returns vs total returns

The above bar charts tell us the same story we’ve seen before. Sure, it’s not as strong, but even with dividends included, returns tend to be less in summer months. If we were to apply the previously used Sell-in-May strategy as done in part 1, but now using total returns, the below graph should show the value development over time:

TR Sell-in-May vs Buy-and-Hold

Ok, yes, I hear you saying the same thing you’ve said before: The active Sell-in-May strategy is below the passive Buy-and-Hold strategy! Then again, this is not the complete picture. Is there positive alpha on the active vs passive strategy?

Yes: We find an annualised alpha of about 5.4%, highly significant, with a beta of 0.42. See the output of analysis_3a.clj for the details.

I promised you applying a vaguely defined term called smart beta in part 2, so let’s do that. This is applied as part of analysis_3b.clj. Given the mechanical and simple Sell-in-May strategy, we don’t need to do much complicated stuff here. I want to end up with an active strategy that gets a beta close to one, so that we can utilise our alpha to end up with a higher absolute value compared to the passive Buy-and-Hold strategy. I’ll leverage our exposure so that we’re 1.5x in when we’re not between May-October. When the Sell-in-May strategy dictates that we should be out-of-market, leverage is reduced to 0.5x. We could have invested the other half in risk-free interest, but that’s not included. Assume instead that we use that interest to fund our increased leverage when we’re 1.5x, keeping it simple.

First let’s see how this performs in distinct 10 year periods:

TR Renormalised Active vs Passive S&P 500

For each and every 10 year period the active ends up with a higher final value than the passive. Put together we get this:

Smart Beta vs Passive TR

Over a 65 year period this active strategy returns almost 3.8x the passive Buy-and-Hold total return strategy. In alpha/beta terms the annualised alpha is around 2.8% with a beta of 0.93.

That concludes our little journey into this market anomaly.

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.


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