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.

Posted in Analysis.