Continuing from Part 1

**Comparing between strategies**

S2 strategy invests in months {1,3,4,7,10,11,12} and yields better Sharpe and higher total return than the benchmark. It also has less negative skew.

S1 invests in only 4 months of the year {3,4,11,12} and so the total profit is much lower. The Sharpe does not improve, but the skew is significantly improved – it is now positive.

S1b squeezes out a little more total return by shorting month 9, giving us less of a max DD, but does not improve on the Sharpe nor the skew, so it might not be worth the effort.

Because this is an active method, the number of trades needed is proportional to the number of months. S2: 7, S1: 4, and S1b: 5.

Active method equity curves

Using the active method, we can see that the curve is significantly smoother than the benchmark, especially for S1 strategies.

Passive method

The passive method is what we normally do in real life – a hypothetical growth of $1. We do not rebalance the amount, but simply let it grow. The percentage returns are compounded, not simply added as per previous method.

Conservative strategies (like S1) are penalized because they tend to miss out on some of the compounding gains accrued in bull runs. This makes a sizeable difference in the long run.

The passive strategy comparisons show that S2 allows us to beat the benchmark, with slightly lower SD and drawdown measures.

S1 strategies are far superior in terms of Sharpe, but don’t eke out as much of a profit. To solve that, use leverage.

Using leverage of 1.5x, we can get the S1 strategies to beat the the total return of S2 and the benchmark, with somewhat similar SD and drawdown.

However, implementation is not so simple – we will need to find a way to get the 1.5x monthly return of the index, and keep compounding it. It’s not as easy to implement as S2.

**Conclusion**

Following a simple strategy like S2 can give us better total and risk-adjusted returns than the benchmark.

**Appendix**

Robustness testing

We will look at the Mean/SD ratio (Sharpe) for each month across the years to see how they vary. We have currently chosen the months in S2 and S1 based on the full range historical average. Now we want to see how robust this indication is, using only 5 years to look back.

Generally, a month with a ratio that flips often is not very reliable – we hope to find months that have a consistent and positive Sharpe.

Here we can see that S1 months satisfy that criteria, and so we have some confidence that it will continue that way. We will have to be on the lookout for when it stops working – there’s no way to predict it.

For other months, we can see that the ratio flips quite often, and so there is no consistent pattern of it being a profitable or unprofitable month.

Notice how Jan changed from a predominantly positive month to (currently) negative, and how May was consistently negative until about 1985. Probably that’s how the saying “sell in May and go away” came about, but that is no longer true.

S2 rolling 5 year ratios show that the core months (S1 strategy) are for most part above water, while Jul and Oct introduce some downside but has upside potential outweighing that, this justifying their inclusion.

Notice that there is negative autocorrelation in monthly performance across the years – some sort of reversion to the 0 mark at least – in that after a streak of lousy performance say 7-10 years, the next 7-10 years are likely to be positive. Each month seems to have a different frequency though – e.g. Jan and Aug seems to be much shorter, while Jun seems to take a while more.