The January Effect – Part 2

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.



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

Continue reading "The January Effect – Part 2"

The January Effect

Many have heard of January effect in stock markets - stocks generally go up in January. Here we take a look at this phenomenon and see if it still persists.

Below are the results for the S&P 500 for 1951 to 2018 using monthly simple percentage returns

It shows that while the mean return is indeed positive, there are many other months with higher mean returns. Might as well call it the January-and-March-and-April-and-July-and-November-and-December-effect.

What's more important is that the Sharpe of the other (Mar, Apr, Jul, Nov, Dec) months are higher.

The only advantage that January has is that it is the only month with a positive skew, albeit very slight.

Below are the return distributions for each month.

We are also interested in the smoothness of the equity curve, and whether the strategy is robust through time.

Below we can note the following observations:

  • The January effect lost its effect from 2000 onwards
  • Mar, Apr, Nov, Dec are remarkably good month
  • Sep is consistently bad
  • Oct (while having the reputation for worst declines) is still on a general up trend

In the next part, we will look at implementing a market timing strategy that invests only in certain months, and see how it fares against the benchmark.

Drawdowns in History

S&P 500 drawdowns from 1950 to 2019-04
Red = On the way down, Yellow = Recovering from trough, Cyan = No -10% drawdown



We focus on the drawdowns exceeding -10% - giving us a sample size of 23.

A simple average would indicate that such drawdowns occur on average every 3.04 years.

The average time between such occurrences (from the end of one to the start of another) is 452 days.

Start End Duration (Days) Nadir (Lowest Point) Date of Nadir
13/6/1950 22/9/1950 101 -14.02% 17/7/1950
6/1/1953 11/3/1954 429 -14.82% 14/9/1953
26/9/1955 14/11/1955 49 -10.59% 11/10/1955
6/8/1956 24/9/1958 779 -21.47% 22/10/1957
4/8/1959 27/1/1961 542 -14.02% 25/10/1960
13/12/1961 3/9/1963 629 -27.97% 26/6/1962
10/2/1966 4/5/1967 448 -22.18% 7/10/1966
26/9/1967 29/4/1968 216 -10.11% 5/3/1968
2/12/1968 6/3/1972 1190 -36.06% 26/5/1970
12/1/1973 17/7/1980 2743 -48.20% 3/10/1974
1/12/1980 3/11/1982 702 -27.11% 12/8/1982
11/10/1983 21/1/1985 468 -14.38% 24/7/1984
26/8/1987 26/7/1989 700 -33.51% 4/12/1987
10/10/1989 29/5/1990 231 -10.23% 30/1/1990
17/7/1990 13/2/1991 211 -19.92% 11/10/1990
8/10/1997 5/12/1997 58 -10.80% 27/10/1997
20/7/1998 23/11/1998 126 -19.34% 31/8/1998
19/7/1999 16/11/1999 120 -12.08% 15/10/1999
27/3/2000 30/5/2007 2620 -49.15% 9/10/2002
10/10/2007 28/3/2013 1996 -56.78% 9/3/2009
22/5/2015 11/7/2016 416 -14.16% 11/2/2016
29/1/2018 24/8/2018 207 -10.16% 8/2/2018
21/9/2018 23/4/2019 214 -19.78% 24/12/2018


Continue reading "Drawdowns in History"

Should you currency hedge your USD portfolio? (Part 2)

Continuing from Part 1 where we concluded that the costs of hedging will almost certainly outweigh the benefits, we now look into detail as to the return drivers of the hedge, and why they amount to nothing.



Currency hedging typically works well when the  foreign currency is negatively correlated with the foreign asset, as this means that the currency hedge gains when the asset is falling and vice versa, with a net effect of reducing the volatility of the hedged portfolio.

In this case, the Pearson correlation between the returns of SPX and the hedge (short USDSGD) is +0.235 (slightly positive), and so that does not help in reducing volatility.

From the scatter plot we can see that the returns are rather evenly clustered around the origin. The R-squared value for the linear regression is a mere 0.055 - suggesting that linear relationship of the two returns are very weak.

Taking a look at rolling correlations, the monthly returns of SGD (short USDSGD a.k.a. the hedge) have been more positive than in earlier periods (1990s and ~2005).

Notably, the 2008 crisis caused the SGD to be rather highly correlated to the SPX for several years. It has more recently subsided to the ranges of 0.30 but this is still positive and this means that leaving it unhedged actually provides some diversification benefits, as the USD strengthens (against SGD) when the S&P is not doing well, and vice versa.

Thus, in the short term, we don't expect to gain much from the hedge.


Fundamentals and regime shifts

Taking a longer-term perspective, it is unlikely that the SGD can repeat such a dramatic ascent from its levels of 2.0 USDSGD to present levels of 1.35, representing a 48% increase in value (SGD terms). This rise can be attributed to Singapore's rapid development which brought her into the ranks of developed countries, which is an unrepeatable event.

Source: United Nations HDI (

Thus, in the long term, we don't expect to gain much from the hedge either.

Altogether, it continues to argue for the case that we should leave the USD unhedged.

Review of AI strategies

2018 performance for the 3 A.I. stock trading strategies at

I recently paid for a membership to take a detailed look at the strategies, and having trawled through the historical data, I present my findings below. 

The very short conclusion is that you cannot simply follow the A.I. signals regardless of Risk On or Risk Off method.

Major edit to this article: I'd like to stress that while I present Risk On on a statistical basis, the underlying data that was presented to me has a fundamental flaw and so the results are biased and misleading (more details in post).

The Risk Off method remains a true reflection of 2018 performance.


Expectations vs Reality

The strategy itself seems good - taking every single trade (at standard lot size of 100 shares) would have earned you $69,829 for the Risk On method, and  $27,463 for the Risk Off method.

Continue reading "Review of AI strategies"