The Effects of Timing your Investments

Below are some visualizations that help to give a sense of to what degree does timing affect the final returns for a particular asset (in this case, index).

A larger and/or more uniform area of colour indicate that timing is not that important, whereas a very small area of different colour (especially blues) indicate that you could only have achieved the highest returns if you invested in the right time.

For the SPY, the areas of highest returns are only achievable if you invested during either of the 2 recent crises (2000 and 2008), and held it until today (end Aug 2020). The similar shades of dark blue show that the 2008 crisis wiped out most of the gains achieved investing in 2000-2008, such that investing in 2008 yields similar returns as investing in 2000.

A dark vertical bar of red at the 2008 area also show that any investment prior to 2008 would have achieved pretty much nothing if exited at that time.

The difference in QQQ is much more pronounced - the highest returns could only have been achieved if you invested in the trough of the 2000 crash.

For the below ETFs representing China and Singapore, investing early was the key to achieving the best returns - see how the blues are in horizontal swathes near the top instead of localized ones as per the SPY and QQQ.

Finally, Bitcoin. Because of the wider range of returns, I've truncated returns above 400% - here all represented by the darkest blue. Early adopters have it the best, but note the red patch near the top left, indicating how they had to suffer severe drawdowns too.

I am not recommending that you should or should not time the market - this simply shows that for some investments, timing plays a huge role in determining whether you make average returns or not. It may be seen one way as "since the odds are against me, I might as well settle for average returns", or "since the rewards of beating the market are so great, I should strive to get the timing right".

*ETF prices and returns are dividend-adjusted

Decomposition of Returns by Hour

Where  do stocks make their greatest moves?

For the SPY ETF, it is the overnight session (closing times + extended hours).

Here we look at the SPY ETF and decompose the movements into overnight and intraday by the hour.

Hour 9 captures the  overnight gap, while hour 10 is captures the price change from 0900 to 1000 local exchange time. Hour 16 captures the action in the last hour of trading from 1500-1600.

Table 1 - Cumulative points gained by the SPY and the contribution of points by the hour

05 May 2008 to 31 Dec 2019

Date 9 10 11 12 13 14 15 16 Total
31 Dec 2019 117.4739 22.9358 -4.3967 8.6097 15.5789 -3.2806 19.6799 4.1291 180.73

Two thirds of the gains from May 2008 are from the extended session + overnight moves! This means that if you pursued a strategy of simply buying at the close and then exiting at the next day's open, you would have captured the majority of the price returns for this whole bull run.


Table 2 - Statistical description of percent changes in each segment

Values in % terms i.e. 0.0171 means 0.0171% not 1.71%, normalized by their price at the top of the hour

The largest changes are seen in the overnight gaps - 9.2% and +10.1% and the hour with the least variation in percent returns is the 1200-1300 time period.

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.

Time Decomposition of FX prices

In this method, I investigate the behaviour of prices in off-market hours - if they have a consistent drift, and whether it could be used as a trading strategy.

The currency pair I've chosen to start with is the USDCAD as both countries share the same broad timezone. This makes for easy identification of 'busy' hours (normal trading hours) and 'quiet' hours (major markets are closed).

From there, we can construct two new price series consisting only of movements within those hours - one for busy, one for quiet.

The preliminary results (for the sample period 2018) indicate that the movements in the pair were driven mainly by activity in the Busy period - seeing how the Busy moves almost alongside the Actual. This is an expected outcome - we expect  that real money (coming in during the market hours) are what drives prices and create permanent impact.

However, the Quiet period, over the course of days/weeks, can move in the opposite direction of the Busy trend. As examples, the major down move from Jul to Oct driven by Busy period was partially offset by the Quiet period upward move. The following rally by Busy was also partially dampened by Quiet in Oct to Dec.

Do note though that this mean reversion in quiet hours is not strong enough on a daily basis to warrant a fade-the-move style of trading. The daily change correlation is near 0, and the cumulative prices correlations are near 0 too.

We need to dig deeper into how this effect plays out on an aggregate level to produce the offsetting effects we see in the 2 example periods highlighted above.