## Tuesday, August 19, 2008

### Thoughts about STI part 2

Was nudged by millionairemind to do a little investigation into the total returns of STI should year 2008 fall by 20%. Since I have not been checking STI absolute value (I did check the daily relative % drop/rise though), I was quite surprised that since the start of the year, we've dropped a cool 20%.

I did post a table with the values of all the CAGR for different years from investing in STI, in this post. I think this time, I better list down my assumptions for calculating the values:

1. Most importantly, the data is taken from Yahoo! finance website. The price is adjusted closing price.

2. The CAGR (compound annual growth rate) is calculated like this:

To find the CAGR from period A to period B:

CAGR = (price at 31-dec of period B / price at 1st-jan of period A)^(1/(B-A)) - 1

If market is not opened on 31st Dec or 1st Jan, the price of the market days closest to the dates will be taken instead.

3. The AVERAGE CAGR is calculated by taking a simple average of all the CAGR of the same period i.e. sum of all CAGR of the same period divided by the number of CAGR taken.

Below is the table calculated for the returns on STI for different periods, assuming that 2008 closed on 31st Dec at 2769, a 20% drop from 1st Jan 2008:

For comparison, here is my earlier table posted, without taking into account 2008:

Here's what can be observed:

1. Average CAGR dropped across most periods. 'Most' is the keyword. Average CAGR for 5-yr, 7-yr, 10-yr actually increased. I don't ascribe any significance to this fact, because of the way I computed the CAGR. I took 1st Jan and 31st Dec as the price for each period of calculation, so I'm very sure that if I changed the starting and ending period to take the price (say, using 1st June to 1st-June next year), the whole data will change.

2. Adding data for 2008 still doesn't change the fact that after investing for 14-yrs, there is not a single year of negative CAGR. This means that based on historical data, if one invests in any year in the past, for 14 years starting from 1st Jan and selling on 31st Dec of the 14th year, you will not make any losses. But the returns are a pathetic 3.1% per annum (on average) for a period of 14 yrs.

Again, this would most definitely change should I change the dates where I calculate my CAGR for different periods.

3. This much I can conclude: Investment period and Average CAGR seem to follow a U-shaped curve. There is a period of declining average CAGR from 1-st year till around the 10-14th year, beyond which, the average CAGR increases with period of years invested. However, the shorter the period of investments, the more volatile the the returns are. Conversely, the longer the period of investments, the less volatile the returns will be.

4. Here's a very interesting observation when I break down the percentage of getting positive CAGR for different investment periods.

------Years----total number of samples----number of +CAGR-----% of +CAGR
-------1 yr-----------------21---------------------12---------------------57%
-------3 yr-----------------19---------------------14---------------------74%
-------5 yr-----------------17----------------------12---------------------71%
-------7 yr-----------------15----------------------10---------------------67%
------10 yr----------------12-----------------------9----------------------75%
------12 yr----------------10-----------------------9----------------------90%
------13 yr-----------------9-----------------------8-----------------------89%
---14 yrs onwards---------------------------------------------------------100%

It's quite obvious that the longer the period of investments, the lesser the number of years in which one gets negative returns, no matter which year they started the investment. As mentioned, on the 14th year onwards, all the sample data gave positive CAGR.

But all these mean nothing if the percentage of losses in sample data is greater than percentage of gains in sample data. What I mean is that even though, based on past data, there are greater chances of getting +ve returns no matter what investment periods I choose, I can still lose money if the % of losses in losing years are greater than the % of gains in winning years.

Let's see this table:

------Years----Average gains of +ve years^----Average losses of -ve years#
-------1 yr-----------------28.1%---------------------16.2%
-------3 yr-----------------12.3%---------------------10.3%
-------5 yr-----------------9.8%-----------------------5.2%
-------7 yr-----------------7.6%-----------------------3.8%
------10 yr-----------------4.4%-----------------------1.7%
------12 yr-----------------3.2%-----------------------0.3%
------13 yr-----------------3.3%-----------------------0.8%
------14 yr-----------------3.1%
------15 yr-----------------3.6%
------16 yr-----------------4.6%
------17 yr-----------------5.0%
------18 yr-----------------5.5%
------19 yr-----------------5.6%
------20 yr-----------------6.3%

^ average gains of +ve years means the simple average of all the gains made for that particular years of investment
# average gains of -ve years means the simple average of all the losses made for that particular years of investment
* There are no average losses data for 14th year of investment periods and beyond, because there are no -ve years.

I am quite surprised by the results. Not only are there higher probability of getting positive years, the average gains for every data for different investment years yield the same results - the average gains of positive years is much more than losses incurred in negative years. But of course, average doesn't mean anything. On average, each family in country X has 2.2 children doesn't really mean they really have 2.2 children. The same logic applies here.

Market Uncle said...

Hi La Papillion,
Good analysis there.

A few things to build on what you've found.

1) Though the compounded 3.1% on average seems pathetic, this is already significantly higher then risk free CPF returns of 2.5% (ignoring the added 1% for the first 20k).

If one can set aside money to invest in STI index fund as long as one stuck his fund in CPF, his returns should be far greater than CPF returns.

2) The way you've calculated is for 'blind' investing, i.e. buying STI index in any year without taking into account whether STI is possibly over or under valued. What if you one invest in STI whenever its possibly undervalue, e.g the collective STI rolling P/E is below 12 and sell whenever its possibly overvalued, e..g above 18, or some other number.

Just my thoughts. I couldn't get my hand on STI rolling (collective) band p/e data over the years.

Somehow, I believe there should be a threshold for over and under value. i.e. 10th percentile p/e and 90th percentile p.e. Selling above and buying below these cut off lines should yield very attractive returns. However, the flip side is hyper boring investment experience and also requires tremendous patience. Imagine transacting STI ETF only a few times in say 30 years?

la papillion said...

Hi market uncle,