The Irrelevance of Time Diversification

Time diversification is the holding of an investment over a long period of time and thereby achieving a diversification of annualised return over time. It is often said that time diversification helps to improve your investment returns. At one point in time, I was an ardent fan of time diversification. However, after thinking further about it, I realised that time diversification, while not totally irrelevant, is quite irrelevant. Let's take a closer look on the case of time diversification.

Using the historical returns of the Straits Times Index from end-1984 till end-2012 as the base data, we can construct the annualised return over different holding periods.

Annualised Returns Over Different Holding Periods

As can be seen in the figure above, the annualised return over a 1-year holding period can vary greatly from +78% to -49%. Anybody holding shares during the worst 1-year period would have suffered a great loss. Over a 2-year period, the worst annualised return improves to -23%. This worst annualised return continues to improve as the holding period increases, eventually reaching a positive figure when the holding period reaches 20 years. This evidence is often used to prove that over long periods of time, share investments can yield positive returns, irrespective of when you start your first investment. The first part of the statement "over long periods of time, share investments can yield positive returns" is true and is where time diversification is relevant. But the second part of the statement "irrespective of when you start your first investment", is one of the reasons why time diversification is irrelevant. I can think of 3 reasons why time diversification is not relevant.

Firstly, consider the worst annualised return of the 1-year and 2-year holding periods. On the surface, the worst annualised return of -23% over a 2-year holding period appears much better than the worst annualised return of -49% over a 1-year holding period. But if you consider the eventual returns for an initial capital of $100,000 at the end of the respective holding periods, it will look as shown in the table below:

Holding Period	1-Year	2-Year
Worst Annualised Return	-49.4%	-23.2%
At End of Year
0	$100,000	$100,000
1	$50,586	$76,810
2		$58,997

At the end of the 1-year holding period, the eventual return is -49%. But at the end of the 2-year holding period, the eventual return is -41%. The annualised return of -23% over a 2-year holding period translates to an eventual return of -41% at the end of the 2-year period. This is not much different from the eventual return of -49% for a 1-year holding period. It is cold comfort to the investor by telling him that the worst annualised return is halved when his holding period is doubled (in the example above). The only comfort he has, if any, is the speed at which the money is lost, over a 2-year period instead of a 1-year period. In essence, time diversification is averaging the eventual return.

Secondly, consider the best case where the worst annualised return is a positive 3.7% in a 20-year holding period. This is just 4.7% off the best annualised return in the same holding period. At the end of the 20-year period, an initial capital of $100,000 would translate to $206,354. This is a very respectable return, considering that this is based on a worst annualised return for the holding period. However, what is the eventual return based on the best annualised return of 8.4%, which is just 4.7% better? The eventual return is $506,421, which is 2.5 times better than the worst eventual return of $206,354. Again, this is cold comfort to the investor that he cannot do worse than $206,354, when he could possibly get 2.5 times more had he made his investment at the best entry time. (The median eventual return is $329,129, which is 59% better than the worst eventual return).

The third and last reason why time diversification is irrelevant is: we only have 1 life; there is ONLY 1 holding period applicable to everyone of us regardless of whether or when you invest.

So, to conclude, time diversification is relevant in the sense that over long periods of time, share investments can yield positive returns. It is irrelevant in the sense that it is the eventual return, not the average annualised return, that counts.


See related blog posts:

• Dollar Cost Averaging Works Best with Volatile Stocks/ Unit Trusts