*Time is an illusion* - Einstein in Theoretical Physics

~~Time ~~Timing is an illusion - Einstein in Stock Markets*

We will straight away jump into what this article will try to answer.

**Question:**

Can a retail investor, one who receives salary every month, time the markets to achieve better returns while doing his Systematic Investment Plan?

**Conditions:**

The retail salaried person only does Index investing in Sensex. Assume that on Christmas in 1979 he decided to start an SIP in BSE Sensex with an ETF or an Index fund with no expense and no tracking error. Hypothetically assume these instruments existed since then (even if there is an expense we can reduce the returns appropriately). His strategy was Buy and Hold forever.

**Short Answer:**

No we cannot time our SIPs.

**Long Answer:**

With a lot of effort (which we will not discuss in this post) we can just scrape ahead of the index but the gains are not substantial enough in this long period of 40 years. At least in my opinion. Let us look at some dirty calculations.

*Thinking about strategy*

*Switzerland is the epicenter of horology and exquisite time pieces. Photo clicked by Deepak at Lugano, Switzerland c. 2011*

We have a situation to invest say 100 rupees every month starting from January 1980. Assume with 100 rupees we can purchase certain number of units of the BSE Sensex index. So for instance the closing index level in January 1980 was 123.54 then we would have got 100/123.54 = 0.80945 units of Sensex index. We do not look at the total return of the index (inclusive of dividends). Now in January 1980 there were 15 trading days. Which was the best day to pick for investing 100 rupees? The best day in hindsight was 2 January 1980 when the index was lowest for the month. The worst day in hindsight was 17 January 1980 when the index was the highest for the month.

So now we have in our crystal clear rear view mirror the minimum index value and maximum index value days for each months. Total of 491 months in this study. So this is long enough I guess. Let us also look at the average index value each month and calculate the standard deviation for each month's index level. What this will help us is in is to know how likely are we able to time the market. Take a guess with a six sigma advantage over the average monthly index level while timing how many bps of excess return in CAGR can we get?

Does it make any difference visually? No.

Index here means last day of closing price of Sensex each month. Now let us add the average values of index each month and bring in one standard deviation variance in buy prices also. Chart below.

Does it still make any difference visually? No.

Below is the CAGR of all these 6 'strategies'. Even if we were the unluckiest people in the Indian stock market and chose the highest index values every month straight from 1980 to 2020 end we would only have a CAGR below the closing monthly prices of index by 7 bps. That is it. The probability of being that unlucky is approximately 1 / 19^491. Vice versa being the luckiest person gets a benefit of only 12 bps of over the index. Probability remains similar.

Now let us see how much do we outperform the average monthly index level in terms of 6 sigma standard deviations. A question which I urged you to think earlier in the post.

The answer is 41 bps. Yes 41. We end with a CAGR of 10.13% over 9.72% of the Index. Well this is not possible with a monthly SIP.

So time to throw timing SIPs out of the window.

But is there a way to still beat the index while investing in the index? In hindsight always yes. In foresight *it depends.*

** I hope he had said that*

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