Ever since I became interested in the topic of investing, I noticed the periodic appearance of articles promoting ‘Systematic Investment Plans’, or SIP, which is an investment strategy where you invest a fixed amount at fixed intervals in the stock market either directly or indirectly. So for example, one could invest 5000 Rupees on the seventh day of each month for a certain period such as one year. The investment instrument could be a certain stock, the “whole market” through an indexed ETF, or a basket of stocks via a mutual fund.
These periodic articles on SIP appear to be written by fund managers and financial advisors, and their message is:
- SIP avoids the issue of timing the market (which is good for the naive investor)
- SIP puts your money to work as early as possible
- SIP gives the benefit of “dollar cost averaging”
In addition, many of these articles also had the following additional messages:
- SIP is good in a rising market
- But do not stop SIP in a falling market
Now, the ideas described in these articles looked sort of plausible, but I wasn’t very clear about the benefits of going for an SIP, especially in a quantitative sense. My doubts were:
- What is “dollar cost averaging” and why is it better?
- If it is better, what is it being compared with?
- Is SIP the best strategy in all cases — namely, rising, flat, or falling markets?
This article will explore these questions and my attempts to answer them through some armchair experiments. But first, let’s examine the argument that SIP is good because it benefits from “dollar cost averaging”: but what does this phrase mean?
Dollar Cost Averaging
In a fluctuating market, one invests a fixed amount of money at fixed intervals, say, once a month. Let’s develop this algebraically. Assume there are n intervals, the fixed amount value is A, and the market prices at times 1 to n are p1, p2, …, pn. The strategy thus buys shares numbering A/pk at the kth interval. Then the total shares B, accumulated at time n are:
Let the harmonic mean of the prices be H, so that
Then B = A n / H and average cost per share is A n / B = H
Stock Averaging (SA)
As an alternative to dollar cost averaging, one can buy a fixed number of shares at each interval. We shall call this ‘stock averaging’ (I didn’t find any commonly known name for this strategy). Using the same nomenclature as was used for dollar cost averaging, but taking b as the number of shares bought in each interval
where M is arithmetic mean price,
And of course, the average cost per share = b n M/ (b n) = M.
Comparing Dollar Cost Averaging with Stock Averaging
It so happens that harmonic means are generally smaller than arithmetic means on the same set of numbers (arithmetic harmonic means inequality),
Therefore, it appears that dollar cost averaging is superior to stock averaging, but there is a caveat — the calculation above does not take into account the time value of money (as different amounts are invested in each interval). Moreover, the practical question is, is the difference between the two significant in real life? That requires some numerical analysis, which we will do later in this article. But first, let us look at another investment strategy that is commonly mentioned in articles on SIP: lump sum investment
Lump Sum Investment (LSI)
This is an extremely simple strategy – invest your whole budget on day 1, and count your chickens on day n.
Thus we buy B shares at price p1, so the average cost per share is simply p1. Compare p1 with M and H of the previous sections. Obviously, this strategy works well when p1 is low, that is, in a rising market.
How to Evaluate Investment Strategies
We still need to figure out how to accurately evaluate different investment strategies. It is not sufficient to simply compare average cost per share, as we did in the previous sections. That is because the time value of money was not factored in. How can one take the time factor into consideration? There is a standard financial formula available to do this, but let us approach that formula indirectly, so as to build a better understanding of it.
So far, we ignored where the money for investment was coming from. To take care of that, let us introduce a banker into the story. The banker will lend us money whenever we ask for it, but eventually loan has to be repaid, along with the “rent” for using the money — that is, the interest on the borrowings. The interest is calculated at a certain rate, say r percent per year. Now with the banker in the picture, any investment strategy can be evaluated fairly — borrow money from the banker as required, then at the end, repay the loan and interest. If any money is left over, that is the profit. Bigger the profit, better the strategy.
However, one problem still remains: absolute profit, by itself, is not a good figure of merit, because if the total amount invested changes, the profit also changes. In other words, the scale of investment needs to be factored out.
So let us take a slightly different approach for this. Instead of measuring the profit for a given rate of interest r, let’s ask the question, what is the highest interest rate r that one can afford to pay the banker without losing money, i.e., at which there is zero profit? Then this critical value at which the banker takes away exactly all the money we made, will be our figure of merit. It is clear that the higher the value of r, the better the strategy. Notice also that for a losing strategy, r can be negative. Further, scaling the investment amounts does not change the critical value r.
Incidentally, formulae for net present value (npv), and extended internal rate of return (xirr) that is based on npv, is equivalent to our story of finding the critical rate r for the banker. Interested readers can look it up on the internet (see NPV, XIRR). Microsoft Excel has built-in XIRR and NPV functions.
My Experiments with Truth (of SIP)
I decided to run some experiments on real life data to get a quantitative understanding of these three investment strategies, namely SIP, SA, and LSI. Here are the details of these experiments:
Download data for two indexes over an extended period:
- Standard & Poor 500 (as represented by SPY ETF) for the US market
- NIFTY 500 for the Indian stock exchange NSE.
From these, identify periods in which the market (1) rose, (2) fell, and (3) was flat (it ended at roughly the same price where it started).
|SPY||RISE||2 Jan 2003||19 Sept 2007||
|SPY||FALL||19 Sept 2007||9 March2009||
|SPY||FLAT||9 July 2003||7 Oct 2008||
|NIFTY500||RISE||19 Feb 2002||11 Oct 2007||
|NIFTY500||FALL||11 Aug 1994||10 Jan 1996||
|NIFTY500||FLAT||24 Jan 1995||5 April 1999||
For each of these periods, subdivide the data set into ten different subsets, as follows: The first data subset contains prices from days 1, 11, 21, … ; the second data subset contains data from days 2, 12, 22, … and so on until the tenth data subset contains data for days 10, 20, 30, …
Thus each data subset contains values for every tenth working day, but each has distinct data.
Now on each subset, evaluate each of the three investment strategies (SIP, UCA, LSI) and compute XIRR values (i.e. critical rate of interest r). The set of XIRR values for each strategy allows us to judge variability arising from market timing (time of entering the market differs by one day for each successive subset). Determine mean, minimum and maximum statistics on the XIRR values. The results are tabulated below. The rightmost column gives the range of XIRR values, i.e. (MaxXIRR – MinXIRR).
The following charts will help us analyze these results. Span of the vertical scale is kept same for all charts, for easy comparison, although the maximum y-value ranges from +45% to -36% in different charts.
Several conclusions can be drawn from this experiment:
- There is a large variation in XIRR within the ten subsets, about 1% to 8%. That is, market timing is an important factor, even for shifting timings by a few days.
- There is no clear-cut winner between the three strategies. LumpSum is worst on NIFTY500 but best on SPY (I don’t understand why this happened). The other two are within about 1% of each other but this effect is swamped by the market timing variation of the order of ~5%.
- In a falling market, all three strategies lose heavily. Common sense tells us that it is prudent to stay out of a falling market! Then why would financial advisors advise their clients to not stop SIP in a falling market? It may be that the naive investor cannot reliably determine market trends so he doesn’t know when to stay out, but I suspect their advice may be influenced by the commissions they get on SIP payments.
- In a flat market, SIP does perform a little bit better than SA (Stock_avg). But net profit in a flat market is close to zero anyway with these simple strategies. So again common sense tells us that it is prudent for a naive investor to stay out of a flat market!
- In a rising market, all strategies do well. Further, there is no clear-cut winner. So common sense tells us that a naive investor should get into and stay into a rising market, and in this case SIP is as good as the others. The caveat of course is that the investor cannot afford to go to sleep at the wheel, and must respond quickly when the market stops rising, so as to adhere to points 3 and 4 above.
This turned out to be fairly long article, and I have not even gone into the details of how all these calculations were carried out, and my adventures along the way.
Now, I would like to close with some key takeaways for the naive investor:
- Learn to identify when the market is rising and when it is not. Then one can use SIP to get into a rising market, but be prepared to exit as soon as the trend changes.
- SIP does not appear to be quantitatively superior in practice, as the argument from harmonic and arithmetic means would have us believe. However, people with a regular disposable income can use SIP to be more disciplined about investing regularly, provided they are personally vigilant about market trends; their financial advisors may not warn them to get out in time, and may even persuade them to stay invested in a falling market, but they must have the courage to act on their convictions. The problem is, when the market falls, it falls swiftly.
Incidentally, lump sum strategy can prove useful even for the investor with a regular weekly or monthly income: Consider that such an investor accumulates his savings in safer instruments while the market is trending flat or down; now these accumulated savings can be used to invest as a lump sum when the market turns around.
It is unfortunate but true that everyone must learn to manage their own finances. Advice is useful, but it has to be examined and validated against your own judgment.
As Gautama Buddha said,
Do not believe in anything simply because you have heard it. Do not believe in anything simply because it is spoken and rumored by many. Do not believe in anything simply because it is found written in your religious books. Do not believe in anything merely on the authority of your teachers and elders. Do not believe in traditions because they have been handed down for many generations. But after observation and analysis, when you find that anything agrees with reason and is conducive to the good and benefit of one and all, then accept it and live up to it
Acknowledgements: Thanks to Manas Sathe for critically reviewing this article.