The Truth About Compounding

If you’ve ever flipped through mutual fund literature on SIPs, the chances are that you would have come across references to “the power of compounding” as one of the benefits of investing in SIPs.  If you’ve ever had the experience of listening to mutual fund salespeople and/or financial advisors talk about the virtues of SIPs, you would have likely heard them use this catchphrase as well.  For added impact, some of them may have quoted Albert Einstein as having called compound interest the “eighth wonder of the world”.

Fact is, there is no record of Einstein ever having praised compound interest (see here and here).  Nonetheless, compounding is, without a doubt, a powerful force that one should take advantage of.  But to do so, one has to have a clear, conceptual understanding.  For instance, one should know that contrary to what many fund houses and advisors say, doing a SIP, in itself, does not assure us benefits from “the power of compounding”.  This post is for those of us who would like to get to the truth about compounding.

Compound interest is the interest that you earn, not just on the amount that you invest, but also on that interest.  As an example, consider a bank deposit (or any other fixed income instrument) in which the interest is automatically reinvested and paid on maturity.   In such a deposit, on maturity, along with your principal, you get interest on your principal, as well as interest on the interest that is reinvested.  It is this interest on interest that is the additional benefit of compounding.  The question: is this really worth such a fuss? 

Depending on the rate of interest and the tenure of the deposit, the interest on interest can make up a significant part of the overall interest.  In fact, it may well make up the majority share of the overall interest that you receive on maturity.  Here are some numbers that illustrate this.

The table below shows the share of interest on interest of the overall interest from a hypothetical recurring deposit in which one makes a fixed annual payment and receive an annual interest of 8% pa that is reinvested.

Rate: 8% pa	Share of Overall Interest
Tenure of Deposit	Interest on Principal	Interest on Interest
5 years	90%	10%
10 years	78%	22%
15 years	67%	33%
20 years	57%	43%
30 years	40%	60%

This table below shows the share of interest on interest of the overall interest from a hypothetical recurring deposit in which one makes a fixed annual payment and receive an annual interest of 12% pa that is reinvested.

Rate: 12% pa	Share of Overall Interest
Tenure of Deposit	Interest on Principal	Interest on Interest
5 years	85%	15%
10 years	68%	32%
15 years	54%	46%
20 years	42%	58%
30 years	23%	77%

In the real world, it may be unlikely to get a quality deposit that pays 12% pa, or even one that has a tenure 20 or 30 years.  So do these numbers have any practical relevance?  And what about mutual funds? Since they don’t pay fixed interest, are these numbers of any use to mutual fund investors?

The concept of compounding is not just restricted to interest.  It also applies to dividends, and even gains.  And if you substitute the tenure of deposit with the number of years of investing that you have left (until retirement), and the rate of interest with the rate of return that you expect to earn on your overall portfolio, a clearer picture of the real-life implications will emerge.  So let’s say that you have 30 years of investing left and you expect to earn 8% pa on your investments.  That would mean that roughly 60% of your potential gains will be on account of compounding.  And if you earn 12% pa on your investments, then, roughly speaking, compounding will account for a whopping 77% of your gains!  Now, that is what the power of compounding is all about.

Bear in mind, these calculations are approximations to facilitate understanding.  More importantly, these hold good only if you reinvest your interest/ dividends/ gains.  If you choose to take dividends and spend that money then you will lose out on the gains on account of compounding.  In effect, this means that to tap into the power of compounding, we should avoid the temptation to encash dividends/ gains and spend that money.  This would apply to all investors, regardless of whether they do a SIP or a one-off investment. 

I must also point out that just as gains are compounded, so are losses.  In other words, for all its power, compounding is not a cure for poor investment choices. 

How important is a fund’s return?

There are some who may dismiss this as a pointless question with an obvious answer.  But if you are willing to read this with an open mind, it might just be worth your while.  Some of the thoughts presented here have been shared in the past, across different posts.  In this post, I’m attempting to connect these together to suggest an answer to the question in the title.

Do past returns really matter?

Most of us, when deciding on a scheme to invest into, look at its past returns.  Whether we admit it or not, most of us believe that a scheme’s past returns (relative to its peers) are a reliable indicator of its future relative returns. In other words, we believe that if Fund A has given a better return than Fund B in the past, it is likely to give a better return in the future as well.

Frankly, I have not seen any data that would compellingly support such a view.  On the contrary, based on the data that I have examined, I question such a belief.  As evidence, I’ve given below some observations from a study that I recently updated.  In this, I looked at the relative returns of domestic, diversified equity schemes over four market phases, listed below.

• 8 January, 2008 to 9 March, 2009 (Falling)
• 9 March, 2009 to 5 November, 2010 (Rising)
• 5 November, 2010 to 20 December, 2011 (Falling)

• 20 December, 2011 to 29 January, 2015 (Rising)

The study covered 141 schemes that had been around across all these four phases.  Based on their return in each phase, I grouped these schemes into quartiles.  These are a few of my findings:

• 33 of the 35 schemes in the top quartile in 2008-09 were not in the top quartile in 2009-10.  Of these, 26 dropped to the third or fourth quartile.
• 29 of the 35 schemes in the top quartile in 2009-10 were not in the top quartile in 2010-11.  Of these, 19 dropped to the third or fourth quartile.
• 30 of the 35 schemes in the top quartile in 2010-11 were not in the top quartile in 2011-15.  Of these, 19 dropped to the third or fourth quartile.
• Not a single scheme managed to be in the top quartile across all four phases.  Only 7 schemes consistently ended up in one of the top two quartiles in each of the four phases.

To me, what emerges from this is that the past ranking of a scheme is not a reliable indicator of what its future ranking will be.  In case you’d like to take a look at the data supporting these findings, please send me an email. 

Do future returns matter?

Once we invest in a scheme, it should be correct to believe that the scheme’s returns will impact our returns, right?  Well, yes and no.  If we make a single investment, then yes.  If we make multiple investments, then maybe not.  Let me illustrate.

Let’s say that 10 years ago, someone decided to start SIPs of an equal amount in the growth options of these schemes:

• Reliance Regular Savings Fund-Equity Option (RRSF)
• SBI Magnum Midcap Fund (SBIMMF)

Over these 10 years, RRSF ended up giving a higher return than SBIMMF.  However, the investor would made more money in SBIMMF than in RRSF.  The table below shows the difference.

Period: 1 May 2006 to 30 Apr 2016	Scheme Return (p.a.)	Investor Return (p.a.)
RRSF	13.8%	13.4%
SBIMMF	11.3%	18.0%

Scheme returns and investor returns have been calculated using the tools at Advisorkhoj and assume a monthly SIP on the first business day of each month.  Loads are not considered. 

Let me try and give these numbers a bit more context.  The growth in the NAV of RRSF over this period was 36% more than the growth in the NAV of SBIMMF.  Yet, the gain to the investor from investing in SBIMMF was 57% more than the gain from investing in RRSF.  I look at this as proof that investing in a scheme that gives better returns, in no way, guarantees that we will get better returns.  Indeed, the returns to us can be far less than what we may imagine.

The role of returns in building wealth

I remember a thought shared by a stock broker in my early days in the business.  I paraphrase: “You may earn a 100% in a year but if all you invested is Rs.100, all you will have at the end of the year is Rs.200.  By no stretch of imagination will you be wealthy just by seeking high returns.”

I have regarded that as a useful comment on how wealth is built.  To refine it a bit, the wealth that we build is most influenced by the amount that we save and invest, and the timeliness of our investments (i.e. our ability to invest regularly, without delay).  We can, and must supplement these with good investment choices.  However, we need to realize that there are practical limits to the rate of return that we can earn from our investments on a sustained basis.  And if the points made earlier are anything to go by, we have limited control over the return that we will end up getting.

Putting all of this together, I would like to suggest that a scheme’s returns are not as consequential as most of us might believe.  But I’ll let you be the final judge of that.  And along with what I have, so far, shared in this post, I’d like to offer you a parting thought that puts a whole different spin on the question in the title.

Most good things in life come at a price.  Generally speaking, the more important something is to us, the higher is the price that we are willing to pay.  Conversely, the higher the price that we are willing to pay for something, the more important it can be considered to be to us.  Thus, the importance of a scheme’s returns to us can well be judged by the price we would be willing to pay or, more accurately, the compromises that we are willing (or not willing) to make.  Let me explain with a personal example.

I have taken a stance to not invest my money with HDFC mutual fund.  To be clear, I have great respect for their Chief Investment Officer as an equity fund manager.  I have no reason to doubt his ability to generate better returns than most of his peers.  On the flip side, I have regarded their disclosures around expense ratios as inconsistent and opaque.  Nonetheless, a few years ago, I went ahead and invested a small portion of my portfolio with them.  I was clear that I was making a compromise.  But then, a series of service issues started popping up which left an extremely bitter taste in my mouth.  To put it bluntly, I felt like I was being yanked around.  After a bit of deliberation, I came to the conclusion that this fund house did not deserve my business, and pulled out my investments.  In other words, this time around, I refused to compromise.

Yes, I am a small investor, and my stance may not affect them.  Some of my well-wishers have argued that I have had more to lose than them by depriving myself of good returns.  Fact is, that doesn’t bother me.  For my part, I am clear on where I draw the line on making a compromise, and my actions reflect that.  And that’s really the question we have to ask ourselves.  Would you be willing to chase the promise of ‘good returns’ at any cost?  Or would you want to draw the line somewhere?  And, if so, where would you draw it?

Fund Volatility and SIP Returns

A few readers of my previous post have said that I was wrong in suggesting that all funds are equally suitable for a SIP.  According to them, if an investor who is proposing to start a SIP, had to choose between two funds, he/she would be better off choosing the fund that is likely to be more volatile (i.e. the fund that is likely to see greater fluctuations in its NAV). 

This is not the first time that I have heard this argument.  Over the years, I have heard many advisors voice a similar view.  Unfortunately, this is a flawed perspective that is, paradoxically, the result of intelligent thinking.  In this post, I propose to clear the air on this.  But since this may not be easy to explain or even follow, let me first cut to the chase, and state my position:

a.       There is no conclusive or compelling evidence that supports this argument.

b.      Pursuing such a strategy can potentially have disastrous consequences if one is forced to redeem one’s investment in a bear phase.

If you’d like some elaboration on this, do read on.

Let me start by questioning the mathematical validity of the volatility argument, if I may call it that.  Imagine, if you can, two equity funds that, over a certain period, start with an identical NAV, and end with an identical NAV.  Let’s further assume that, over this period, these funds have an identical average NAV.  This may be a hypothetical scenario but it is one that immensely favors the volatility argument.  If the argument truly has merit, then in such a scenario, an investor opting for a SIP in both funds, should always gain more in the more volatile of the two funds.  Yet the fact is that even in such a favorable scenario, there is no certainty that that will happen.

For those who prefer empirical evidence, I’d like to present some data on three of the oldest equity schemes in the country.  The table below gives the data for the period from April 2012 through March 2015.  All the data has been taken from the fund factsheets.

Apr 2012 - Mar 2015	Fund A	Fund B	Fund C
Standard Deviation*	14.2	16.5	15.8
Fund Return (p.a.)	18.6%	17.1%	34.9%
SIP Return (p.a.)	24.9%	25.2%	35.2%

*Standard Deviation (SD) is a measure of volatility. The higher the SD, the more volatile a fund.

Over this period, Fund B was more volatile than Fund A, and despite its lower return, an investor opting for a SIP would have gained more in this fund than in Fund A.  One may say that this data supports the volatility argument.  However, when we compare Fund B with Fund C, the picture appears to be somewhat different.  Fund B was also more volatile than Fund C but an investor opting for a SIP would have gained less in this fund than in Fund C.  One may think that this was because of the much higher return of Fund C over the period.  But before drawing any conclusions, let’s look at the data for the preceding 3 year period.

Apr 2009 - Mar 2012	Fund A	Fund B	Fund C
Standard Deviation	22.5	27.9	28.3
Fund Return (p.a.)	27.9%	26.7%	34.6%
SIP Return (p.a.)	8.8%	4.5%	9.3%

 

This period was marked by a significantly higher level of volatility across all funds.  Yet when you look at Funds A & B, despite a much higher return over this period (compared to Apr 2012 – Mar 2015), an investor who opted for a SIP in these funds over this period would have gained much less than a similar investor in these funds over the subsequent 3 year period.  Fund C had almost the same return across both periods but here, too, an investor who opted for a SIP over this period would have gained much less than a similar investor in this fund over the subsequent 3 year period.  Clearly, the volatility argument does not hold good.

You may also note that during this period, Fund C was more volatile than Fund B.  However, in the subsequent period, Fund B was more volatile than Fund C.  Thus, even if volatility were to matter, to whatever extent, historical volatility of a fund (absolute or relative) can be no indicator of future volatility.  Just to be clear, the investment objectives of these funds did not change over these years.  In fact, these are among the most consistently well-managed funds in the industry.

Let me now flip back another three years to a period that highlights some of the risks of investing in highly volatile funds.

Apr 2006 - Mar 2009	Fund A	Fund B	Fund C
Standard Deviation	28.4	31.5	33.2
Fund Return (% p.a.)	-3.1%	-2.7%	-17.5%
SIP Return (% p.a.)	-13.9%	-13.7%	-30.2%

To put these numbers into context, the value of a SIP over this period in Fund A or Fund B would have been almost 20% below the amount invested, by the end of the period.  The value of a similar SIP in Fund C would have been almost 40% below the amount invested.  So much for the volatility argument.

SIP Returns

A number of investment portals offer tools that enable one to calculate the so-called ‘SIP returns’ of mutual fund schemes.  Most fund houses also offer similar calculators for their schemes.  Some offer these calculations in their monthly fact sheets.  But does looking at the SIP return of a fund serve any purpose?  In this post, I will attempt to show that SIP returns are of little use, and that one is better off not using these returns to draw any conclusions.  To keep things simple, I will restrict my thoughts to SIP returns of equity funds.

The SIP return of a fund is not a representation of its performance. It only tells us the return that an investor would have got if he/she had opted for an SIP in that fund, over a particular period.  The SIP return from investing in a fund can be, and indeed often is, very different from the fund’s actual return over the same period.  As an illustration of this, I have given below some data of two of the oldest diversified equity funds in India. (PS: All the SIP calculations in this post assume equal monthly investments made on the first business day of each month from the starting month till the penultimate month.  Loads are not considered in any of the calculations.)

	Fund A	Fund B
NAV- 01 July 2004	70.67	47.73
NAV- 02 July 2007	228.91	142.70
Absolute Fund Return	223.9%	199.0%
Absolute SIP Return	65.4%	75.9%
Fund Return (p.a.)	47.9%	44.0%
SIP Return (p.a.)	35.5%	40.3%

Over the 3 year period mentioned above, investors in both funds who opted for a SIP saw a lesser return than those who put a similar amount at one go, at the start.  You may also notice that while Fund A gave a higher return than Fund B, investors who opted for a SIP in that fund saw a lesser return than those who opted for a SIP in Fund B.

If we now look at the 3 year period that immediately followed, a pretty different picture emerges.

	Fund A	Fund B
NAV- 02 July 2007	228.91	142.70
NAV- 01 July 2010	263.45	195.03
Absolute Fund Return	15.1%	36.7%
Absolute SIP Return	41.7%	35.1%
Fund Return (p.a.)	4.8%	11.0%
SIP Return (p.a.)	24.0%	20.6%

Investors in Fund A who opted for a SIP over this period, saw a better return than those who put a similar amount at one go, at the start.  Investors who opted for a SIP in Fund B saw a lesser return, in absolute terms, than those who made a lump sum investment, at the start.  However, if you consider the time value of money, as reflected in the annualized returns, the SIP investors benefitted more.  In contrast to the previous 3 years, over this period, Fund B gave a higher return than Fund A, but investors who opted for a SIP in that fund saw a lesser return than those who opted for a SIP in Fund A. 

In the examples above, both the fund returns and the SIP returns were positive.  Yet, it is possible for one or both of these to be negative.  The data below, of another diversified equity fund, illustrates the possibility of a fund’s return being negative, and SIP return being positive.

NAV- 01 Jan 2008	40.71
NAV- 01 Jan 2013	33.49
Absolute Fund Return	-17.7%
Absolute SIP Return	24.9%
Fund Return (p.a.)	-3.8%
SIP Return (p.a.)	8.8%

There is also the possibility of a fund’s return being positive, and SIP return being negative, as the data below, of yet another diversified equity fund, shows.

NAV- 01 Dec 2003	29.86
NAV- 02 Mar 2009	51.98
Absolute Fund Return	74.1%
Absolute SIP Return	-2.3%
Fund Return (p.a.)	11.1%
SIP Return (p.a.)	-0.9%

So, what explains these numbers?

While a fund’s return does influence the SIP return, the extent of that influence depends on the pattern of NAV movements over the period.  Odd as it may sound, some patterns cause the SIP return to exceed the fund’s return, while others bring down the SIP return to below the fund’s return.  But knowing the effect that a particular pattern has, doesn’t really help because neither can a fund manager control the pattern of NAV movements for a fund, nor is it possible to predict the future pattern for any fund.

In this backdrop, consider this: even if we believe that a more competent fund manager is likely to generate better fund returns than a less competent one, the pattern of NAV movements may make it possible for a SIP in a poorly performing fund to give a better return than a SIP in a well performing fund.  The only thing resembling any kind of certainty is that the longer we carry on a SIP, the more likely it is for the SIP return to mirror the fund’s return. 

Yet, every now and then I come across supposed advisors who wax eloquent about how some funds are “more suitable for a SIP.” At the start of each year, and occasionally in-between, I also see recommendations pop up for “the best funds for SIPs.”  To anyone who understands the maths of SIP returns, these are flawed notions which consciously or not, capitalize on the misconceptions of investors.  But all of these pale in comparison to a remark that was brought to my attention, that The Economic Times attributed to the CEO of a fund house: “our CIO-equity runs… …the number 1 fund in the country in 10-year SIP (systematic investment plan) returns.”  The statement may be factually correct, but to me, the mention of SIP returns in that sentence is nothing short of deception.

As I see it, SIP returns serve little purpose and are best ignored.

The real benefits of a Systematic Investment Plan

Let me start by sharing what a prominent investment portal has to say about the benefits of opting for a Systematic Investment Plan (SIP).

“Systematic Investing in a Mutual Fund is the answer to preventing the pitfalls of equity investment and still enjoying the high returns. This SIP Calculator will show you how small investments made at regular intervals can yield much better returns over a long period of time.”

I recommend treading with caution while relying on such supposed advice. 

Systematic Investment Plans are a key part of the efforts made by fund houses to attract investors towards equity funds.  A number of financial advisors and investment portals also encourage investments through SIPs.  However, as I see it, a lot of the stuff out there necessitates reading between the lines, and filtering fact from fiction.  The quote at the start of this post is just one example of this.  Opting for a SIP can, indeed, be beneficial, but not in the way that this portal would have us believe.

For those of us who rely on the regular income from our profession to build wealth, a SIP is a convenient and effective way to invest regularly.  In an earlier post, I had mentioned that the wealth that we build is influenced by the amount that we save, the timeliness of our investments and the quality of our investment choices.  In my previous post, I had built on this to make a case for saving more and investing regularly.  This is a useful framework to understand the importance of a SIP.  It is a means to channelize, in a timely fashion, the amount we choose to save, into the funds that we choose. 

In other words, we are responsible for our investment choices and the amount that we invest; a SIP has no role to play in that. Furthermore, merely opting for a SIP cannot compensate for poor investment choices, or for a lack of thrift.  It is up to us to decide how much to save and how to allocate this between equity funds and debt funds.  A SIP ensures that we will not delay investing and will, thus, use time to our advantage.  Therein lies its importance.

SIPs can also be beneficial for those of us in a dilemma when deciding to invest a large sum of money into equity funds (or anything that is susceptible to frequent, steep price fluctuations).  Such dilemmas exist because of the uncertainty attached to the price- Is the current price a good price to invest at?  Or is it better to wait for the price to fall?  In effect, we have three choices:

1. Invest this at one go, now
2. Invest this at one go, on a later date
3. Invest this in smaller tranches, over a period of time

There is no basis for anyone to say for sure, as to which of these choices will result in the best returns.  We will only know in hindsight which course of action would have been the best.  Some of us may be inclined to take a call on the price movement and, hence, go with the first or the second option.  Those of us who would like to hedge out bets would opt for the third choice.  A SIP (or a Systematic Transfer Plan) is a convenient way to exercise this third choice.   It may or may not yield better returns as compared to the first two choices, but in all likelihood, it will enable us to sleep more peacefully.