In the second part 2, let us address the 'kitna milega?' with a little more analysis. The first part is **here**. Before we being to answer, *what return one can expect*,* *the objective of the study must be clear.

We will be using *past* *data* to figure out, for a given duration (say 15 years), what is the *average return* and how much individual returns can deviate from this average.

To what extent this can be done is a big question mark, as explained below. Assuming we can find

- the average return and
- the average deviation from the return

we will have to recognise that the average past return is not of much use. Future returns from equity as an asset class, combined the specific duration an investor will stay in equity implies that the past average has no bearing on the future average.

*However,* 100+ years of US market history and 30+ years of our market history point to one indisputable fact:

**regardless of when we measure and regardless of how long we measure it for, the volatility of the market is nearly constant! **

To know more about this, read: **Understanding the nature of stock market returns**

Therefore, although the past average is not be of much use (future returns will depend on inflation, economy ...), the past *average deviation*, or the spread about the average is important.

For example, we shall see below that for 15 year periods, individual returns can vary from the average by as much as 4%. We will understand how to interpret this 4% spread below.

I see no reason to believe that the next 15 years will have a lower spread. It can be higher, but 4% is what I would set as the minimum.

This is the objective of this post. To mentally prepare new equity investors to face the kind of fluctuations that the market has to offer. There is a misconception that things will get better with time. They will not! You need to review the folio at least annually.

The above spread is for a buy-and-hold portfolio. With a simple annual review, it may be possible to minimize this spread.

**'Kitna milega?', nahi!**

**'vichalan kitna hoga?' **(apologies for the poor Hindi. Vichalan is the closest I could find for deviation or spread.)

Instead of vichalan, Harrsh Ankola suggested at Asan Ideas for Wealth that, '**kita hilega?'** would sound better. I agree.

Now over to the analysis.

**The normal distribution**

Mathematics is the language of nature and therefore of god (for those who choose to believe in one). If we try to avoid math and use our common tongue, we end up making mistakes or confusing ourselves and others.

One of the most extraordinary manifestations of nature is the so-called normal distribution. If we start measuring the blood pressures of a million people, the distribution of blood pressures would look like this.

The x-axis would represent different BP ranges (above numbers are random) and the y-axis the probability for each BP range.

The average blood pressure has the highest probability (centre of the peak). Few have a BP higher than average (right of the peak) and few lower than average (left of the peak).

If we measure BP on enough number of people, we will always end up with this kind of distribution.

Most distributions tend to a normal distribution if the number of measurements increases. That is how nature/god works. There are a few exceptions (perfection is a gift that eludes even god!) - the stock market being the most notable!

Perhaps God lost money (like Newton did!) and cursed the markets!

You can google for examples of normal distribution and you will find it in different walks of life. At the IITs we use it to grade large classes, similar to what rating portals try to do.

**The standard deviation**

Assuming a distribution is normal, the standard deviation play a pivotal role. The standard deviation is a measure of how much individual data points can deviation from the average.

The point is, once I have a normal distribution, I use the mean(average) which is the peak value and the standard deviation in the following way:

**Expected value:** average+/-standard deviation

Here the expected value refers to expectation up to 68% probability.

**Annual returns S&P 500**

The X-axis is return range and Y-axis probability of each return bin.

The Notice the absence of symmetry. The red line present the total probability count. You can ignore it.

Such a distribution is known as a skewed distribution.

## Sensex Annual Return

The lone point on the right is due to Mr. Harshad Mehta! Even if we remove that point, the rest of the points are not normal.

## 15 year CAGR distribution

Still not normal and skewed to the right (which is probably a good thing!). In such distribution, the average return is meaningless. Instead of the average or mean, we should use the median. The median divides the distribution into two exact halves.

Fortunately, it is possible to transform a non-normal distribution to a normal distribution by using the square root of the returns instead of the returns.

## Square root 15 Y distribution

The x-axis here is the square root of the return. Exact values do not matter.

This distribution is not 100% normal but is nearly so. Therefore, the average and standard deviation are reasonable approximations.

**Conclusion**

** ** Over a 15 year period, Sensex returns in the past (for buy-and-hold) have returned 14% on average, but with a spread of 4%.

That is returns can typically vary from 10% to 18%.

Therefore do not expect too much from equity: 10% is an extremely safe expectation; 12% is reasonable; 14% is borderline okay. Anything above that is nuts!

moronbuffett" ..Therefore do not expect too much from equity: 10% is an extremely safe expectation; 12% is reasonable; 14% is borderline okay. Anything above that is nuts!.... "

Excellent!

Dr. Murari, some of your posts are worthy of publication at least in statistics / economics / siam journals. What do you feel ?

All your posts follow a problem statement, analysis, data validation and conclusion methodology anyway.

pattuThanks man. Been doing this for 20Y. So need to do this a lot better that this. As for publishing, I think exposure in a blog like this, with incisive feedback from you guys is more important to me than getting published in an obscure journal. Have enough of those.

moronbuffett" ..Therefore do not expect too much from equity: 10% is an extremely safe expectation; 12% is reasonable; 14% is borderline okay. Anything above that is nuts!.... "

Excellent!

Dr. Murari, some of your posts are worthy of publication at least in statistics / economics / siam journals. What do you feel ?

All your posts follow a problem statement, analysis, data validation and conclusion methodology anyway.

pattuThanks man. Been doing this for 20Y. So need to do this a lot better that this. As for publishing, I think exposure in a blog like this, with incisive feedback from you guys is more important to me than getting published in an obscure journal. Have enough of those.

Kanav KaliaSpot on, as always! Very nice and detailed analysis...

pattuThank you

Kanav KaliaSpot on, as always! Very nice and detailed analysis...

pattuThank you

PradeepAs usual, mind-blowing analysis.... And thanks for introducing the hindi word Vichalan. Kitna milta hai could be up by couple of points up, if we consider that most funds manage to beat the benchmark?

pattuThank you. Yes expectations can be a touch higher.

PradeepAs usual, mind-blowing analysis.... And thanks for introducing the hindi word Vichalan. Kitna milta hai could be up by couple of points up, if we consider that most funds manage to beat the benchmark?

pattuThank you. Yes expectations can be a touch higher.

RamamurthyWhy dont you do a post on INTRINSIC value and MARGIN of SAFETY please?

How to calculate etc>

pattuHave include necessary models in the stcok valuation sheets, sir. Will need to learn more to write about it. Will try.

RamamurthyWhy dont you do a post on INTRINSIC value and MARGIN of SAFETY please?

How to calculate etc>

pattuHave include necessary models in the stcok valuation sheets, sir. Will need to learn more to write about it. Will try.

Abhay TanejaDo you think there can be saturation in equity markets (may be after 100 yrs or so) and they could start giving constant returns like fixed deposits?

pattuThere is no way that the market could give constant returns. After 100Y of US market history, it is as volatile as ever. Returns will always be related to inflation.

Abhay TanejaDo you think there can be saturation in equity markets (may be after 100 yrs or so) and they could start giving constant returns like fixed deposits?

pattuThere is no way that the market could give constant returns. After 100Y of US market history, it is as volatile as ever. Returns will always be related to inflation.

AK AnandSo if one is not too greedy, it should be ok at 10-14%. I suppose that is a perfectly fine and decent return.

AK AnandSo if one is not too greedy, it should be ok at 10-14%. I suppose that is a perfectly fine and decent return.

AK AnandThere are all types of companies in the market, some will excel, and there will be some laggards. Plus there are all types of investors/players. So IMO there may never be stagnation, which would be probably good for everyone.

pattuYes, one company or the other should profit for society to function!

AK AnandThere are all types of companies in the market, some will excel, and there will be some laggards. Plus there are all types of investors/players. So IMO there may never be stagnation, which would be probably good for everyone.

pattuYes, one company or the other should profit for society to function!

Pattabiraman MurariYes I agree.

Pattabiraman MurariYes I agree.

Alok JhaExcellent interpretation of a statistician!

Alok JhaExcellent interpretation of a statistician!

Alok JhaA similar post is expecting on the dynamic asset allocation strategy based on equity debt yield ratio to obtain return with less volatility.

Alok JhaA similar post is expecting on the dynamic asset allocation strategy based on equity debt yield ratio to obtain return with less volatility.

Shankaryou are doing a great service for beginners to understand information from raw data.

Shankaryou are doing a great service for beginners to understand information from raw data.

freefincalPost authorThank you very much.

Toohey ShroffExcellent post. Do your numbers factor in dividends for sensex as well? I'm to sure it does. In that case, perhaps return expectation could be increased by 1-2% p.a.

Toohey ShroffExcellent post. Do your numbers factor in dividends for sensex as well? I'm to sure it does. In that case, perhaps return expectation could be increased by 1-2% p.a.

Rohit Agnihotri UllooHe is saying that expectation of anything above 14% is nuts. I would conclude 14 is normal but 10 is as probable as 18%... Also, if you do NOT hold when the market is southward, the net percentage can be higher that even 18.

Rohit Agnihotri UllooHe is saying that expectation of anything above 14% is nuts. I would conclude 14 is normal but 10 is as probable as 18%... Also, if you do NOT hold when the market is southward, the net percentage can be higher that even 18.

freefincalPost authorYes spot on. 10% is as probable as 18%. Active management will probably reduce the spread.

ltinvestmentHow to arrive 14% on average, but with a spread of 4%.. I am stuck there. Please enlighten. Thanks for your post which is clearly isolates Quick money making minded people from Market which is healthy scneario.

freefincalPost authorThe mean and std dev of the square root distribution is converted back to the normal distribution to get 14% and 4%

ltinvestmentHow to arrive 14% on average, but with a spread of 4%.. I am stuck there. Please enlighten. Thanks for your post which is clearly isolates Quick money making minded people from Market which is healthy scneario.

freefincalPost authorThe mean and std dev of the square root distribution is converted back to the normal distribution to get 14% and 4%

Pattabiraman MurariThanks Alok

Pattabiraman MurariThanks Alok

Pattabiraman MurariI did one based on the yield gap when the DSP BR fund was started.

Pattabiraman MurariI did one based on the yield gap when the DSP BR fund was started.

Pattabiraman MurariThank you. They include dividends.

Pattabiraman MurariThank you. They include dividends.

DivyaSir. A great post. You have broken down a huge mountain to a pile of stones that a beginner like me can pick easily.

Alok JhaPattabiraman Murari , I saw that on the posting date itself. DSP BR yield gap fund is interesting for me! If I remember correctly the volatility is not measured in your post. Another point what I wanted to make is that the pricing of gold in India would always give an indication of sensex top/bottom. In the case of boom and bust gold will hedge, though it is not a growth asset class. If the portfolio is made based on a mathematical model of dynamic asset allocation of equity, debt and gold , it would give superior risk adjusted return then any other models; It is my personal line of thinking. The equity allocation; I take some function e.g {SIN EDYR(Equity Debt Yield Ratio)*50}*100 and for gold I would keep it a function based on some multiple of sensex/gold 10g price in Rs. It is still in an exploratory stage. Please comment if my line of thinking is wrong. Rgds,

Bharat ArvindWhen I retired in 2005, I was 90% invested in equity mutual funds. Now 10 yrs later, with a 95% allocation (suits my risk profile, not yours!), have a +12% return despite several misjudgements. Am more than content, as calculated with 10% return, and can testify that pattu's mathematical model is practical. However, make sure that an emergency fund exists that can take care of the returns volatility. Simple way - if the market has returned 40 - 50% in past year, set aside funds for the next 18 months as your safety net.

All in all, fantastic article and analysis... No words enough to thank you for the good deed of educating others.

SuhasWhen ever a number is posted like this w.r.t return i'am always skeptical w.r.t type of investment, in this case you have analyzed buy and hold, i.e someone buys X at time T and return is 14% with a deviation of 4% at T+15 yrs, but how is dynamic when a person does a SIP over the period of T+15 and not just buy at T and hold for 15?

freefincalPost authorIt will certainly be different. I have tool called comprehensive investment comparator tool. You can check sip results for different durations there.

sundararajanThanks for an excellent article. I have a Match background, but never used / seen math is used in a real life situation like this. Of course, my math knowledge helped in my job to analyze lot. I have one quick question, this return 14% (10 to 18%) is it net of MF expenses or expenses have to be taken out from this? Please let me know. Thanks

freefincalPost authorThank you. In the above study, expenses are not included. Such returns from mutual funds after expenses is not impossible.