Valuation of sensex, a innovative new approach

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Date: 7th February, 2011

To develop a method that evaluates whether the markets are over

or under valued.

Dissertation Report

Submitted in Partial Fulfilment of the Requirement of the Dissertation in the Master of Business Administration Programme (Full Time)

Batch 2009-2011

Faculty guide:-

Prof. Neeraj Amarnani

Submitted By:-

Tanesh Gagnani

Roll No. 081121

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Contents

To develop a method that evaluates whether the markets are over or under valued. ..................... 0

Dissertation Report ................................................................................................................................. 0

Table of appendices, graphs and tables giving titles and page references ............................................ 2

Letter of Approval ................................................................................................................................... 3

CERTIFICATE ..................................................................................................................................... 3

Acknowledgements ................................................................................................................................. 4

Executive Summary ................................................................................................................................. 5

Introduction ............................................................................................................................................ 7

Background ............................................................................................................................................. 8

Review of Literature ................................................................................................................................ 9

Objectives ............................................................................................................................................. 13

Plan ....................................................................................................................................................... 15

Description ........................................................................................................................................ 15

Using this model as a market timing tool ......................................................................................... 15

Process .............................................................................................................................................. 16

Using this model as a market timing tool ......................................................................................... 28

Correlation with Economic and Market Factors ................................................................................... 28

Problems ............................................................................................................................................... 28

Limitations ............................................................................................................................................ 30

Tools used for data collection and Data analysis .................................................................................. 31

Result from analysis of data .................................................................................................................. 33

Correlations & Regression .................................................................................................................... 34

Discussion of result obtained in backdrop of reasoning and support drawn from past research ....... 37

Conclusion ............................................................................................................................................. 39

Implications ........................................................................................................................................... 40

Bibliography .......................................................................................................................................... 42

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Table of appendices, graphs and tables giving titles and page

references

Sr. No. Graphs and Tables Page

No.

Table 1 Calculation of Sensex A 17

Table 2 Calculation of Sensex B 21

Table 3 Calculation of implied Growth

Rate 24

Table 4 Implied Growth rates(calculated) 33

Graph 1 Graph for implied growth rates 33

Table 5 Correlation Table 34

Table 6 Regression statistics 34

Table 7 Anova 34

Table 8 Residual output 36

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Letter of Approval CERTIFICATE

This is to certify that Mr. Tanesh Gagnani (Roll No: 081121), a student of Full time MBA,

Batch- 2009-11, is currently doing his Dissertation Project on the topic – „To develop a

method to which evaluates whether the markets are over or under valued’ under my

guidance and has submitted his draft report on the same.

Date: 10 January, 2011

MBA Programme Officer

Institute Of Management

Nirma University

Prof. Neeraj Amarnani

Faculty (Finance)

Institute of Management, Nirma University

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Acknowledgements

At the onset, I would like to express my profound gratitude to Prof. Neeraj Amarnani (Faculty,

Finance, IMNU), for his constant mentoring during the course of dissertation. It could not be

completed without his able support and guidance.

I would also take the opportunity to thank Prof Nina Muncherji, MBA Programme

Chairperson, IMNU for providing me the necessary information, guidance and help throughout

the course. Further a project of this nature calls for support from the officials of Library,

IMNU who helped me in providing the databases and journals as and when required.

Tanesh Gagnani

Roll No. 081121

MBA-FT 2009-2011

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Executive Summary The main idea of this research was to create a system by which a layman could time

his entry and exit in the stock market. To time the entry and exit a system was needed

which could indicate whether the market is over or under-valued. This was

determined by calculating implied growth rate of a Market Index which would justify

the level of Index (share prices of all the companies comprising that index),

considering the trailing twelve months „earnings per share‟ and their cost of equity

individually.

Implied growth rate for Sensex was calculated for the period from June 2008 to

January 2011. According to that the Indian equity markets are overvalued at 20022

points. The correct value of Sensex should be at around 14589.

This model can also be used as a market timing tool using mean +/- standard

deviation as exit and entry points. Upon testing it for the above stated period it gave

better returns than long term investing for the same period.

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Section – I

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Introduction The main idea of this research was to create a system by which a layman could time

his entry and exit in the stock market. To time the entry and exit a system was needed

which could indicate whether the market is over or under-valued. This was

determined by calculating implied growth rate of a Market Index which would justify

the level of Index (share prices of all the companies comprising that index),

considering the trailing twelve months „earnings per share‟ and their cost of equity

individually.

Index in this study will be chosen as an indicator because it is comparatively easy to

track than multiple companies.

In this model calculated implied growth rates have been correlated with economic and

market factors which would have a bearing on values of market indicators (Indices).

The correlation with implied growth rate was calculated for Rate of Inflation, GDP

growth rate, Benchmark Interest Rate (Reverse Repo), Net Foreign Institutional

Investments, Net Mutual Fund Investments and net Domestic Institutional

Investments. These correlations have found be well below significant levels.

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Background The main reason for researching on this tool was to create a simple system which

could guide investors about over-whelming (irrational) exuberance and sheer pessimism of

market in terms of share prices.

Besides the reason stated above another reason is overreliance of price of earnings ratio and

the fact that there has already been a lot of research done on it. Robert Shiller specifically has

done extensive work on it and now there is very limited scope of further research at the very

basic level. There is also a problem with P/E indicator that it is a ratio and a complex one its

value is dependent upon three variables – risk, growth and cash-flow generating potential1.

While implied growth rate as an indicator just indicates the growth that market is assuming

for the market. This has much less factors on which it is dependent and hence it will be much

easier to use this implied growth rate as an input in other research.

This is a relatively new concept and very little research has been done on it. Hence researcher

has found it to be perfect contender for research.

1 [page 245] Damodaran, Aswath (2006). Damodaran on Valuation (2nd ed). Wiley India Pvt. Ltd.

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Review of Literature

USA, Federal Government (unconfirmed). Fed valuation model.

The Fed Valuation Model is a simple method to sort out relative valuations between the bond

versus stock markets. It is acknowledged to be one of the Federal Reserve‟s favorite tools to

measure investor sentiment.

The Fed Model inherently assumes there is a “guns or butter” type of trade-off between

owning stocks versus owning bonds. Is assumes the relative attraction of one over the other,

and therefore the relative valuation of one over the other, is ultimately rooted in certain

fundamentals (stock prices, corporate earnings, corporate earnings growth, bond yields). The

model also embraces the view that other important factors, including qualitative and

“emotional” ones, can temporarily account for the attraction of one investment over the other.

Said another way, the model assumes the fundamental elements of prices, cash-flow,

earnings, and earnings growth determine a “central tendency” in the relationship between

equity and bond valuations, but this tendency is sort of a mean, or median relationship. The

simple math doesn‟t always hold true, because there are many peripheral elements driving

relative valuations in addition to the primary ones.

A Treasury bond‟s long-term yield-to-maturity (BY) has very few variables associated with

it. It is not much of a stretch for an investor to consider it her expected ROI. It is a “safe”

return in all respects. This is not the case with a stock‟s earnings yield (EY). On the negative

side, you don‟t know what the company will do with the earnings – dividend them out,

reinvest them successfully in the company‟s growth, use them for spurious loans to dishonest

corporate executives, etc.

On the positive side, if/when corporate earnings grow, stockholders will ultimately derive a

direct and increasing benefit not available to bondholders. It is this ability to benefit from

growing returns that makes stocks fundamentally attractive for a long-term investor. The

more earnings growth perceived to be out there, the more attractive today‟s stock(s) are.

When earnings growth expectations are very high, the relative attractiveness of stocks versus

bonds increases, and you‟ll accept less current earnings yield compared to bond yield. The

EY/BY ratio is poised to decline below its normal range. It will, as stocks are bid up versus

bonds, unless realized earnings growth is fast enough to deliver on the high equity

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expectations. Then, as was the case in 1996-98, the ratio stays in its normal range even as the

equity markets soar (it also helped that interest rates declined).

Ultimately, growth expectations reach a point where corporate earnings can‟t deliver on

them. Stock prices are bid up faster than earnings rise (you‟ve heard of a market that is

increasingly “priced for perfection”) and the EY/BY ratio drops below its normal range, even

if bond yields have dropped. This can be a period like 1999-2000, where earnings were rising

sharply but expectations were rising even faster. Or it can be a period like 1991, where the

market began anticipating an earnings recovery (growth) that didn‟t materialize for some

time.

Unrewarded “animal spirits” (Keynes‟ term) or irrational exuberance (Greenspan‟s term) is

eventually unsettling for investors, and the high relative attraction of stocks versus bonds

begins slipping. The EY/BY ratio begins to rise. This can occur even as corporate earnings

growth is finally coming on strong (like in 1993-94), or if the market expects a drop in bond

yields will be quickly reversed (1995-96). In these two cases, equity markets became cheap

because they had gained less than they fundamentally “deserved” to based on earnings

growth and interest rates. This period represented the buying opportunity of a generation.

On the other hand, the high EY/BY ratio on March 2001 represented an insidious value trap.

Market values had fallen very sharply from a wildly overvalued state 12 months earlier, even

though bond yields were dropping. The kicker was forward-looking earnings (2001), which

were poised to produce the greatest one-year percentage decline since the 1930‟s. That is,

stock prices had fallen more than trailing earnings, but not nearly enough to compensate for

the earnings decline to come.

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Yardeni, Edward (2001). Asset Valuation & Allocation Models, Deutsche Bank

Alex. Brown, Global Strategy, Equity Research.

The Yardeni model addresses some of the criticisms of the Fed model. In creating the model,

Yardeni assumed the investors valued the earnings rather than dividends. With the

assumption that markets set price equal to intrinsic value, P (t=0) = V (t=0), a constant

growth valuation model that values earnings is presented as ( ) ( )

. E(t=1) is an

estimate of next year‟s earnings, r is required rate of return and g is the earnings growth rate.

The FSVM is a very simple stock valuation model. It should be used along with other stock

valuation tools, including the New Improved version of the model. Of course, there are

numerous other more sophisticated and complex models. The Fed model is not a market-

timing tool. As noted above, an overvalued (undervalued) market can become even more

overvalued (undervalued). However, the Fed model does have a good track record of

showing whether stocks are cheap or expensive. Investors are likely to earn below (above)

average returns over the next 12-24 months when the market is overvalued (undervalued).

The next logical step is to convert the FSVM into a simple asset allocation model. I‟ve done

so by subjectively associating the “right” stock/bond asset mixes with the degree of

over/under valuation as shown in the table below. For example, whenever stocks are 10% to

20% overvalued, I would recommend that a large institutional equity portfolio should have a

mix with 70% in stocks and 30% in bonds.

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Chen, Yong. Liang, Bing (Dec 2007). Do Market Timing Hedge Funds Time the

Market?, Journal of Financial & Quantitative Analysis, Dec2007, Vol. 42 Issue

4, p827-856, 30p.

This paper examines whether self-described market timing hedge funds have the ability to

time the U.S. equity market. They have a new measure for timing return and volatility jointly

that relates fund returns to the squared Sharpe ratio of the market portfolio. This paper does

prove timing is possible in equity markets.

Damodaran, Aswath (2006). Damodaran on valuation. New Jersey, John Wiley

& Sons, Inc.

Book is referred for understanding valuation which will be required in this paper.

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Objectives

Develop a method evaluates whether the markets are over or under-valued or fairly

priced.

Test whether this model gives out better returns than long term investing.

To evaluate whether Indian Equity Markets are over or under-valued.

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Section – II

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Plan The idea here is to find the implied growth rates for an index over a period time and then to

figure out logic according to which an entry and an exit points could be found out and an

investor would invest or divest only upon the breach of these points.

Description To calculate implied growth rate for any stock what we need is

1. The stock price (P)

2. Its cost of equity (r)

3. Earnings per share (trailing twelve months preferred) (E).

Formula used in this is ( ) ( )

„g‟ used in this formula is implied growth rate keeping that all other variables are known.

Which are E(t=1) which is Earnings at time T=1. Which is calculated by E(1+g). By

slightly modifying this formula we get formula for „g‟.

( )

( )

For calculation of growth rate of entire index we need to find out that common value of

„g‟ for which the prices (calculated using „ ( ) ( )

where all variables mean

same as above) of all the stocks forming that index when used to calculate the index value

result in actual index value at that time.

Then we calculate the mean and standard deviation of calculated growth rates and using

those mean and standard deviations create range (value of „g‟) at which we buy or sell the

stocks.

Using this model as a market timing tool To use this model as a market timing tool one can mean and stand deviation of last few years of

implied growth rate and use ‘mean – x standard deviation’ as an entry point and ‘mean + x standard

deviation’ as an exit point.

‘X’ can vary with the user of this tool based on his own needs.

Assumption: All the investments made using this model will be into same index funds

for which we are calculating implied growth rate.

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Process First we need to choose the index for which we will calculate the implied growth rate. For our

purpose the index must have following qualities

1. It should be a popular index.

This is just to have a better penetration of this model, the more people we have

familiar with the index, the bigger is its target user group.

2. It should have less number of stocks

This model is just a demonstrator and is intended to be used only for educational,

learning, understanding or research purpose. This model is not a final product which

could be used for actual trading. Lesser number of stocks will make the calculation

easier and it will be easier to find out the mistakes and understand effectiveness and

working of this model.

3. It should not be a sectorial index

Since the main purpose of this model is to find out whether markets are over or under-

valued we need an Index which is diversified. Sectors might be following a different

trend (certain sector stocks might be over or under-valued more or in opposite

direction of rest of the market) and in that Sectorial index will not fulfill the purpose.

Selected Index: SENSEX

o It is the most popular index.

o It is not a sectorial index and is well diversified.

o It consists of only 30 companies which will make calculation of implied

growth rate relatively easier.

Note: In reality it is better and will give output with lesser error if we choose the

greater number of companies.

Then we calculate the implied growth rate using the technique discussed above. An

instance of implied growth rate calculation is shown on the next page.

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May-08

May-08

May-08

Company Name Free Float

No of shares

30 days Avg.

Closing

Beta EPS

A C C Ltd. 0.55 187745356 693.7 0.85 65.33

Ambuja Cements Ltd.

0.55 1525617511 106.81 0.78 8.14

Bajaj Auto Ltd. 0.55 289367020 297.7 0.91

Bharat Heavy Electricals Ltd.

0.35 489520000 1748.36 1.01 58.65

Bharti Airtel Ltd. 0.35 3797530096 424.8 0.68 32.9

Cipla Ltd. 0.65 802921357 209.23 0.51 9.02

D L F Ltd. 0.25 1697403220 632.53 1.63 15.1

Dr. Reddy'S Laboratories Ltd.

0.75 169201575.00 660.47 0.48

Grasim Industries Ltd.

0.75 91685012.00 2284.88 0.87 238.03

H D F C Bank Ltd.

0.80 459690703 1443.18 0.92 44.86

Hero Honda Motors Ltd.

0.50 199687500 801.58 0.44

Hindalco Industries Ltd.

0.70 1913476324 171.44 1.33 18.91

Hindustan Petroleum Corpn. Ltd.

0.50 338627250.00 245 0.78

Hindustan Unilever Ltd.

0.50 2182080402 242.02 0.47 8.06

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Housing Development Finance Corpn. Ltd.

0.90 290951303 533.22 0.92 63.35

I C I C I Bank Ltd. 1.00 1115458683 882.06 1.38 37.36

I T C Ltd. 0.70 3818176790 110.48 0.47 8.2

Infosys Technologies Ltd.

0.85 573901101 1842.43 0.45 76.03

Jaiprakash Associates Ltd.

0.55 2124634633 168.14 1.7 5.09

Jindal Steel & Power Ltd.

0.45 933943010 385.21 1.45

Larsen & Toubro Ltd.

0.90 603167122 1457.05 1.2 74.33

Mahanagar Telephone Nigam Ltd.

0.45 630000000.00 102.73 1.04

Mahindra & Mahindra Ltd.

0.75 578434478 327.93 1.1 37.87

Maruti Suzuki India Ltd.

0.50 288910060 784.11 0.74 60.22

N T P C Ltd. 0.20 8245464400 186.44 0.69 8.99

Oil & Natural Gas Corpn. Ltd.

0.20 2138872530 957.96 0.9 76.28

Ranbaxy Laboratories Ltd.

0.40 420754157.00 492.15 0.8 13.26

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Reliance Communications Ltd.

0.35 2064026881 564.1 1.31 12.53

Reliance Industries Ltd.

0.55 3270714336 1289.12 1.03 101.3

Reliance Infrastructure Ltd.

0.60 244870262 1368.14 1.54 42.46

Satyam Computer Services Ltd.

0.60 1176424871.00 493.8 0.72 25.56

State Bank Of India

0.45 634883509 1642.18 1.08 105.99

Sterlite Industries (India) Ltd.

0.45 3361207534 220.37 1.41

Sun Pharmaceutical Inds. Ltd.

0.40 207116391 276.83 0.31

Tata Consultancy Services Ltd.

0.30 1957220996 479.05 0.49 42.48

Tata Motors Ltd. 0.65 506381356 635.6 1.16 52.61

Tata Power Co. Ltd.

0.70 237307236 1393.62 1.01

Tata Steel Ltd. 0.70 887214196 867.51 1.45 66.21

Wipro Ltd. 0.20 2449412810 298.97 0.75 20.96

Table 1 for Calculation of Sensex A

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May-08 Jun-08

Company Name cost of equity

No of Free float shares

30 days Avg.

Closing

Sensex Contribution

30 days Avg.

Closing

Sensex Contribution

A C C Ltd. 0.1597 103259945.80 693.70 71631424401 618.27 63842526689.77

Ambuja Cements Ltd.

0.1527 839089631.05 106.81 89623163492 85.47 71716990765.84

Bajaj Auto Ltd. 0.1656 159151861.00 0.00 0 0.00 0.00


0.1756 171332000.00 1748.36 299550015520 1456.50 249545058000.00

Bharti Airtel Ltd. 0.1427 1329135533.60 424.80 564616774673 398.36 529474431164.90

Cipla Ltd. 0.1258 521898882.05 209.23 109196903091 212.38 110840884569.78

D L F Ltd. 0.2373 424350805.00 632.53 268414614687 488.20 207168063001.00


0.1228 126901181.25 0.00 0 0.00 0.00


0.1617 68763759.00 2284.88 157116937664 2152.15 147989923931.85

H D F C Bank Ltd.

0.1666 367752562.40 1443.18 530733143004 1148.90 422510918941.36


0.1188 99843750.00 0.00 0 0.00 0.00


0.2075 1339433426.80 171.44 229632466691 151.54 202977741497.27


0.1527 169313625.00 0.00 0 0.00 0.00

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0.1218 1091040201.00 242.02 264053549446 227.35 248047989697.35


0.1666 261856172.70 533.22 139626948407 447.87 117277524067.15

I C I C I Bank Ltd. 0.2124 1115458683.00 882.06 983901485927 741.08 826644120797.64

I T C Ltd. 0.1218 2672723753.00 110.48 295282520231 101.03 270025280765.59


0.1198 487815935.85 1842.43 898766714688 1861.53 908083999062.85


0.2443 1168549048.15 168.14 196479836956 118.36 138309465339.03


0.2194 420274354.50 0.00 0 0.00 0.00


0.1945 542850409.80 1457.05 790960189599 1298.31 704788115547.44


0.1786 283500000.00 0.00 0 0.00 0.00


0.1846 433825858.50 327.93 142264513778 280.59 121727197636.52


0.1487 144455030.00 784.11 113268633573 724.63 104676448388.90

N T P C Ltd. 0.1437 1649092880.00 186.44 307456876547 161.31 266015172472.80

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0.1646 427774506.00 957.96 409790865768 862.49 368951233679.94


0.1547 168301662.80 492.15 82829663347 540.95 91042784491.66


0.2055 722409408.35 564.10 407511147250 522.32 377328882169.37


0.1776 1798892884.80 1289.12 2318988795653 1112.06 2000476821470.69


0.2284 146922157.20 1368.14 201010080152 1017.06 149428649201.83


0.1467 705854922.60 493.80 348551160780 476.69 336473983054.19

State Bank Of India

0.1826 285697579.05 1642.18 469166850364 1289.30 368349888669.17


0.2154 1512543390.30 0.00 0 0.00 0.00


0.1059 82846556.40 0.00 0 0.00 0.00


0.1238 587166298.80 479.05 281282015440 452.64 265774953488.83

Tata Motors Ltd. 0.1905 329147881.40 635.60 209206393418 491.72 161848596242.01

Tata Power Co. Ltd.

0.1756 166115065.20 0.00 0 0.00 0.00

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Tata Steel Ltd. 0.2194 621049937.20 867.51 538767031020 805.45 500224671917.74

Wipro Ltd. 0.1497 489882562.00 298.97 146460189561 288.93 141541768638.66

Zee Entertainment Enterprises Ltd.

0.1696 586845678.00 0.00 0 0.00 0.00

total

11866140905131

10473104085361.10 Table 2 Calculation of Sensex B

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May-08 Jun-08

Company Name cost of equity

No of free-float shares

EPS*(1+g)/(r-g)

Available MarketCap

EPS*(1+g)/(r-g)

Available MarketCap

A C C Ltd. 0.1597 103259945.80 409.182012 42252112358 944.842167 97564350958.86

Ambuja Cements Ltd.

0.1527 839089631.05 53.3113277 44732982269 144.86944 121558444808.45

Bajaj Auto Ltd. 0.1656 159151861.00 0 0 0 0.00


0.1756 171332000.00 334.00533 57225801271 768.369304 131646249659.64

Bharti Airtel Ltd. 0.1427 1329135533.60 230.50838 306376878086 744.076128 988978021154.15

Cipla Ltd. 0.1258 521898882.05 71.7033928 37421920539 279.50434 145873002409.35

D L F Ltd. 0.2373 424350805.00 63.619664 26997055612 116.645058 49498424409.23


0.1228 126901181.25 0 0 0 0.00


0.1617 68763759.00 1472.4841 101253541897 3606.8429 248020075608.65

H D F C Bank Ltd.

0.1666 367752562.40 269.215997 99004872709 577.84419 212503681546.67


0.1188 99843750.00 0 0 0 0.00


0.2075 1339433426.80 91.1465865 122084784645 182.300977 244180022096.30


0.1527 169313625.00 0 0 0 0.00


0.1218 1091040201.00 66.1675369 72191442715 287.363568 313525205165.00

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0.1666 261856172.70 380.179077 99552238109 1160.21827 303810315886.57

I C I C I Bank Ltd. 0.2124 1115458683.00 175.854797 196158760717 327.718564 365556518286.28

I T C Ltd. 0.1218 2672723753.00 67.3168489 179919341071 277.536276 741777798050.38


0.1198 487815935.85 634.535136 309536351216 2938.77978 1433583609183.13


0.2443 1168549048.15 20.8333333 24344771836 35.7198879 41740440990.90


0.2194 420274354.50 0 0 0 0.00


0.1945 542850409.80 382.12009 207434047709 816.956245 443485032351.59


0.1786 283500000.00 0 0 0 0.00


0.1846 433825858.50 205.190724 89017041945 419.887441 182158029423.27


0.1487 144455030.00 404.965569 58499313446 1089.70475 157413331685.37

N T P C Ltd. 0.1437 1649092880.00 62.5504439 103151491687 165.260131 272529304946.32


0.1646 427774506.00 463.313897 198193873407 1243.06496 531751497602.21


0.1547 168301662.80 85.7253685 14427722063 100.044765 16837700380.36

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0.2055 722409408.35 60.9803578 44052784202 94.3646452 68169907483.11


0.1776 1798892884.80 570.421425 1026127042538 1296.21605 2331753835102.48


0.2284 146922157.20 185.91495 27315025548 337.043496 49519157549.86


0.1467 705854922.60 174.218878 122973252506 540.288738 381365465082.05

State Bank Of India

0.1826 285697579.05 580.550808 165861960494 1282.799 366492567842.10


0.2154 1512543390.30 0 0 0 0.00


0.1059 82846556.40 0 0 0 0.00


0.1238 587166298.80 343.123001 201470262455 1392.56946 817669852872.74

Tata Motors Ltd. 0.1905 329147881.40 276.1158 90882930472 528.953271 174103848515.24

Tata Power Co. Ltd.

0.1756 166115065.20 0 0 0 0.00

Tata Steel Ltd. 0.2194 621049937.20 301.750068 187401861006 569.334056 353584879948.03

Wipro Ltd. 0.1497 489882562.00 140.01336 68590103537 374.026552 183229085582.10

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Zee Entertainment Enterprises Ltd.

0.1696 586845678.00 0 0 0 0.00

Sensex value

16844

16707.36 implied growth rate

8.97%

Table 3 Calculation of implied Growth Rate

These three tables and intermediate data in them represent the steps involved in calculation of

implied growth rate for Sensex.

For calculation of implied growth one must first understand how Sensex is calculated. For calculation

of Sensex following inputs are required.

1. Free-Float for all the stocks that constitute Sensex: Shareholding of investors that

would not, in the normal course come into the open market for trading are treated as

'Controlling/ Strategic Holdings' and hence not included in free-float. Specifically, the

following categories of holding are generally excluded from the definition of Free-

float.

2. Previous period Sensex value.

3. Previous period Market Capitalization.

Present Sensex value will be:

The market capitalization used in formula is free-float adjusted i.e. sum of all the share

prices of individual stocks multiplied with corresponding free-float of that share and number

of shares.

I have used 30 days average closing prices of stocks instead of taking a daily price. This is

done simply because for final calculation of implied growth rate, ‘goal seek’ function of

excel is used which cannot be inserted in a macro. Hence all the growth rates were required

28 | P a g e

to be calculated manually and to make this research meaningful I need to find implied

growth rate for at least 2 years.

After that I used the formula free-float*EPS*(1+g)/(r-g) for calculation of share prices then

used goal seek function to find the value of „g‟ for which. The calculated value of Sensex

based on prices taken using the above formula becomes equal to the value of Sensex

calculated using the BSE prescribed method already discussed above. The value of „g‟ at

which the value of both methods of calculation becomes equal is the „Implied growth rate for

Sensex‟.

This implied growth rate calculated should be equal to or nearly equal to the risk free rate of

the economy. Since the basic economic principle suggests that since we are talking about

infinitely long period of time, no company can earn at a growth more than the risk free rate.

Using this model as a market timing tool

Here I have chosen implied growth rate‟s „mean – 1 standard deviation’ as an entry point and

‘mean + 1 standard deviation’ as an exit point.

Correlation with Economic and Market Factors

Correlation with Economic and Market factors have been calculated in an attempt to further

improve this calculated implied growth rate. If we find the factors on which implied growth

rate is dependent upon then „rational guesses‟ could be made about implied growth rate when

it should be higher and when it should be lower by the average of implied growth rate or

whatever benchmark chosen.

Problems To get the best out of this model following things need to be taken care of but these could not

be implemented by me.

1. Index chosen should be such that it has a large number of companies this will reduce

the error as the total error in this model will get divided by square root of number of

29 | P a g e

companies in that index. Considering the time constraint, my own inexperience and

chances of manual error I chose not to choose an index with large number of

companies.

2. This model ideally should be implemented on a long time duration (least 10 years) but

I was not able to do it due to lack of availability of data. Prowess and capitaline plus

would not handle a query for such large data. A long time duration would give the

user an opportunity to understand, estimate or calculate the range for acceptable

„g‟(implied growth rate for index).

3. It should be implemented on an continues basis (or at least on daily basis) so as to

have a correct picture and a better understanding of fluctuations of implied growth

rate.

4. It should be implemented on few market indices of similar economies (eg: developing

countries), it would have been beyond the scope of this course to have undergone

such an extensive research.

30 | P a g e

Limitations

This model does illustrate to a great degree ability to capture any irrational exuberance and

irrational pessimism present in the market but this requires further validation.

31 | P a g e

Tools used for data collection and Data analysis

Prowess was used for price, EPS, Beta data collection.

BSE website was used for free float related data collection.

Capitaline plus was used for number of shares data collection.

Excel was used as the only for data analysis.

32 | P a g e

Section – III

33 | P a g e

Result from analysis of data When applied the model discussed above on Sensex following growth rate were output.

Date Jun-08 Jul-08 Aug-08 Sep-08 Oct-08

implied growth

rate 8.97% 8.52% 9.00% 8.51% 6.65%

Date Nov-08 Dec-08 Jan-09 Feb-09 Mar-09

implied growth

rate 5.76% 6.12% 6.07% 5.99% 5.79%

Date Apr-09 May-09 Jun-09 Jul-09 Aug-09

implied growth

rate 7.35% 8.63% 9.37% 9.48% 9.84%

Date Sep-09 Oct-09 Nov-09 Dec-09 Jan-10

implied growth

rate 10.12% 10.24% 10.81% 10.68% 10.82%

Date Feb-10 Mar-10 Apr-10 May-10 Jun-10

implied growth

rate 10.46% 10.56% 10.65% 10.41% 10.86%

Date Jul-10 Aug-10 Sep-10 Oct-10 Nov-10

implied growth

rate 11.01% 11.36% 11.52% 11.70% 11.54%

Date Dec-10 Jan-11

Table 4 Implied Growth rates(calculated)

The graph for the same is

Table 5 Graph for implied growth rates

When this model was used as a market timing tool the entry point came at October 2008 and

exit point came at September 2010. Considering the investor buys and sells only 1 Sensex

fund. The profits came out to be Rs.8791 on an investment of Rs.10775 compared to a long

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

Jun

-08

Au

g-0

8

Oct

-08

Dec

-08

Feb

-09

Ap

r-0

9

Jun

-09

Au

g-0

9

Oct

-09

Dec

-09

Feb

-10

Ap

r-1

0

Jun

-10

Au

g-1

0

Oct

-10

Dec

-10

implied growth rate

implied growth rate

34 | P a g e

term investment from June 2008 to January 2011‟s profit at Rs.3178 on an investment of

Rs.16844.

Correlations & Regression

Correlation

implied growth rate

Rate of Inflation

GDP Growth

Benchmark Interest Rate

FII Activity

MF Activity

DII Activity

implied growth rate 1 0.05906596 0.08352238 -0.2291252 0.5162704 -0.416876 -0.38418

Rate of Inflation 1 0.68901215 -0.54221643 0.2139766 -0.302406 -0.01766

GDP Growth 1 -0.09079406 0.3348126 -0.438436 -0.29427

Benchmark Interest Rate 1 -0.41155 0.2047424 0.128871

FII Activity 1 -0.648252 -0.76595

MF Activity 1 0.747332

DII Activity 1

None of the correlations were high enough that they should be considered significant.

Regression Statistics

Multiple R 0.555443318

R Square 0.30851728

Adjusted R Square 0.142561427

Standard Error 0.01810421

Observations 32

ANOVA

df SS MS F Significance

F

Regression 6 0.003655926 0.000609321 1.859032233 0.128066677

Residual 25 0.008194061 0.000327762 Total 31 0.011849986

35 | P a g e

Coefficients Standard Error t Stat P-value

Intercept 0.100369537 0.028089526 3.573201521 0.001468769

Rate of Inflation -0.051385892 0.198735439 -0.258564314 0.798088347

GDP Growth

-0.089661106 0.277695296 -0.322875856 0.74947426

Benchmark Intrest Rate

-0.070064108 0.487680138 -0.143668159 0.886914315

FII Activity 9.58456E-07 5.60567E-07 1.709798134 0.099688669

MF Activity -2.41753E-06 2.22256E-06 -1.087720383 0.28709436

DII Activity 7.72388E-07 1.19659E-06 0.645491737 0.524489255

Lower 95% Upper 95% Lower 95.0% Upper 95.0%

0.042518075 0.158220999 0.042518075 0.158220999

Rate of Inflation -0.46068919 0.357917406 -0.46068919 0.357917406

GDP Growth -0.661585274 0.482263061 -0.661585274 0.482263061

Benchmark Intrest Rate

-1.074460154 0.934331939 -1.074460154 0.934331939

FII Activity -1.96053E-07 2.11297E-06 -1.96053E-07 2.11297E-06

MF Activity -6.99498E-06 2.15993E-06 -6.99498E-06 2.15993E-06

DII Activity -1.69203E-06 3.23681E-06 -1.69203E-06 3.23681E-06

36 | P a g e

RESIDUAL OUTPUT

Observation Predicted Y Residuals Standard Residuals

1 0.074042015 0.015614593 0.960421634

2 0.081685687 0.003535205 0.217443239

3 0.085744795 0.00426982 0.26262785

4 0.078388209 0.006669353 0.410218231

5 0.075297705 -0.008787018 -0.540471492

6 0.085946163 -0.028297557 -1.740524729

7 0.087986599 -0.02680934 -1.648987549

8 0.088454099 -0.027799015 -1.709860466

9 0.090390794 -0.030526054 -1.877595

10 0.088154272 -0.030213926 -1.858396657

11 0.094709581 -0.021163412 -1.301718077

12 0.102606082 -0.016259586 -1.000093811

13 0.091035476 0.00266189 0.163727399

14 0.097826422 -0.003060001 -0.18821439

15 0.093022384 0.005345462 0.328788395

16 0.109690813 -0.008498501 -0.522725395

17 0.104957379 -0.002595622 -0.159651386

18 0.09206396 0.016064013 0.988064494

19 0.098805358 0.008037361 0.49436159

20 0.102196654 0.005978103 0.367700856

21 0.089353553 0.01527134 0.939308844

22 0.105940954 -0.000322123 -0.019813143

23 0.098224433 0.00823694 0.506637327

24 0.079286818 0.024858522 1.528996755

25 0.091477422 0.01707668 1.050351604

26 0.105963878 0.004166673 0.256283523

27 0.099026663 0.014568113 0.896054804

28 0.120150869 -0.004962355 -0.305224302

29 0.112546373 0.004423089 0.272055111

30 0.1043298 0.011066575 0.680682343

31 0.095268441 0.020469939 1.259064022

32 0.094875416 0.020980839 1.290488379

37 | P a g e

Discussion of result obtained in backdrop of reasoning and support

drawn from past research The January 2011 average closing level of Sensex is 20021.79 (calculated on 7

th January) and

for this level of Sensex the calculated implied growth rate comes out to be 4.11%. Which is

approximately equal to the global risk free rate of 4%, which is calculated by using the

formula „Indian Risk Free Rate – Default Spread‟2(7.5% - 3.5% = 4%).

Using this model as a market timing tool

Using this model as a timing tool has given better profits than long term investment during

the same period but to make any conclusive statement it requires further testing with a longer

term horizon.

2 http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/ctryprem.html

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/ctryprem.html

38 | P a g e

Section – IV

39 | P a g e

Conclusion The intended model is complete, implied growth rates for the period intended has been done.

Results obtained from this model suggest that at present Indian Equity markets are overvalued.

When this model was tested as a market timing tool it gave positive results with much better returns

than long term investment.

40 | P a g e

Implications This model requires further testing to determine what is the correct implied growth rate? If this

model or some improved version of this model is further researched there is a possibility of another

system which would be equally if not less capable than P/E ratio as an equity markets indicator.

As for its capability as a timing tool one testing done in this paper showed some promising results

but further testing is required so as to validate it. If this model is found to have some accuracy then

this can become a very important tool for layman as a market timing instrument.

41 | P a g e

Section – V

42 | P a g e

Bibliography www.moneycontrol.com

www.bseindia.com

www.capitaline.com

Prowess – Database

www.tradingeconomics.com

http://www.moneycontrol.com/

http://www.bseindia.com/

http://www.capitaline.com/

Economy & Finance

Valuation of sensex, a innovative new approach