Understanding Risk Return Anomaly

Understanding Risk-Return Anomaly Project Report

BBE III Year

COMPUTATIONAL TECHNIQUES FOR BUSINESS ECONOMICS

Sri Guru Gobind Singh College of Commerce

ABSTRACT

The traditional investment theory tells us that high returns of stocks are associated with high

risks, this paper shows in that under certain conditions, a portfolio with low beta stocks can yield

higher returns than a high-beta portfolio, a phenomenon known as ‘risk-based anomaly’. The

motivation behind this research paper is the relatively new phenomenon of ‘Risk-basedanomaly’,

which has been extensively investigated in the US and a few other countries in the last few years;

but not in emerging market, particularly India. Using a low-Beta portfolio strategy over a 8 year

period (from 2006 to 2012) with rolling quarterly iterations in the Indian market, the paper finds

that as compared to a high-Beta portfolio, a low Beta portfolio produces higher absolute returns.

DECLARATION

This is to certify that the material embodied in this project report entitled is based on our original

research work. Our indebtedness to other works, studies and publications have been duly

acknowledged at the relevant places. This project work has not been submitted in part or in full

for any other diploma or degree in this or any other university.

Group Members:Project Supervisor:

• Aayush Maheshwari – 115013 Abhishek Kumar (Assistant Professor)

• Piyush Devgun – 115017 University of Delhi

• Deepansh Jain – 115042 • Shubham Bansal – 115060 • Digvijay Jain – 115063

• Akhilesh Gupta – 115068

ACKNOWLEDGEMENT

It is a great pleasure for us to acknowledge the kind of help and guidance extended to us during

the completion of this project work. We are fortunate enough to get the support from a large

number of people to whom we shall always remain grateful.

We sincerely thank Mr. Abhishek Kumar , Assistant Professor (University of Delhi), for

assigning such a challenging task which has enriched our knowledge and work experience.

Without his cordialsupport, constant encouragement, valuable information and critical feedback,

this project would not have been possible.

Aayush Maheshwari – 115013 Piyush Devgun – 115017 Deepansh Jain – 115042 Shubham Bansal – 115060 Digvijay Jain – 115063 Akhilesh Gupta – 115068

Table of Contents INTRODUCTION ................................................................................................ 1

LITERATURE REVIEW .................................................................................... 4

SCOPE AND LIMITATION ................................................................................ 7

• Scope of Study ............................................................................................. 7

• Limitation of Study ...................................................................................... 7

NEED FOR THE STUDY ................................................................................... 8

DATA AND METHODOLOGY ......................................................................... 9

• Sampling ...................................................................................................... 9

• Data Collection ............................................................................................ 9

• Bonus and Split Adjustment .............................................................................................10

• Return Calculation ............................................................................................................10

• Systematic Risk ..................................................................................................................10

Portfolio Formation ...............................................................................................................11

Empirical Testing ....................................................................................................................12

Statement of Hypothesis .......................................................................................................13

RESULTS AND ANALYSIS .............................................................................. 17

• Case 1 ......................................................................................................... 17

• Case 2 ......................................................................................................... 21

Possible Reasons.................................................................................................. 36

CONCLUSION ................................................................................................... 37

Appendix ............................................................................................................. 38

BIBLIOGRAPHY ............................................................................................... 42

1

INTRODUCTION

“The other end of risk is reward…” Or so is the saying. According to the ‘Modern Portfolio

Theory’, there exist a direct relationship between risk and the expected return. It means

thathigher the risk, the higher should be the expected return. In an efficient market, investors

canexpect to realize above average returns only by taking above-average risks. Risky

stocksgenerally give higher returns than the average, while safe stocks do not. Thus, investors

wouldexpect higher returns for additional risks that they bear.

This approach is well accepted in formalist theories of decision making that are based on notions

of individual rationality and maximization of utility. Agency theory, a formalist theory, is based

on assumptions of rational behaviour and economic utilitarianism (Ross, 1973), and assumes a

linear positive relationship between risk and return. Risk behaviour has been associated with

assumptions of rational behaviour, outcome weighing, and utility maximization. Financial theory

posits that risk averse behaviour is manifest when low risk is associated with low return, as

wellas when high risk is rewarded by high return (Fisher & Hall, 1969). This risk averse outlook

also assumes that for each strategic alternative, firms, managers and other investors will

choosethat alternative which maximizes utility (Schoemaker, 1982). Aaker and Jacobson (1987)

found support for a positive association between performance and both systematic and

unsystematic risk, when risk was defined using accounting data. A number of other studies have

also found support for a positive risk-return relationship (Bettis, 1981).

The question, then immediately comes to mind, is, “Is it possible to have portfolios which give

returns greater than the market portfolio with lower risk by exploring the risk anomaly?” This is

the basic premise behind “Understanding Risk Return Anomaly.”

2

Risk anomaly has drawn attention of researchers only in last ten years and studies are undertaken

to explore risk anomaly and how to design an investment strategy to take advantage of it in

generating superior risk return trade-off. The two strategies frequently used to exploit this risk

anomaly are – [a] Low beta (Low volatility) portfolio and [b] Minimum variance (MV) portfolio.

Here is a brief explanation of above mentioned investment strategies:

(A) Low-Beta investing – This strategy sorts all the stocks by their volatility and/ or beta and

then takes a subset, which comprises the stocks with the lowest beta and/ or volatility.

(B) Minimum-Variance investing – It relies on observations and/ or estimates of correlations of

individual stocks. A portfolio created by optimal diversification so as to produce minimum risk

is identified as the Minimum Variance Portfolio.

These strategies have been tested in several studies done globally where portfolios with overall

lower risks have outperformed the broad index as well as the portfolios with higher risks.

Therisks have been measured either by the volatility of the stock prices or the variability of the

stock prices with respect to a benchmark like the market index (i.e. beta), or both.

This study employs Low Beta investment strategy to explore risk anomaly in Indian markets.

The low beta investment strategy based on creating equally weighted portfolio from the stocks in

the lowest beta group is the response to the sub-optimal nature of the market capitalisation

weighted portfolios. The main issue with market cap-weighted portfolios is the dominance of a

few heavy weight stocks. This can subdue the superior returns that a small or medium sized

company with good fundamentals can give to the portfolio. For example, in Indian markets, ITC

has a lion’s share of 10.02% as of 30th September, 2013 in Nifty. Hence, any market-cap

weighted portfolio that replicates the Nifty composition would give more weight to ITC than

other stocks and this may lead to sub-optimal performance of the portfolio when ITC yields

lesser returns than relatively smaller Nifty companies. Low Beta investment strategy typically

allocates equal weights to all the stocks in the portfolio—thus overcoming the bias of market

capitalization-weighted portfolios.

Low Beta investment strategy is noteworthy in the sense that it has been able to achieve higher

absolute returns as well as risk-adjusted returns consistently, including in bearish periods.

3

Low volatility portfolios are least hit during the bearish periods when high beta/ high volatility

stocks plummet. In other words, low volatility portfolio suffers less drawdown during the bearish

period.

In this paper, low-Beta portfolios are used to explore the risk anomaly in Indian equity markets.

The risk is measured using volatility of the stock prices, which is calculated using standard

deviation of monthly returns.

4

LITERATURE REVIEW

Across the world, in different markets there have been many instances of low-volatility

stocksgiving higher risk-adjusted returns. Robert Haugen (1967) noted an abnormality—lower-

risk portfolios provided superior returns to the supposedly efficient market portfolio.

Nevertheless, this insight has had limited empirical support and was not verified until the last

decade.

It was only in the previous decade that Roger Clarke, Harvin de Silva, and Steven Thorley

(2006) carried out an interesting study on the characteristics of minimum-variance (MV)

portfolios. These authorsfound that MV portfolios, based on the 1,000 largest U.S. stocks over

the period 1968-2005 achieved a volatility reduction of about 25% while delivering comparable

or even higher average returns than the broad market portfolio. They found that MV portfolios

gave on average a 6.5% excess return above T-Bills with a volatility of 11.7% whereas the

market index gave average excess return of 5.6% with a volatility of 15.4%.

Blitz and Vliet (2007) presented that portfolios of stocks with the lowest historical volatility are

associated with Sharpe-ratio improvements that are even greater than those documented by

Clarke et al (2006), and have a statistically significant positive alpha. Blitz et al (2007) found

that low volatility stocks have superior risk-adjusted returns relative to the FTSE World

Development Index. They also found that low beta stocks had higher returns than predicted

while the reverse held for high beta stocks. State Street (2009) used the monthly returns for

Russell 3000 Universe from December 1986 to October 2007 to note that low beta stocks

outperform high beta stocks. According to this study, lowest beta stocks do not necessarily

produce the highest returns, thus implying that some success can be attributed to portfolio

construction.

Some of the earliest studies tried to find out risk anomalies by using CAPM Model.Blume

(1970), Black, Jensen and Scholes (1972) and Blume and Friend (1973) worked on portfolio

returns. They found that the estimates of beta for diversified portfolios were more precise than

estimates for individual securities. Fama and MacBeth (1973) estimated month-by-month

cross-sectional regression of monthly returns on betas so as to address the problem caused by

correlation of the residuals. Additionally they included (i) squared market betas to test whether

5

the relationship between expected returns and beta is linear and (ii) standard deviation of least

square residuals from regressions of expected returns on the market return to test whether the

market beta is the only measure of risk. It was found that these additional variables did not add to

the explanation of average returns provided by beta.

Gharghori, Lee, and Veeraraghavan (2009) investigated the size effect, book-to-market effect,

earnings-to-price effect, cash flow-to-price effect, leverage effect and the liquidity effect.

Sarma, S.N.(2004) examined the multiple indices for possible seasonality. An analysis of

returns’ pattern of multiple indices is helpful in identifying the presence or otherwise of the stock

market seasonality associated with various portfolios and for testing the efficacy of investment

game based on the observed patterns of the returns. Bodla, B. S., Jindal, Kiran (2006) found

that that none of anomalies exist in the US market and thus this market can be considered as

informationally efficient. On the other hand, the Indian stock market reveals turn of the month

effect as well as semi-monthly effect but the day effect is not found.

The latest study in this field has been done in early 2012 by Rohan Laxmichand Rambhia, S P

Jain Institute of Management & Research, Mumbai. In his paper, low-volatility portfolios were

used to explore the risk anomaly in Indian equity markets. The risk was measured using volatility

of the stock prices, which was calculated using standard deviation of monthly returns.

The results found in the Indian markets are similar to those found in some other countries such as

the US: the low-volatility portfolio strategy gives a higher absolute return over a long period than

both the high-volatility portfolio and the broad market index and it requires patience to reap its

benefits. Not only does LV give higher absolute returns, but it also gives higher risk-adjusted

returns, as seen from its higher Sharpe ratio. It also provides a useful cushion against the ‘draw-

down effect’. Thus, it can be considered a very good strategy when the markets do not exhibit

any specific direction and the volatility in general is relatively high. In such situations, it ensures

minimum erosion of wealth while ensuring that an investor does not miss the upside returns

entirely. The study provides empirical support to the usefulness of this strategy in the Indian

context.

Another recent study was done by Shyam Lal Dev Pandey, Associate Professor-Finance,

Alliance University, Bangalore (Karnataka) and his objective was to study the risk return trade of

6

situation in Indian equity market. On the basis of his study it can be inferred that due diligence is

required while investing in high risk equity stocks. The traditional belief in high risk high return

philosophy could lead to significant losses. Over a long duration, it can be recommended with

certainty that portfolio of low risk stocks would yield higher returns. The risky assets could be

beneficial in a short run but it still suffers from significant probability of yielding negative

returns when compared to market and less risky assets. The inefficiency of Indian stock market

was clearly established through our study.

7

SCOPE AND LIMITATION

Scope of Study

The study tries to explore the risk return anomaly in Indian Equity Market over the time span of

8 years from October 2005 to November 2013. S&P CNX Nifty 50 is selected to represent

Market Portfolio or return on market. Systematic Risk represented by beta for each stock was

calculated using Sharpe “Single Index Model”. Formation period was of two years while holding

period of stocks was only one year.

Limitation of Study

There are few limitations of this study which need to be acknowledged.

Reliability: This study is based on analysis of secondary data. Thus the data might not be

reliable.

Accuracy: The results of this study might not be accurate due to limitations of time span

and secondary data.

Time Period:The time span of only 8 years is considered for examining risk return

anomaly in Indian equity market.

Transactional Cost: Cost of adjusting portfolio every quarter is not considered while

calculation of return.

Portfolio Beta: Beta of portfolio is calculated using simple average of all beta of stock in

that portfolio respectively.

8

Need for the study

‘Risk-based Anomaly’ is a relatively new phenomenon in the context of equity anomalies.

It was first noted in early 1967 by Robert Haugen but since then there was no significant

development in this theory. Now it has been extensively verified in the developed markets like

the US markets and with the global stock indices; but remains to be tested in emerging markets

like India.

In the US markets, low-volatility investing for the long term has become the latest investment

philosophy after the ‘Value’, ‘Size’ and “Momentum’ investing philosophies that have been fully

explored. In fact the index provider MSCI offers several MV indices as benchmarks for

financialinstitutions. S&P has just announced the next launch of S&P500 LV index6. Many big

investment houses such as the Deutsche Bank in Europe and Canada, Martingale

Assetmanagement7, Morgan Stanley, Analytic Investors LLC8 for US and Global markets, etc.

have already launched funds to benefit from this strategy. Russell and iShare and have already

launched low volatility exchange traded funds (ETFs).

The sole motivation for this study is to test this anomaly in Indian equity market.

9

DATA AND METHODLOGY

Sampling

The sample for the study consists of the constituent stocks from CNX NIFTY 50 index.

The CNX Nifty, also called the Nifty 50 or simply the Nifty, is National Stock Exchange of

India's benchmark index for Indian equity market. Nifty is owned and managed by India Index

Services and Products Ltd. (IISL), which is a wholly owned subsidiary of the NSE Strategic

Investment Corporation Limited. The reason behind selecting S&P CNX NIFTY 50 constituents

stocks as sample is that in addition to the index representing it also covers almost the entire

market. It also helps avoiding issues associated with small and illiquid stocks dominating the

results.

Data Collection

Adjusted daily closing prices 35 of the stocks on NSE for the sample stocks for the period

October 2005- November 2013 were obtained from the nseindia.comdatabase, with the analysis

period being October 2005- November 2013 for TEST 1, January 2006 –January 2013 Test 2 .

The period from 2005 to mid-2013 is used because this period represents all the recent ups and

downs of Indian stock market. This period also covers both bullish and bearish phases: ‘Bull

Run’ between 2005 to January 2008, the global financial meltdown of 2008-2009 and then the

recovery period which started thereafter.

Out of 50 companies of CNX NIFTY, companies with insufficient data were rejected.

10

Bonus and Split adjustment

If a company has undergone stock splits over its lifetime, comparing historical stock prices to

those of the present day would not accurately reflect performance. For this reason, we must

compare split-adjusted share prices. A 2-for-1 split would result in the company having twice the

number of shares, investors having twice as many shares, and each share being worth half as

much. Therefore, each investor has the same percentage of equity in the company, but the

individual shares would cost half as much to purchase. Unfortunately, if the price of the stock

suddenly drops by 50%, this can look pretty bad in a chart. If a stock splits 2-for-1, the price of a

stock is cut in half. Therefore, all of the prices after this stock split also need to be doubled half

to maintain continuity in the pricing.

Return Calculation

Stock return are measured daily using following formula ln(Pi/Pi-1) where Pi is current day price

And Pi-1 is the price of previous day. The main advantage of using logarithmic returns is that it

is not affected by the base effect problem. For example, an investment of Rs.100 that yields an

arithmetic return of 20% followed by an arithmetic return of -20% results in a return value of Rs.

96; while an investment of Rs.100 that yields a logarithmic return of 20% followed by a

logarithmic return of -20% results in Rs. 100.

Systematic Risk

Systematic risk represents risk that is “un-diversifiable risk” or the risk which applies to the

whole market, such as, interest rate, inflation rate, exchange rates, wars, recession represent

systematic risk and that’sbecause these factors affect whole of the market and cannot be

diversified.

11

Calculation of β (systematic risk)

For calculation of β Sharpe’s single index model was used. This model regresses Ri on Rm to

obtain estimates of � and β. β represents systematic risk.

Ri = α + βRm + µi.

Ri : Return on stock i

Rm : Return on index

β is a measure of systematic risk, of a security or a portfolio in comparison to the market as a

whole. Beta is used in the capital asset pricing model (CAPM), a model that calculates the

expected return of an asset based on its beta and expected market returns.

Portfolio Formation

Case 1

Daily returns of each stock for the period of October 2005- November 2013 were regressed on

daily return on nifty and β value was calculated for each of the stocks. Stocks were then ranked

on basis of their � value. Stock with lowest β value was given first rank and so on. Then stocks

were divided into groups of five in increasing order of β values. Seven equally weighted

portfolios of five stocks each were constructed this way.P1 represents the portfolio of five stocks

with lowest values, whereas P8 represents portfolio of stocks with highest β values.

Case 2

To improve robustness of earlier study done in Case 1 method was used. Daily returns of each

stock for the period of January 2006- January 2011 were regressed on daily return on nifty and β

value was calculated for each of the stocks. Here we specifically use a strategy to select create

portfolios on the basis of their β values over past 2 years(Formation Period) and then hold them

for next one year(Holding Period).At the beginning of each 17 quarters over the time period of

January 2006- January 2009 stocks are ranked on the basis of increasing beta values and 8

equally weighted portfolio’s are created for each containing 4 stocks. Each portfolio was held for

next one year.

12

Empirical Testing

Rpi-Rpj = α(pi-pj) + β(pi-pj)Rm + µ i

Where, RPi: daily return on portfolio with lowest beta stocks.

RPj: daily return on portfolio with highest beta stocks

Statistically significant and positive α(pi-pj)value represents that the stocks of portfolio Pihas

outperformed stocks of portfolio Pj .

Statistically significant and negative α(pi-pj)value represents that the stocks of portfolio Pihas

given inferior returns in comparison with stocks of portfolio Pj .

13

Statement of Hypothesis

Case 1

Null:There is no significant difference in returns of P1 & P8 in time period October 200 to

November 2013

Alternate: There is significant difference in returns of P1 & P8 in time period October 200 to

November 2013

Case 2

NULL HYPOTHESIS

H0: There is no significant difference in returns of P1 & P8 in time period January 1, 2008 to

January 1,2009

H0: There is no significant difference in returns of P1 & P8 in time period April 1, 2008 to April

1,2009

H0: There is no significant difference in returns of P1 & P8 in time period July 1, 2008 to July

1,2009

H0: There is no significant difference in returns of P1 & P8 in time period October 1, 2008 to

October 1,2009


January 1,2010


1,2010

14

H0: There is no significant difference in returns of P1 & P8 in time period 1 July, 2009 to July

1,2010


October 1,2010


January 1,2011


1,2011


1,2011


October 1,2011


January 1,2012


1,2012


1,2012


October 1,2012


January 1,2013

Alternate Hypothesis

HA: There is significant difference in returns of P1 & P8 in time period January 1, 2008 to

January 1,2009

15

HA: There is significant difference in returns of P1 & P8 in time period April 1, 2008 to April

1,2009

HA: There is significant difference in returns of P1 & P8 in time period July 1, 2008 to July

1,2009

HA: There is significant difference in returns of P1 & P8 in time period October 1, 2008 to

October 1,2009


January 1,2010


1,2010


1,2010


October 1,2010


January 1,2011


1,2011


1,2011


October 1,2011


January 1,2012

16


1,2012


1,2012


October 1,2012


January 1,2013

17

Results & Analysis

CASE 1

Result 1

Significant difference in returns of portfolio 1(low beta) and portfolio 7(high beta)

Sr. no. SECURITIES RETURN

1 LUPIN, SUN PHARMA, DR REDDY, TCS, ASIAN PAINT 579.19%

2 RANBAXY, ULTRA TECH , ITC, INFOSYS , BHEL 292.05%

3 AIRTEL, GAIL,GRASIM,ACC,NTPC 162.03%

4 HDFC, ONGC, HCL, HDFC BANK, WIPRO 333.93%

5 L&T, BOB, PNB,M&M,TATA POWER 274.17%

6 TATA MOTORS, RELIANCE,JINDAL STEEL,KOTAK,SBI 350.91%

7 JPASSOCIAT, IDFC, TATA STEEL,ICICI , INDUSIND BANK 200.78%

As we can see, returns from portfolio P1 to P7 conform to our basic assumption of investment

that for “higher the risk,higher the expected return”. Returns show downward trend with

decreasing β.

0.00%

100.00%

200.00%

300.00%

400.00%

500.00%

600.00%

700.00%

P1 P2 P3 P4 P5 P6 P7

Returns

returns

18

To empirically establish that there is difference in return between these two portfolios

Following regression model was used and the understated hypothesis was tested.

Result 2

R1 – R7 = α(R1-R7) + β(R1-R7) RM

Hypothesis

H0 : α(R1-R7) = 0

H1 : α(R1-R7) ≥ 0

Value of α was found significant at 95% confidence intervalHence there is significant difference

in daily return of these two portfolios. Returns from portfolio P7 is significantly higher than

returns from the portfolio P1 .

This result points towards existence of risk return anomaly at both highest and lowest band of

risk.

Variable t-statistic p-value Result

α(R1-R7) 2.885612 .0039484 H0Rejected

β(R1-R7) -50.3088 0

19

Result 3

β values for each portfolio was found using “Single Factor Model”.

Rp = α + β Rm + µi , where

Where Rp = Return on portfolio

Rm =Return on market.

And then risk and return was plotted for each portfolio.

The following results were obtained.

Table 1: Author's Calculation

PORTFOLIO BETA PORTFOLIO RETURN

P1 0.354971656 5.7919124

P2 0.53952259 2.9205181

P3 0.83936621 1.6203186

P6 0.923024124 3.5090692

P4 0.943719403 3.3392518

P5 1.007214375 2.7417274

p7 1.40958767 2.0078402

* The value 5.79 implies that return is 579% and so on.

20

Figure : Author's Calculation

Existence of risk return anomaly is easily visible in this plot.

We can easily make out that with decrease in β value there has been increase in return.

Portfolio 1 has the lowest beta value but the highest return whereas portfolio 7 (p7) gives lower

return.

0

1

2

3

4

5

6

7

P1 P2 P3 P6 P4 P5 p7

return

Beta

21

CASE 2

Result 1

Return VS Beta

Following graphs depict the variation that comes in return of portfolio as beta β of portfolio increases.

1-Jan-08 to 31-Dec-08

Figure 1: Author’s Calculation

Portfolio P1 P2 P3 P4 P5 P6 P7 P8

Beta 0.5346 0.7629 0.85911 0.9475 0.99044 1.026 1.1009 1.321409

Return -0.21175 -0.22587 -0.47146 -0.5184 -0.59695 -0.47035 -0.56922 -0.69641

This chart shows an inverse relationship between beta and return. As beta increases, the return of the portfolios ranked accordingly decreases. This depicts a risk return anomaly for this period.

-1

-0.5

0

0.5

1

1.5

P1 P2 P3 P4 P5 P6 P7 P8

beta

return

22

1-Apr-08 to 31-Mar-09



Beta 0.51 0.7592 0.8854 0.905 0.963 1.0255 1.1007 1.420124

Return -0.13799 -0.23516 -0.3525 -0.44587 -0.35713 -0.28259 -0.44403 -0.43547

This chart shows risk return anomaly as with increase in beta there is decrease in return.

1-Jul-08 to 30-Jun-09



Beta 0.47 0.7318 0.8538 0.8954 1.017 1.2627 1.1199 1.428554

Return -0.14378 0.221095 0.261 0.216304 0.401732 0.278714 0.442922 0.531592

In this chart there is an inconsistent relationship between return and beta although the return trend is that it increases with increase in beta. The risk return anomaly exists for portfolios 2 to portfolios to 4, 5 and 6 and 7.

-1

-0.5

0

0.5

1

1.5

2

P1 P2 P3 P4 P5 P6 P7 P8

RETURN

BETA

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

P1 P2 P3 P4 P5 P6 P7 P8

RETURN

BETA

23

1-Oct-08 to 30-Sep-09


In this chart there is an inconsistent relationship between return and beta. The risk return anomaly exists for portfolios 3 to portfolios to 7.

1-Jan-09 to 31-Dec-09



Beta 0.442 0.6545 0.8256 0.933 0.9593 1.052 1.18 1.439008

Return 0.648458 1.252362 1.340004 1.494304 0.928331 0.897726 0.85008 2.587143

In this chart there is a very inconsistent relationship between return and beta.The risk return anomaly exists for portfolios 4 to portfolios to 7.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

P1 P2 P3 P4 P5 P6 P7 P8

RETURN

BETA

0

0.5

1

1.5

2

2.5

3

P1 P2 P3 P4 P5 P6 P7 P8

return

beta


Beta 0.46 0.7158 0.811 0.89622 1.047 1.089 1.1569 1.472012

Return 0.154384 0.460682 0.60962 0.480613 0.18453 0.431339 0.4698 1.263772

24

1-Apr-09 to 31-Mar-10



Beta 0.4126 0.6352 0.8058 0.9292 0.9676 1.063 1.2104 1.478384

Return 0.822896 1.312607 1.16788 0.860018 0.882121 1.286061 0.740503 2.003713

In this chart also there is a very inconsistent relationship between return and beta.The risk return anomaly exists for portfolios 3 to portfolios to 5 and 7and 8.

1-Jul-09 to 30-Jun-10



Beta 0.2756 0.5968 0.7654 0.9134 0.9576 1.066 1.2093 1.473676

Return 0.764853 0.60826 0.084493 0.194107 0.530701 0.301086 0.132813 0.209084

In this chart there exists a risk return anomaly between return and beta except few portfolios like portfolio 4 to 6.

0

0.5

1

1.5

2

2.5

p1 p2 p3 p4 p5 p6 p7 p8

return

beta

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

25

1-Oct-09 to 30-Sep-10



Beta 0.4046 0.6268 0.7942 0.8966 0.9623 1.078 1.2105 1.48567

Return 0.600954 0.487901 0.112911 0.205551 0.535116 0.401685 0.199154 0.054069

In this chart there exists a risk return anomaly between return and beta except few portfolios like portfolio 3 to 5.

1-Jan-10 to 31-Dec-10



Beta 0.401 0.6327 0.77864 0.88067 0.9584 1.089 1.2102 1.501046

Return 0.567951 0.337433 0.020721 0.126047 0.29583 0.219793 0.033281 0.008168

In this chart also there exists a risk return anomaly between return and beta except few portfolios like portfolio 3 to 5.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

26

1-Apr-10 to 31-Mar-11



Beta 0.3867 0.5955 0.75203 0.861 0.96433 1.11 1.19727 1.546878

Return 0.24574 0.257702 -0.02382 0.053141 0.121109 0.126856 0.016076 -0.10713


1-Jul-10 to 30-Jun-11



Beta 0.36911 0.5741 0.7457 0.8361 0.95005 1.103 1.2011 1.554504

Return 0.327286 0.176741 0.110916 -0.07357 0.173391 0.048534 0.061934 -0.00668

In this chart also there exists a risk return anomaly between return and beta except few portfolios like portfolio 4 to 6.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

27

1-Oct-10 to 30-Sep-11



Beta 0.355 0.5674 0.7557 0.8081 0.92251 1.096 1.1979 1.548497

Return 0.086025 0.094112 -0.0103 -0.22877 -0.27985 -0.33508 -0.2453 -0.36413


1-Jan-11 to 31-Dec-12



Beta 0.326 0.5741 0.7181 0.8249 0.9421 1.146 1.2105 1.532561

Return -0.09695 0.059792 -0.10026 -0.26132 -0.19391 -0.2259 -0.37794 -0.46418


-0.5

0

0.5

1

1.5

2

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

-1

-0.5

0

0.5

1

1.5

2

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

28

1-Apr-11 to 31-Mar-12



Beta 0.4104 0.6172 0.7104 0.78137 0.90691 1.122 1.23207 1.463014

Return 0.197857 0.267428 -0.01911 -0.15041 -0.07976 -0.20275 -0.09668 -0.18148

In this chart also there exists a risk return anomaly between return and beta except few portfolios like portfolio 1,2, portfolio 4 to 6.

1-Jul-11 to 30-Jun-12



Beta 0.462 0.6168 0.6405 0.77025 0.96203 1.094 1.241 1.538304

Return 0.192647 0.254567 0.126002 -0.26551 -0.02878 -0.24282 -0.01428 -0.06367

In this chart also there is a very inconsistent relationship between return and beta.The risk return anomaly exists for portfolios 3 to 4 and 5and 6.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

-0.5

0

0.5

1

1.5

2

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

29

1-Oct-11 to 30-Sep-12



Beta 0.4595 0.5476 0.6624 0.7711 0.93291 1.086 1.2171 1.523029

Return 0.202605 0.455923 0.405701 -0.03678 0.204032 -0.02627 0.141675 0.143727

In this chart also there is a very inconsistent relationship between return and beta.The risk return anomaly exists for portfolios 3 to 4 and 5and 6.

1-Jan-12 to 31-Dec-13



Beta 0.4731 0.5649 0.6828 0.8234 0.9396 1.106 1.2004 1.542823

Return 0.413354 0.403531 0.146292 0.060558 0.241029 0.412013 0.044139 0.662435

In this chart also there is a very inconsistent relationship between return and beta.The risk return anomaly exists for portfolios 2 to 4 and 6 to 7.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

P1 P2 P3 P4 P5 P6 P7 P8

return

beta

30

These 17 charts show the returns for the different portfolios ranked according to betas.

The chart for the period January 1, 2008 to January 1, 2009 shows an inverse relationship between beta and return. As beta increases, the return of the portfolios ranked accordingly decreases. This depicts a risk return anomaly for this period. The chart for the period April 1, 2008 to April 1, 2009 shows risk return anomaly as with increase in beta there is decrease in return.

In the period July 1, 2008 to June 30, 2009, there is an inconsistent relationship between return and beta although the return trend is that it increases with increase in beta. The risk return anomaly exists for portfolios 2 to portfolios to 4, 5 and 6 and 7 and 8.

The anomaly can also be seen in the charts for the periods 1 July’10 to 1 July’11,1 October’10 to 1 October’11,1 January’11 to 1 January’12.

Result 2

Mean comparison between returns on all portfolios.

Pairwise Comparisons

Dependent Variable Return on Index

Portfolio 1 Mean Difference (I-J) Std. Error Sig.a P1 P2 -9.145 17.026 .592

P3 8.278 17.026 .628

P4 17.203 17.026 .314

P5 9.841 17.026 .564

P6 13.662 17.026 .424

P7 19.473 17.026 .255

P8 11.658 17.026 .495 P2 P1 9.145 17.026 .592

P3 17.423 17.026 .308

P4 26.348 17.026 .124

P5 18.986 17.026 .267

P6 22.806 17.026 .183

P7 28.617 17.026 .095

P8 20.803 17.026 .224 P3 P1 -8.278 17.026 .628

P2 -17.423 17.026 .308

P4 8.925 17.026 .601

P5 1.563 17.026 .927

31

P6 5.383 17.026 .752

P7 11.194 17.026 .512

P8 3.380 17.026 .843 P4 P1 -17.203 17.026 .314

P2 -26.348 17.026 .124

P3 -8.925 17.026 .601

P5 -7.362 17.026 .666

P6 -3.541 17.026 .836

P7 2.270 17.026 .894

P8 -5.545 17.026 .745 P5 P1 -9.841 17.026 .564

P2 -18.986 17.026 .267

P3 -1.563 17.026 .927

P4 7.362 17.026 .666

P6 3.820 17.026 .823

P7 9.632 17.026 .573

P8 1.817 17.026 .915

P6 P1 -13.662 17.026 .424

P2 -22.806 17.026 .183

P3 -5.383 17.026 .752

P4 3.541 17.026 .836

P5 -3.820 17.026 .823

P7 5.811 17.026 .733

P8 -2.004 17.026 .907 P7 P1 -19.473 17.026 .255

P2 -28.617 17.026 .095

P3 -11.194 17.026 .512

P4 -2.270 17.026 .894

P5 -9.632 17.026 .573

P6 -5.811 17.026 .733

P8 -7.815 17.026 .647 P8 P1 -11.658 17.026 .495

P2 -20.803 17.026 .224

P3 -3.380 17.026 .843

P4 5.545 17.026 .745

P5 -1.817 17.026 .915

P6 2.004 17.026 .907

P7 7.815 17.026 .647

32

Profile Plots

33

Result 3

R1 – R8= α(R1-R8) + β(R1-R8) RM

Hypothesis

H0 : α(R1-R8) = 0

H1 : α(R1-R8) ≥ 0

This results tries to see if there is statistically significant difference in returns of portfolio 1 and portfolio 8.

Time Interval

P-Value

Accept/Reject

Result

1-Jan-08 to 1-Jan-09 0.3024

Accept No statistically

significant difference in returns of Portfolio 1

and 8

1-Apr-08 to 1-Apr-09 0.1987



and 8

1-Jul-08 to 1-Jul-09 0.3502



and 8

1-Oct-08 to 1-Oct-09 0.382



and 8

1-Jan-09 to 1-Jan-10 0.412



and 8

34

1-Apr-09 to 1-Apr-10 0.631 Accept No statistically significant difference in

returns of Portfolio 1 and 8

1-Jul-09 to 1-Jul-10 0.136 Accept No statistically significant difference in


1-Oct-09 to 1-Oct-10 0.013 Reject Statistically significant difference in returns of

Portfolio 1 and 8

1-Jan-10 to 1-Jan-11 0.010 Reject Statistically significant difference in returns of

Portfolio 1 and 8

1-Apr-10 to 1-Apr-11 0.221 Accept No statistically significant difference in


1-Jul -10 to 1-Jul-11 0.227 Accept No statistically significant difference in


1-Oct-10 to 1-Oct-11 0.074063



and 8

1-Jan-11 to 1-Jan-12 0.231 Accept No statistically significant difference in


1-Apr-09 to 1-Apr-10 0.722 Accept No statistically


and 8

1-Jul-09 to 1-Jul-10 0.816 Accept No statistically significant difference in


35

From these results we can conclude that there is no statistically significant difference in return of portfolio 1 and portfolio 2 over 1 year of time period. Even though it can be seen it is quite evident from Result 1 and Result 2 that lower beta portfolios outperform higher beta portfolios.

1-Oct-09 to 1-Oct-10 0.96025



and 8

1-Jan-10 to 1-Jan-11 0.788751



and 8

36

POSSIBLE REASONS

People struggle with application of probability and expected payoffs to determine best allocation of resources and optimization of their portfolio returns. People would rather buy a lottery ticket with a one in a lakh chance to win a crore than invest in a portfolio even if they have the same expected payoffs..Eg A person can buy a lottery ticket worth 5 rupees which has a winner for every lakh tickets. The person can alternatively invest in a strategy which has a 50% chance to provide returns of 20 rupees on his initial investment of 100 rupees and a 50% chance of a loss of 10 rupees on his investment{0.00001*1000000 – 5 =5 ; (120*.5 +90*.5) -100=5}.

There are also representative issues which provide bias to an investor’s decision making. Investors find it extremely difficult to judge and differentiate between great stories and great investments. The popularity of high growth stocks in hot and in trend sectors remains high among investors. This translates to high attention to these stocks. Most of the times, this attention translates to high demand and these stocks trade at high levels. When these stocks donot provide results in sync with this level of attention and popularity to justify high prices, the returns of these stocks are dismal. On the other hand, unpopular stocks are traded at a discount at stock exchanges and provide better returns even with their average returns as they were a value buy in the first place.

These issues have been studied and analyzed in detail previously. The third reason which helps us in understanding risk return anomaly and which explains the persistence of it is the overconfidence of investors. Investors generally think they are better and different from others when selecting a stock with a high systematic risk and also think that others wouldn’t make the same decision.

Large Institutional investors also may not take advantage of this anomaly. This is because the institutional mandates are subdivided into specialist categories like equity, real estate debt, commodity etc and their performances are benchmarked. Therefore, the equity portfolio manager would prefer to keep the beta value of the portfolio at 1 even though choosing stocks with lower beta values (and thus decreasing the beta of the portfolio) may result in higher gains. The way the performance of the institutional managers is estimated may leave no incentive for the manager to invest in stocks with lower beta. These reasons lead to the observation and likely persistence of the pattern of higher returns for portfolios with lower betas.

37

CONCLUSION

The results of Indian market is similar to those found in some other countries such as United States of America: the portfolio of stocks with low value of beta (β) gives higher return over long period of time than portfolio made of high beta stocks.

Investing on stocks with lower beta is a good investment strategy given that the investor plans on investing for a long period of time. This strategy not just only minimizes the wealth erosion but also ensures that investor would not miss the upside returns entirely.

38

Appendix

1. Normal Curve of Rp1-Rp7

39

2. Normality Curve of Rm

40

3. Normality of Residuals.

41

4. Colinearity Diagnostics

Model Dimension Eigenvalue Condition Index

Variance Proportions

(Constant) x

1 1 1.028 1.000 .49 .49

2 .972 1.028 .51 .51

a. Dependent Variable: y

42

BIBLIOGRAPHY

Serial No. Source Details

NSE - www.nseindia.com

Yahoo Finance - finance.yahoo.com

Slideshare - www.slideshare.com

2 Text Book Basic Econometrics - D. Gujarati

Internet1

Understanding Risk Return Anomaly

Documents