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PROJECT FINANCIAL DECISION MAKING

TOPICTHE VARIABILITY OF BETA OVER TIME

SUBMITTED TOSIR KHALID SOHAIL

SUBMITTED BYSANUM NASIMSP14-RBA-010-ISB

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TABLE OF CONTENTIntroduction03Shell Pakistan limited.......04Attock refinery limited................05What is beta..06Variability of beta over time...........07 Beta calculations and Methodologies 08Beta Interpretations and estimation 09Shell monthly data regression model11Shell monthly data Scatter diagram11Attock beta estimation summary14Attock monthly data regression model14Attock monthly data Scatter diagram..15Analysis and over all estimation..16Conclusions ..17Calculation ..18References.19

INTRODUCTION:Stocks or securitys betas may vary substantially depending upon whether it is estimated on the basis of daily, weekly, fortnightly or monthly returns of that security. Basically the betas of securities with smaller market value than the average of the market will decrease as the return interval is shortened, whereas the betas of securities with a large market value relative to the market will increase. This suggest that betas measured over return intervals of arbitrary length will tend to be less risky than truly are, whereas securities with relatively large market values may appear to be more risky than they truly are. Securitys historical rate of returns can be used to estimate its systematic risk. Rate of returns can be calculated as daily, weekly, fortnightly and monthly basis then with the help of those returns on different time interval betas can be estimated and its variability over time.

1.SHELL:Shell Pakistan Limited (SPL) is a subsidiary of Royal Dutch Shell Plc and has been in South Asia for over 100 years. Shells flagship business in Pakistan is the downstream retail marketing company, Shell Pakistan Limited, which has interests in downstream businesses including retail, lubricants and aviation. Shell Pakistan has a primary listing on Karachi Stock Exchange. Its also listed on Lahore and Islamabad Stock Exchange. SHELL PAKISTAN LIMITED AT GLANCE: The second largest oil company in the country, Shell Pakistan has successfully positioned itself as the preferred oil and Gas Company in Pakistan, leading the field in its commitment to customer service, quality of products, safety and environmental protection. Shell is a global group of energy and petrochemical companies. HISTORY:The Shell brand name enjoys a 100-year history in this part of the world. The history of Royal Dutch Shell in Indo Pak subcontinent dates back to 1903. In 1928, Royal Dutch Shell and the Burmah Oil Company Limited in India were merged and Burmah Shell Oil Storage & Distribution Company of India was borne. After the independence of Pakistan in 1947, the name was changed to the Burmah Shell Oil Distribution Company of Pakistan. In 1970, when 51% of the shareholding was transferred to Pakistani investors, the name of changed to Pakistan Burmah Shell (PBS) Limited. The Shell and the Burmah Groups retained the remaining 49% in equal propositions. In February of 1993, as economic liberalization began to take root and the Burmah divested from PBS, Shell Petroleum stepped into raise its stake to 51%. The years 2001-2 have seen the Shell Petroleum Company successively increasing its share, with the Group now having a 76% stake in Shell Pakistan Ltd (SPL) - an expression of confidence. PRODUCTS: Shell Pakistan Limited (Shell Pakistan) is engaged in marketing of compressed natural gas and petroleum. The company provides different types of lubricating oil and caters to businesses and motorists. The company for businesses provides Shell cards, aviation customer service, exploration and production, transport, liquefied petroleum gas and industrial operations for power, automotive and sugar. Shell Pakistan for motorists provides customer service, car care tips, shell Helix motor oil and Shell advance motorcycle oil. The company also participates in Pakistan is headquartered in Karachi, Pakistan.

2.ATTOCK REFINERYLIMITED:

Attock Refinery Limited (ARL) is the pioneer in crude oil refining in the country with its operations dating back to the early nineteen hundreds. Backed by a rich experience of more than 90 years of successful operations, ARLs plants have been gradually upgraded and replaced with state-of-the-art hardware to remain competitive and meet new challenges and requirements

ATTOCK REFINERY PAKISTAN LIMITED AT GLANCE:Attock Refinery Pakistan Limited is a member of Attock Group of Companies, a fully integrated group covering all segments of oil and gas industry from exploration to production, and refining to marketing of a wide range of petroleum products in Pakistan. Besides being also engaged in power generation, manufacturing and trading of cement and other entrepreneurial activities in Pakistan. Pakistan Refinery Limited was incorporated in Pakistan as a public limited company in May 1960 and is quoted on the Karachi and Lahore Stock Exchanges. The Refinery is situated on the coastal belt of Karachi, Pakistan. HISTORY:Since its commissioning in 1922, ARL has passed through various stages of transformation and stood the test of time through war and peace. From batch distillation stills of 2,500 barrels per day (BPD), today it has grown into a modern state-of-the-art refinery with a capacity of 43,000 BPD.It was subsequently converted into a Public Limited Company in June 1979 and is listed on the three Stock Exchanges of the country. The company is also registered with the Central Depositary Company of Pakistan (CDC). PRODUCTS:Attock Refinery Limited is a Pakistan-based company engaged in the refining of crude oil. The Company produces a range of petroleum products, such as liquefied petroleum gas (LPG); unleaded petroleum solvent grade (PMG); naphtha; premium motor gasoline; mineral turpentine (MTT); JP-1; JP-8; kerosene oil; high speed diesel (HSD); light diesel oil (LDO); jute batching oil (JBO), furnace fuel oil (FFO); low sulfur fuel oil (LSFO), paving grade asphalts, cut back asphalts and polymer modified bitumen (PMB). The Company had one wholly owned subsidiary, Attock Hospital (Private) Limited and Attock Oil Company Limited with 65.32% shares of the Company.

WHAT IS BETA.!!!!

BETA is a measure of riskIt is the measure of the volatility, or systematic risk of a security and a portfolio in comparison to the market as a whole where risk is a consideration in every investment decision and, for a stock, risk is quantified by beta. 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. Beta measures how sensitive are the returns of asset - to the returns of the market portfolio Beta is the slope (coefficient) in the regression of asset - return (risk premium) on the markets return (market risk premium) Beta is a relative measure of risk Beta < 1 : defensive asset Beta = 1: neutral asset Beta > 1: aggressive asset It is basically the asset's risk in relation to the market. Roughly speaking, a security with a beta of 1.5 will have move, on average, 1.5 times the market return. More precisely, that stock's excess return over and above a short-term money market rate is expected to move 1.5 times the market excess return. According to the capital asset pricing theory beta represents the type of risks or systematic risks so when using beta there are a number of issues that you need to be aware of; Betas may change through time. Betas may be different depending on the direction of the market i.e. betas may be greater for down moves in the market rather than up moves. The estimated beta will be biased if the security does not frequently trade. The beta is not necessarily a complete measure of risk (you may need multiple betas). Also, note that the beta is a measure of co-movement it is possible for a security to have a zero beta and higher volatility than the market.In general beta is calculated by using regression analysis as per the beta having the tendency of a security's returns to respond to swings in the market. A beta of 1 indicates that the price of a security will move in tandem with the market; a beta less than 1 means that the security will be less volatile than the market. A beta more than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, theoretically, it's 20% more volatile than the market. Perhaps the single most important measure of stock risk or volatility is a stock's beta. It's one of those at-a-glance measures that can provide serious stock analysts with insights into the movements of a particular stock relative to the overall market. BETA VARIABILITY:BETAS CANNOT BE STABLE OVER TIME:Stock analysts use beta the statistical measure all the time to get a sense of stocks' risk profiles. It estimate the risk in equilibrium in which investors maximize a utility function that depends on the mean and variance of returns of their portfolio. The variance of returns is a questionable measure of risk for at least two reasons: First, it is an appropriate measure of risk only when the underlying distribution of return is symmetric. Second, it can be applied straight forwardly as a risk measure only when the underlying distribution of returns is normal. However, both the symmetry and the normality of stock returns are seriously questioned by the empirical evidence on the subject. The stability of Beta has also been a controversial issue in the literature. In reality only the historical returns are available to estimate Beta, which as a result will also be the historical Beta. There is a big question mark on using the historical Beta as an estimate of future Beta because empirically evidence shows that Betas on individual stocks have not been stable over time. Basically securitys historical rate of returns can be used to estimate its systematic risk. Rate of returns can be calculated as daily, weekly, fortnightly and monthly basis then with the help of those returns on different time interval betas can be estimated and its variability over time number of studies emerged to investigate the stability of Beta. In various studies it is used different sets of data over various time periods and observed the change in Beta estimates through time. Their outcomes, in general, indicate that stock Betas are not stable because betas are not statistically related to returns as stock does not stay constant over time. It only measures the past volatility. The future performance and volatility of the stock depends on the current and future set of economics and the choices that management makes in the future.

BETA CALCULATIONS AND METHODOLOGIES:It's possible to find calculated beta values on all of the major stock reporting websites, including Yahoo Finance, MSN Money, and Google Finance. It's also possible to calculate beta using a fairly straightforward linear regression technique that's available in a spreadsheet application such as Microsoft's Excel or Open Offices Calc.In fact, to calculate a stock's beta two sets of data are needed: Closing stock prices for the stock being examined. Closing prices for the index being chosen as a proxy for the stock market.Most of the time, values are calculated using the month-end stock price for the security, and the month end closing prices.

METHODOLOGIES AND FORMULAS:Beta can be calculated by various methodologies and formulas some of them are; AVERAGE FORMULA

COMPUTATIONAL FORMULA

CONCEPTUAL FORMULAN (sum XY)-sum XY/N (sum X^2)-(sum X)^2

SLOPE, COVARIANCE AND VARIANCE FORMULA

BETA INTERPRETATIONS AND ESTIMATIONSThis project findings are based on two companies Shell Pakistan limited and Attock Refinery Pakistan Limited and their returns at daily, weekly, fortnightly and monthly basis with their estimated betas of three-year periods from July 2011 to June 2014, which have been estimated using 36 monthly returns, 250 daily returns, 72 fortnightly and 156 weekly returns by considering KSE-100 index as market proxy.

SHELL PAKISTAN LIMITED ESTIMATED BETAS : MARKET MODEL BETASMARKET MODELDAILYWEEKLYFORTNIGHTLYMONTHLY

1st year0.56410.229207885-0.495339650.305148831

2nd year0.265400.8811614861.4740865981.3875303

3rd year0.09380.8727838611.3658357792.196878513

CAPM:CAPMDAILYWEEKLYFORTNIGHTLYMONTHLY

1st year0.56400.220793-0.495340.305149

2nd year0.26540.8830431.4740871.38753

3rd year0.93500.8712911.3658362.196879

Computation BetaConceptual Beta

Year 1Year 1

0.3050.2936

Year 2

1.43901.4390

Year 3 Year 3

2.19872.1987

SCATTER DIAGRAM:

REGRESSION ANALYSISSUMMARY OUTPUT

Regression Statistics

Multiple R0.525461483

R Square0.27610977

Adjusted R Square0.253488201

Standard Error0.09739641

Observations34

ANOVA

dfSSMSFSignificance F

Regression10.1157830360.11578303612.205597330.001416828

Residual320.303553940.009486061

Total330.419336977

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept-0.0101450.019254-0.9424080.353044-0.057360.0210-0.057360.02107

0.0314841.21007030.346363.4936510.001410.504551.915580.504531.91558

ANALYSIS:While estimating betas of Shell I have analyzed that the concept of beta as a measure of individual stock risk relative to the overall risk of the stock market. As analyzed here higher risk stocks come up with either more high and low returns as compare to the lower risk stocks to get a better feel for a stock's risk profile. As per interpreting here stock risk price movements are compared to the movements of an overall market indicator such as a market index, over the same period of time which interpret the CAPMs beta as that if high beta stocks are more probable than low beta stocks either very high or very low returns which is also has taken into account in our analysis of stocks which experiences that high beta stocks are more risky as compare to the lower beta stocks. So we can say this that in a rising market, it is advantageous to have high-beta stocks, but in a declining market you would be better served to low-beta stocks. So according to the stock risk factors having high and low betas. Shell Pakistan limited estimated betas returns are 0.22920,-0.495339, and 0.305148estimated on weekly, fortnightly and monthly basis whereas the daily beta is 0.5641 in 1st year which is greater than the weekly, fortnightly and monthly basis so as securities with a larger market value than the average of all securities outstanding will generally have an increasing beta. On the other hand if there the return interval is shortened and the other securities with a smaller market value than the average of all securities outstanding (the market) will generally have decreased beta. ATTOCK REFINERY PAKISTAN LIMITED ESTIMATED BETAS: MARKET MODEL BETASMARKET MODELDAILYWEEKLYFORTNIGHTLYMONTHLY

1st year1.25650.9171604410.9758540.558452128

2nd year0.20631.036668710.611154-0.80919615

3rd year0.14221.2643519151.7423741.408541635

CAPM:CAPMDAILYWEEKLYFORTNIGHTLYMONTHLY

1st year1.25640.9172120.9758540.558452

2nd year0.20631.040250.611154-0.8092

3rd year0.14221.2651031.7423741.408542

Computation BetaConceptual Beta

Year 1Year 1

0.5580.559

Year 2

-o.7170-0.7170

Year 3 Year 3

1.40731.4073

SCATTER DIAGRAM:

REGRESSION ANALYSIS

Regression Statistics

Multiple R0.391077683

R Square0.152941754

Adjusted R Square0.126471184

Standard Error0.09063638

Observations34

ANOVA

DfSSMSFSignificance F

Regression10.0474643870.0474643875.7778040.022195958

Residual320.2628785090.008214953

Total330.310342895

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept-0.00076460.017917678-0.0426760.966224-0.037260.035732-0.0372610.035732

0.0318480.7747687240.3223225542.4037062080.0221960.1182191.4313180.11821911.431318

ANALYSISWhile estimating betas of Attock I have analyzes the concept of beta as a measure of individual stock risk relative to the overall risk of the stock market. As analyzed here higher risk stocks come up with either more high and low returns as compare to the lower risk stocks to get a better feel for a stock's risk profile. As per interpreting here stock risk price movements are compared to the movements of an overall market indicator such as a market index, over the same period of time which interpret the CAPMs beta as that if high beta stocks are more probable than low beta stocks either very high or very low returns which is also has taken into account in our analysis of stocks which experiences that high beta stocks are more risky as compare to the lower beta stocks. So we can say this that in a rising market, it is advantageous to have high-beta stocks, but in a declining market you would be better served to low-beta stocks. So according to the stock risk factors having high and low betas Attock Refinery Pakistan limited estimated betas returns are 0.917212, 0.975854, and0.558452 estimated on weekly, fortnightly and monthly basis whereas the daily beta is 1.2565 in 1st year and it is analyzed that the it is larger market value than the average of all securities outstanding soas here as well securities with a larger market value than the average of all securities outstanding will generally have an increasing beta. And on the other hand if there the return interval is shortened and with the following occurs, securities with a smaller market value than the average of all securities outstanding (the market) will generally have decreased beta. Market value is also commonly used to refer to the market capitalization of a publicly-traded company, and is obtained by multiplying the number of its outstanding shares by the current share price.Number of Shares Outstanding:Shell Pakistan Limited =107,012,330Attock Refinery Limited = 85,293,000Market value of Share OutstandingMVSO of Shell Pakistan Limited=276.28 x 107,012,330 = 29,565,366,532MVSO of Attock Refinery Limited=212.29 x 85,293,000= 18,106,850,970OVER ALL ESTIMATIONShell Pakistan limited estimated betas returns are 0.22920,-0.495339, and 0.305148estimated on weekly, fortnightly and monthly basis whereas the daily beta is 0.5641 in 1st year which is greater than the weekly, fortnightly and monthly basis so as securities with a larger market value than the average of all securities outstanding will generally have an increasing beta. On the other hand Attock Refinery Pakistan limited estimated betas returns are 0.917212, 0.975854, and0.558452 estimated on weekly, fortnightly and monthly basis whereas the daily beta is 1.2565 in 1st year and it is analyzed that the it is larger market value than the average of all securities outstanding so as here as well securities with a larger market value than the average of all securities outstanding will generally have an increasing beta. And on the other hand if there the return interval is shortened and with the following occurs, securities with a smaller market value than the average of all securities outstanding (the market) will generally have decreased beta.

CONCLUSIONSSo it is concluded that a stock's price variability is important to consider when assessing risk where risk as the possibility of a stock losing its value as beta has appeal as a proxy for risk. Intuitively, it makes sense that stock with a price that bounces up and down more than the market because securities with large market value of shares outstanding will have estimated betas that are biased upward, whereas securities with small market value of shares outstanding will have estimated betas that are biased downward considered as market of arbitrary length are biased so high market values will appear to be more risky as compare to the lower market values so other way round we can say that it's hard not to think that stock will be riskier than say a safe-haven utility industry stock with a low beta. As in this project it has figured out three patterns out of that the beta stability seemed to be dependent on the return interval and also the analysis on portfolios implies that diversification and beta stability are positively correlated.In general, the betas of securities with a smaller market value than the average of all securities outstanding will decrease as the return interval is shortened whereas the betas of the securities with the large market value relative to the market will increase. And it is concluded that betas measured over return interval of arbitrary length will tend to be biased. In particular securities with relative market values may appear to be less risky than they truly are, whereas securities with relatively large market values may appear to be more risky than they truly are.

Calculations

REFRENCES

Michael D. Carpenter and David E. Upton, Trading Volume and Beta Stability, Journal of Portfolio Management 7, no. 2 (Winter 1981): 6064. Roger G. Ibbotson, Paul D. Kaplan, and James D. Peterson, Estimates of Small-Stock Betas Are Much Too Low, Journal of Portfolio Management 23, no. 4 (Summer 1997): 104111. Meir Statman, Betas Compared: Merrill Lynch vs. Value Line, Journal of Portfolio Management 7, no.2 (Winter 1981): 4144. Frank K. Reilly and David J. Wright, A Comparison of Published Betas, Journal of Portfolio Management 14, no. 3 (Spring 1988): 6469. William F. Sharpe and Guy M. Cooper, Risk-Return Classes of New York Stock Exchange Common Stocks: 19311967, Financial Analysis Journal 28, no. 2 (MarchApril 1972): 4654S. P. Kothari, Jay Shanken, and Richard G. Sloan, Another Look at the Cross Section of Expected Stock Returns, Journal of Finance 50, no. 2 (March 1995): 185224. Kevin Grundy and Burton Malkiel, Reports of Betas Death Have Been Greatly Exaggerated, Journal of Portfolio Management 22, no. 3 (Spring 1996): 3644. Lee, C.F., Chen, C.R. 1982. Beta Stability and Tendency: An Application of a Variable Mean Response Regression Model, Journal of Economics and Business, 34, 210-206

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