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![Portfolio PerformancePortfolio Performance
Measurement…………Measurement…………
Jensen’s Differential Return MeasureJensen’s Differential Return Measure, α:, α:
It is calculated as the difference between what theIt is calculated as the difference between what the
portfolio actually earned and what it was expectedportfolio actually earned and what it was expected
to earn given the portfolio’s level of systematic risk.to earn given the portfolio’s level of systematic risk.
ααpp=(=(RpRp –– RF)RF) –– [[βpβp (R(RMM –– RF)]RF)]
=Actual return=Actual return ––required returnrequired return
RRMM -- RFRF
RpRp -- RFRF
00
XX
YY
ZZ](https://image.slidesharecdn.com/securitiesanalysisandportfoliomanagement-140808145606-phpapp02/85/Securities-analysis-and-portfolio-management-48-320.jpg)
![Portfolio PerformancePortfolio Performance
Measurement…………Measurement…………
Jensen’s Differential Return MeasureJensen’s Differential Return Measure, α:, α:
It is calculated as the difference between what theIt is calculated as the difference between what the
portfolio actually earned and what it was expectedportfolio actually earned and what it was expected
to earn given the portfolio’s level of systematic risk.to earn given the portfolio’s level of systematic risk.
ααpp=(=(RpRp –– RF)RF) –– [[βpβp (R(RMM –– RF)]RF)]
=Actual return=Actual return ––required returnrequired return
RRMM -- RFRF
RpRp -- RFRF
00
XX
YY
ZZ](https://image.slidesharecdn.com/securitiesanalysisandportfoliomanagement-140808145606-phpapp02/75/Securities-analysis-and-portfolio-management-48-2048.jpg)
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Securities analysis and portfolio management
- 1. Securities AnalysisSecurities Analysis && PortfolioManagementPortfolio Management Presented ByPresented By Md.Md. AshrafulAshraful IslamIslam Director, SECDirector, SEC
- 2. ContentsContents PartPart--A: Investment fundamentalsA:Investment fundamentals Understanding investmentUnderstanding investment Some definitionsSome definitions Sources and types of riskSources and types of risk RiskRisk--return tradereturn trade--off in different types of securitiesoff in different types of securities Important considerations in investment processImportant considerations in investment process PartPart--B: Securities AnalysisB: Securities Analysis Securities analysis concept and typesSecurities analysis concept and types Framework of fundamental securities analysisFramework of fundamental securities analysis Intrinsic valuation & relative valuationIntrinsic valuation & relative valuation PartPart--C: Portfolio ManagementC: Portfolio Management Portfolio conceptPortfolio concept Modern Portfolio Theory:Modern Portfolio Theory: MarkowitzMarkowitz Portfolio TheoryPortfolio Theory Determination of optimum portfolioDetermination of optimum portfolio SingleSingle--Index model, MultiIndex model, Multi--Index modelIndex model Capital Market TheoryCapital Market Theory Portfolio performance measurementPortfolio performance measurement
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- 4. Understanding investmentUnderstanding investment InvestmentInvestmentis commitment of fund to one or more assets thatis commitment of fund to one or more assets that is held over some future time period.is held over some future time period. Investing may be very conservative as well as aggressivelyInvesting may be very conservative as well as aggressively speculative.speculative. Whatever be the perspective, investment is important toWhatever be the perspective, investment is important to improve future welfare.improve future welfare. Funds to be invested may come from assets already owned,Funds to be invested may come from assets already owned, borrowed money, savings or foregone consumptions.borrowed money, savings or foregone consumptions. By forgoing consumption today and investing the savings,By forgoing consumption today and investing the savings, investors expect to enhance their future consumptioninvestors expect to enhance their future consumption possibilities by increasing their wealth.possibilities by increasing their wealth. Investment can be made to intangible assets like marketableInvestment can be made to intangible assets like marketable securities or to real assets like gold, real estate etc. Moresecurities or to real assets like gold, real estate etc. More generally it refers to investment in financial assets.generally it refers to investment in financial assets.
- 5. InvestmentsInvestments refers tothe study of the investment process,refers to the study of the investment process, generally in financial assets like marketable securities togenerally in financial assets like marketable securities to maximize investor’s wealth, which is the sum of investor’smaximize investor’s wealth, which is the sum of investor’s current income and present value of future income. It hascurrent income and present value of future income. It has two primary functions: analysis and management.two primary functions: analysis and management. Whether Investments is Arts or Science?Whether Investments is Arts or Science?
- 6. Some definitions:Some definitions: Financialassets:Financial assets: These are pieces of paper (orThese are pieces of paper (or electronic) evidencing claim on some issuer.electronic) evidencing claim on some issuer. Marketable securities:Marketable securities: Financial assets that are easily andFinancial assets that are easily and cheaply traded in organized markets.cheaply traded in organized markets. Portfolio:Portfolio: The securities held by an investor taken as aThe securities held by an investor taken as a unit.unit. Expected return:Expected return: Investors invest with the hope to earnInvestors invest with the hope to earn a return by holding the investment over a certain timea return by holding the investment over a certain time period.period. Realized return:Realized return: The rate of return that is earned afterThe rate of return that is earned after maturity of investment period.maturity of investment period. RiskRisk:: The chance that expected return may not beThe chance that expected return may not be achieved in reality.achieved in reality.
- 7. RiskRisk--Free Rate ofReturn:Free Rate of Return: A return onA return on risklessriskless asset,asset, oftenoften proxiedproxied by the rate of return on treasury bills.by the rate of return on treasury bills. RiskRisk––Adverse Investor:Adverse Investor: An investor who will not assume aAn investor who will not assume a given level of risk unless there is an expectation ofgiven level of risk unless there is an expectation of adequate compensation for having done so.adequate compensation for having done so. Risk Premium:Risk Premium: The additional return beyond risk fee rateThe additional return beyond risk fee rate that is required for making investment decision in riskythat is required for making investment decision in risky assets.assets.
- 8. DefinitionsDefinitions conticonti….…. Passive InvestmentStrategy:Passive Investment Strategy: A strategy that determinesA strategy that determines initial investment proportions and assets and make fewinitial investment proportions and assets and make few changes over time.changes over time. Active Investment Strategy:Active Investment Strategy: A strategy that seeks toA strategy that seeks to change investment proportions and assets in the beliefchange investment proportions and assets in the belief that profits can be made.that profits can be made. Efficient Market Hypothesis(EMH):Efficient Market Hypothesis(EMH): The proposition thatThe proposition that security markets are efficient, in the sense that price ofsecurity markets are efficient, in the sense that price of securities reflect their economic value based on pricesecurities reflect their economic value based on price sensitive information.sensitive information. WeakWeak--form EMHform EMH SemiSemi--strong EMHstrong EMH Strong EMHStrong EMH
- 9. Definitions Conti….Definitions Conti…. Facevalue or Par value or Stated value:Face value or Par value or Stated value: The value at whichThe value at which corporation issue its shares in case of common share orcorporation issue its shares in case of common share or the redemption value paid at maturity in case of bond.the redemption value paid at maturity in case of bond. New stock is usually sold at more than par value, withNew stock is usually sold at more than par value, with the difference being recorded on balance sheet asthe difference being recorded on balance sheet as “capital in excess of par value”.“capital in excess of par value”. Book Value:Book Value: The accounting value of equity as shown inThe accounting value of equity as shown in the balance sheet. It is the sum of common stockthe balance sheet. It is the sum of common stock outstanding, capital in excess of par value, and retainedoutstanding, capital in excess of par value, and retained earnings. Dividing this sum or total book value by theearnings. Dividing this sum or total book value by the number of common shares outstanding produces thenumber of common shares outstanding produces the book value par share. Although it plays an importantbook value par share. Although it plays an important role in investment decision, market value par share isrole in investment decision, market value par share is the critical item of interest to investors.the critical item of interest to investors.
- 10. Sources and Typesof RiskSources and Types of Risk Sources of Risk:Sources of Risk: Interest rate riskInterest rate risk Market riskMarket risk Inflation riskInflation risk Business riskBusiness risk Financial riskFinancial risk Liquidity riskLiquidity risk Exchange rate riskExchange rate risk Country riskCountry risk Broad Types:Broad Types: Systematic/Market RiskSystematic/Market Risk NonNon--systematic/Nonsystematic/Non--market/Companymarket/Company--specific Riskspecific Risk
- 11. RiskRisk--return tradereturn trade--offin different types of securitiesoff in different types of securities Various types of securities:Various types of securities: Equity securitiesEquity securities may bemay be --Ordinary share or Common share, gives real ownership because holOrdinary share or Common share, gives real ownership because holder bearsder bears ultimate risk and enjoy return and have voting rightsultimate risk and enjoy return and have voting rights --Preferential share, enjoy fixed dividend, avoids risk, do not haPreferential share, enjoy fixed dividend, avoids risk, do not have voting right.ve voting right. Debt securitiesDebt securities may bemay be --Bond, a secured debt instrument, payable on first on liquidityBond, a secured debt instrument, payable on first on liquidity --Debenture, an unsecured debt instrument,Debenture, an unsecured debt instrument, Derivative securitiesDerivative securities are those that derive their value in whole or inare those that derive their value in whole or in part by having a claim on some underlying value. Options andpart by having a claim on some underlying value. Options and futures are derivative securitiesfutures are derivative securities Corporate bondsCorporate bonds Common stocksCommon stocks OptionsOptions FuturesFutures RFRF Expected returnExpected return RiskRisk
- 12. Factors Affecting SecurityPricesFactors Affecting Security Prices Stock splitsStock splits Dividend announcementsDividend announcements Initial public offeringsInitial public offerings Reactions to macro and micro economic newsReactions to macro and micro economic news Demand/supply of securities in the marketDemand/supply of securities in the market Marketability of securitiesMarketability of securities Dividend paymentsDividend payments Many othersMany others
- 13. Direct investment andindirectDirect investment and indirect investmentinvestment InIn Direct InvestingDirect Investing, investors buy and sell, investors buy and sell securities themselves, typically throughsecurities themselves, typically through brokerage accounts. Active investors maybrokerage accounts. Active investors may prefers this type of investing.prefers this type of investing. InIn Indirect InvestingIndirect Investing, investors buy and sell, investors buy and sell shares of investment companies, which in turnshares of investment companies, which in turn hold portfolios of securities. Individual whohold portfolios of securities. Individual who are not active may prefer this type of investing.are not active may prefer this type of investing.
- 14. Important considerations ininvestmentImportant considerations in investment decision process:decision process: Investment decision should be considered based on economy,Investment decision should be considered based on economy, industry consideration and company fundamentals includingindustry consideration and company fundamentals including management & financial performancemanagement & financial performance Investment decision process can be lengthy and involvedInvestment decision process can be lengthy and involved The great unknown may exist whatever be the individual actionsThe great unknown may exist whatever be the individual actions Global investment arenaGlobal investment arena New economyNew economy vrsvrs old economy stocksold economy stocks The rise of the internetThe rise of the internet-- a true revolution for investmenta true revolution for investment information.information. Institutional investorsInstitutional investors vrsvrs individual investorindividual investor RiskRisk--return preferencereturn preference Traditionally, investors have analyzed and managed securities usTraditionally, investors have analyzed and managed securities using aing a broad twobroad two--step process:step process: security analysis andsecurity analysis and portfolio managementportfolio management
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- 16. Security Analysis Concept& TypesSecurity Analysis Concept & Types Security analysisSecurity analysis is the first part of investment decision processis the first part of investment decision process involving the valuation and analysis of individual securities. Tinvolving the valuation and analysis of individual securities. Two basicwo basic approaches of security analysis are fundamental analysis and tecapproaches of security analysis are fundamental analysis and technicalhnical analysis.analysis. Fundament analysisFundament analysis is the study of stocks value using basicis the study of stocks value using basic financial variables in order to order to determine company’s intfinancial variables in order to order to determine company’s intrinsicrinsic value. The variables are sales, profit margin, depreciation, taxvalue. The variables are sales, profit margin, depreciation, tax rate,rate, sources of financing, asset utilization and other factors. Additsources of financing, asset utilization and other factors. Additionalional analysis could involve the company’s competitive position in theanalysis could involve the company’s competitive position in the industry, labor relations, technological changes, management, foindustry, labor relations, technological changes, management, foreignreign competition, and so on.competition, and so on. Technical analysisTechnical analysis is the search for identifiable and recurring stockis the search for identifiable and recurring stock price patterns.price patterns. Behavioral Finance Implications:Behavioral Finance Implications: Investors are aware of marketInvestors are aware of market efficiency but sometimes overlook the issue of psychology inefficiency but sometimes overlook the issue of psychology in financial marketsfinancial markets-- that is, thethat is, the role that emotions playrole that emotions play. Particularly,. Particularly, in short turn, inventors’ emotions affect stock prices, and markin short turn, inventors’ emotions affect stock prices, and marketsets
- 17. Framework for FundamentalAnalysis:Framework for Fundamental Analysis: BottomBottom--up approach,up approach, where investors focus directly on a company’swhere investors focus directly on a company’s basic. Analysis of such information as the company’s products, ibasic. Analysis of such information as the company’s products, itsts competitive position and its financial status leads to an estimacompetitive position and its financial status leads to an estimate of thete of the company's earnings potential and ultimately its value in the marcompany's earnings potential and ultimately its value in the market.ket. TheThe emphasis in this approach is on finding companies with goodemphasis in this approach is on finding companies with good growth prospectgrowth prospect, and making accurate, and making accurate earnings estimatesearnings estimates. Thus. Thus bottombottom--up fundamental research is broken in two categories:up fundamental research is broken in two categories: growthgrowth investinginvesting andand value investingvalue investing Growth Stock:Growth Stock: It carry investor expectation of above average future growth inIt carry investor expectation of above average future growth in earningsearnings and above average valuations as a result of high price/earningsand above average valuations as a result of high price/earnings ratios.ratios. Investors expect these stocks to perform well in future and theyInvestors expect these stocks to perform well in future and they areare willing to pay high multiples for this expected growth.willing to pay high multiples for this expected growth. Value Stock:Value Stock: Features cheap assets and strong balance sheets.Features cheap assets and strong balance sheets. In many cases, bottomIn many cases, bottom--up investing does not attempt to make a clear distinctionup investing does not attempt to make a clear distinction between growth and value stocks. Topbetween growth and value stocks. Top--down approach is better approach.down approach is better approach.
- 18. TopTop--down Approachdown Approach Inthis approachIn this approach investors begin with economy/market consideringinvestors begin with economy/market considering interest rates and inflation to find out favorable time tointerest rates and inflation to find out favorable time to invest in common stockinvest in common stock then consider future industry/sector prospect tothen consider future industry/sector prospect to determine which industry/sector to invest indetermine which industry/sector to invest in Finally promising individual companies of interest inFinally promising individual companies of interest in the prospective sectors are analyzed for investmentthe prospective sectors are analyzed for investment decision.decision.
- 19. Fundamental Analysis atFundamentalAnalysis at Company Level:Company Level: There are two basic approaches for valuation ofThere are two basic approaches for valuation of common stocks using fundamental analysis,common stocks using fundamental analysis, which are:which are: Intrinsic Valuation:Intrinsic Valuation: Discounted cash flow(DCF)Discounted cash flow(DCF) technique. One form of DCF is Dividend Discounttechnique. One form of DCF is Dividend Discount Model(DDM), that uses present value method byModel(DDM), that uses present value method by discounting back all future dividendsdiscounting back all future dividends Relative ValuationRelative Valuation Model, uses P/E ratio, P/BModel, uses P/E ratio, P/B ratio and P/S ratioratio and P/S ratio
- 20. Intrinsic Valuation, DDM:IntrinsicValuation, DDM: In this method, an investor or analyst carefully studies the futIn this method, an investor or analyst carefully studies the futureure prospects for a company and estimates the likely dividends to beprospects for a company and estimates the likely dividends to be paid,paid, which are the only payments an investor receives directly from awhich are the only payments an investor receives directly from a company. In addition, the analyst estimates an appropriate requicompany. In addition, the analyst estimates an appropriate required ratered rate of return on the risk foreseen in the dividends. Then calculateof return on the risk foreseen in the dividends. Then calculate thethe estimated discounted present value of all future dividends as beestimated discounted present value of all future dividends as below:low: PV of stock, VPV of stock, Voo= D1/(1+k) +D2/(1+k)= D1/(1+k) +D2/(1+k)22+ D3/(1+k)+ D3/(1+k)33+…..+….. =D1/(k=D1/(k –– g) …… (after simplification)g) …… (after simplification) where, D1, D2, D3..are future 1st, 2nd , 3rd years dividends, kwhere, D1, D2, D3..are future 1st, 2nd , 3rd years dividends, k is required rate of returnis required rate of return Now,Now, If Vo > Po, the stock is undervalued and should be purchasedIf Vo > Po, the stock is undervalued and should be purchased If Vo < Po, the stock is overvalued and should be not be purchasIf Vo < Po, the stock is overvalued and should be not be purchaseded If Vo = Po, the stock is at correctly pricedIf Vo = Po, the stock is at correctly priced AlternativelyAlternatively,, in practice, investors can use DDM to select stocksin practice, investors can use DDM to select stocks. The expected. The expected rate of return, k, for constant growth stock can be written asrate of return, k, for constant growth stock can be written as k= D1/Pk= D1/Poo ++ g, where D1/Pg, where D1/Poo is dividend yield and the 2is dividend yield and the 2ndnd part g is price changepart g is price change componentcomponent
- 21. Relative ValuationRelative Valuation Relativevaluation technique uses comparisons toRelative valuation technique uses comparisons to determine a stock’s value. By calculating measures suchdetermine a stock’s value. By calculating measures such as P/E ratio and making comparisons to someas P/E ratio and making comparisons to some benchmark(s) such as the market, an industry or otherbenchmark(s) such as the market, an industry or other stocks history over time, analyst can avoid having tostocks history over time, analyst can avoid having to estimate g and k parameters of DDM.estimate g and k parameters of DDM. In relative valuation, investors use several differentIn relative valuation, investors use several different ratios such as P/E, P/B, P/S etc in an attempt toratios such as P/E, P/B, P/S etc in an attempt to assess value of a stock through comparison withassess value of a stock through comparison with benchmark.benchmark.
- 22. Earning Multiplier orP/E RatioEarning Multiplier or P/E Ratio Model:Model: This model is the bestThis model is the best--known and most widely usedknown and most widely used model for stock valuation. Analysts are moremodel for stock valuation. Analysts are more comfortable taking about earning per share (EPS) andcomfortable taking about earning per share (EPS) and P/E ratios, and this is how their reports are worded.P/E ratios, and this is how their reports are worded. P/E ratio simply means the multiples of earningsP/E ratio simply means the multiples of earnings at which the stock is sellingat which the stock is selling.. For example, if a stock’sFor example, if a stock’s most recent 12 months earning ismost recent 12 months earning is TkTk 5 and its is selling5 and its is selling now atnow at TkTk 150, then it is said that the stock is selling for150, then it is said that the stock is selling for a multiple of 30.a multiple of 30.
- 23. Determinants of P/ERatio:Determinants of P/E Ratio: For a constant growth model of DDM,For a constant growth model of DDM, Price of a stock, P=D1/(kPrice of a stock, P=D1/(k -- g)g) Or, P/E=(D1/E)/(kOr, P/E=(D1/E)/(k -- g)g) This indicates that P/E depends on:This indicates that P/E depends on: 1.1. Expected dividend payout ratio, D1/EExpected dividend payout ratio, D1/E 2.2. Required rate of return, k, which is to be estimatedRequired rate of return, k, which is to be estimated 3.3. Expected growth rate of dividendsExpected growth rate of dividends Thus following relationship should hold, being other things equaThus following relationship should hold, being other things equal:l: 1.1. The higher the expected payout ratio, the higher the P/E ratioThe higher the expected payout ratio, the higher the P/E ratio 2.2. The higher the expected growth rate, the higher the P/E ratioThe higher the expected growth rate, the higher the P/E ratio 3.3. The higher the required rate of return, the lower the P/E ratioThe higher the required rate of return, the lower the P/E ratio
- 24. Valuation Using P/ERatio:Valuation Using P/E Ratio: To use the earnings multiplier model for valuation ofTo use the earnings multiplier model for valuation of a stock, investorsa stock, investors must look ahead because valuation is always forward looking. Themust look ahead because valuation is always forward looking. They cany can do this by making a forecast of next year’s earnings per share Edo this by making a forecast of next year’s earnings per share E1,1, assuming a constant growth model, asassuming a constant growth model, as Next years earning per share, E1=Next years earning per share, E1=EoEo(1+g)(1+g) where, g=ROEwhere, g=ROE XX (1(1 -- Payout ratio)Payout ratio) Then calculate the forward P/E ratio asThen calculate the forward P/E ratio as Forward P/E ratio= Po/E1, where E1 is expected earning for nextForward P/E ratio= Po/E1, where E1 is expected earning for next yearyear In practice, analysts often recommend stocks on the basis of thiIn practice, analysts often recommend stocks on the basis of thiss forward P/E ratio or multiplier by making a relative judgment wiforward P/E ratio or multiplier by making a relative judgment with someth some benchmark.benchmark.
- 25. Other Relative ValuationRatios:Other Relative Valuation Ratios: Price to Book Value(P/B):Price to Book Value(P/B): This is the ratio of stockThis is the ratio of stock price to per share stockholders’ equity.price to per share stockholders’ equity. Analysts recommend lower P/B stock compared to itsAnalysts recommend lower P/B stock compared to its own ratio over time, its industry ratio, and the marketown ratio over time, its industry ratio, and the market ratio as a whole.ratio as a whole. Price to Sales Ratio(P/S):Price to Sales Ratio(P/S): A company’s stock priceA company’s stock price divided by its sales per share.divided by its sales per share. A PSR 1.0 is average for all companies but it isA PSR 1.0 is average for all companies but it is important to interpret the ratio within industryimportant to interpret the ratio within industry bounds and its own historical average.bounds and its own historical average.
- 26.
- 27. IIf the ratesof return on individual securities are dependent onlf the rates of return on individual securities are dependent only ony on companycompany--specific risks of that company and these returns arespecific risks of that company and these returns are statistically independent of other securities’ returns, then instatistically independent of other securities’ returns, then in that case,that case, the standard deviation of return of the portfolio (formed by nthe standard deviation of return of the portfolio (formed by n number of securities) is given bynumber of securities) is given by σσii σσpp== ------------------------(1)(1) √n√n Risk DiversificationRisk Diversification-- the objective of portfolio formationthe objective of portfolio formation without affecting the return significantlywithout affecting the return significantly Standarddeviationof portfolioreturn No. of securities Systematic riskSystematic risk CompanyCompany--specificspecific riskrisk Total riskTotal risk
- 28. Risk DiversificationRisk Diversification Riskdiversification is the key to theRisk diversification is the key to the management of portfolio risk, because it allowsmanagement of portfolio risk, because it allows investors to significantly lower the portfolio riskinvestors to significantly lower the portfolio risk without adversely affecting return.without adversely affecting return. Diversification types:Diversification types: Random or naive diversificationRandom or naive diversification Efficient diversificationEfficient diversification
- 29. Random or naivediversificationRandom or naive diversification:: It refers to the act of randomly diversifyingIt refers to the act of randomly diversifying without regard to relevant investment characteristics suchwithout regard to relevant investment characteristics such as expected return and industry classificationas expected return and industry classification. An. An investor simply selects relatively large numberinvestor simply selects relatively large number of securities randomly.of securities randomly. Unfortunately, in such case, the benefits ofUnfortunately, in such case, the benefits of random diversification do not continue as werandom diversification do not continue as we add more securities, the reduction becomesadd more securities, the reduction becomes smaller and smaller.smaller and smaller.
- 30. Efficient diversificationEfficient diversification EfficientdiversificationEfficient diversification takes place in an efficienttakes place in an efficient portfolio that has the smallest portfolio risk for a givenportfolio that has the smallest portfolio risk for a given level of expected return or the largest expected returnlevel of expected return or the largest expected return for a given level of risk. Investors can specify a portfoliofor a given level of risk. Investors can specify a portfolio risk level they are willing to assume and maximize therisk level they are willing to assume and maximize the expected return on the portfolio for this level of risk.expected return on the portfolio for this level of risk. Rational investorsRational investors look for efficient portfolios, becauselook for efficient portfolios, because these portfolios are optimized on the two dimensions ofthese portfolios are optimized on the two dimensions of most importance to investorsmost importance to investors-- return and risk.return and risk.
- 31. Modern Portfolio TheoryModernPortfolio Theory In 1952,In 1952, MarkowitzMarkowitz, the father of modern portfolio theory, developed, the father of modern portfolio theory, developed the basic principle of portfolio diversification in a formal wthe basic principle of portfolio diversification in a formal way, inay, in quantified form, that shows why and how portfolio diversificatioquantified form, that shows why and how portfolio diversification worksn works to reduce the risk of a portfolio to an investor.to reduce the risk of a portfolio to an investor. Modern PortfolioModern Portfolio theory hypothesizes how investors should behavetheory hypothesizes how investors should behave.. According toAccording to MarkowitzMarkowitz, the portfolio risk is not simply a weighted, the portfolio risk is not simply a weighted average of the risks brought by individual securities in the poraverage of the risks brought by individual securities in the portfolio buttfolio but it also includes the risks that occurs due to correlations amongit also includes the risks that occurs due to correlations among thethe securities in the portfolio. As the no. of securities in the porsecurities in the portfolio. As the no. of securities in the portfoliotfolio increases, contribution of individual security’s risk decreasesincreases, contribution of individual security’s risk decreases due todue to offsetting effect of strong performing and poor performing securoffsetting effect of strong performing and poor performing securities inities in the portfolio and the importance of covariance relationships amothe portfolio and the importance of covariance relationships amongng securities increases. Thus the portfolio risk is given bysecurities increases. Thus the portfolio risk is given by σσ22pp=∑w=∑wii22σσii22 + ∑ ∑+ ∑ ∑wwiiwwjjρρijijσσiiσσjj =∑ ∑=∑ ∑wwiiwwjjρρijijσσiiσσjj (the 1(the 1stst term is neglected for large n)term is neglected for large n)
- 32. Efficient FrontiersEfficient Frontiers Riskσ E ( R ) A Global minimum portfolio C B Portfolio on AB section are better than those on AC in risk-return perspective and so portfolios on AB are called efficient portfolios that offers best risk-return combinations to investors Graph for the riskGraph for the risk--return tradereturn trade--off according tooff according to MarkowitzMarkowitz portfolio theory isportfolio theory is drawn below.drawn below.
- 33. Computing Problem withOriginalComputing Problem with Original MarkowitzMarkowitz Theory, and Later SimplificationTheory, and Later Simplification As n increases, n(nAs n increases, n(n--1)1) covariancescovariances (inputs) are required(inputs) are required to calculate underto calculate under MarkowitzMarkowitz model. Due to thismodel. Due to this complexity of computation, it was mainly used forcomplexity of computation, it was mainly used for academic purposes before simplification.academic purposes before simplification. It was observed that mirror images ofIt was observed that mirror images of covariancescovariances werewere present inpresent in Markowitz’sMarkowitz’s model. So after excluding themodel. So after excluding the mirror images in the simplified form, n(nmirror images in the simplified form, n(n--1)/2 unique1)/2 unique covariancescovariances are required for using this model and sinceare required for using this model and since then it is being used by investors.then it is being used by investors.
- 35. MarkowitzMarkowitz Model forSelection of OptimalModel for Selection of Optimal Asset ClassesAsset Classes--Asset Allocation Decision:Asset Allocation Decision: MarkowitzMarkowitz model is typically thought of in termsmodel is typically thought of in terms of selecting portfolios of individual securities. Butof selecting portfolios of individual securities. But alternatively, it can be used as a selectionalternatively, it can be used as a selection technique for asset classes and asset allocation.technique for asset classes and asset allocation.
- 36. Single Index ModelSingleIndex Model -- An AlternativeAn Alternative Simplified Approach to DetermineSimplified Approach to Determine Efficient FrontiersEfficient Frontiers SingleSingle--Index model assumes that the risk of return from eachIndex model assumes that the risk of return from each security has two componentssecurity has two components-- the market related component(the market related component(βiRβiRMM)caused by macro events and)caused by macro events and the companythe company--specific component(specific component(eiei) which is a random residual) which is a random residual error caused by micro events.error caused by micro events. The security responds only to market index movement asThe security responds only to market index movement as residual errors of the securities are uncorrelated. The residuresidual errors of the securities are uncorrelated. The residualal errors occur due to deviations from the fitted relationshiperrors occur due to deviations from the fitted relationship between security return and market return. For any period, itbetween security return and market return. For any period, it represents the difference between the actual return(represents the difference between the actual return(RiRi) and the) and the return predicted by the parameters of the model(return predicted by the parameters of the model(βiRβiRMM))
- 37. The Single Indexmodel is given by the equation:The Single Index model is given by the equation: RiRi==αiαi ++ βiRβiRMM ++ eiei ………for security i, where………for security i, where RiRi= the return on security= the return on security RRMM=the return from the market index=the return from the market index αiαi =risk free part of security=risk free part of security i’si’s return which is independentreturn which is independent of market returnof market return βiβi=sensitivity of security i, a measure of change of=sensitivity of security i, a measure of change of RiRi for perfor per unit change Runit change RM,M, which is a constantwhich is a constant eiei=random residual error, which is company specific=random residual error, which is company specific ei RM Ri Single Index Model Diagram βi ααii
- 38. Single Index Model……SingleIndex Model…… Total risk of a security , as measured by its variance, consistsTotal risk of a security , as measured by its variance, consists ofof two components: market risk and unique risk and given bytwo components: market risk and unique risk and given by ααii22 =βi=βi22 [[ααMM22 }+}+ ααeiei22 =Market risk + company=Market risk + company--specific riskspecific risk This simplification also applies to portfolios, providing anThis simplification also applies to portfolios, providing an alternative expression to use in finding the minimum variance sealternative expression to use in finding the minimum variance sett of portfolios:of portfolios: ααpp22 =β=βpp22 [[ααMM 22 }+}+ ααepep22 The SingleThe Single--Index model is an alternative toIndex model is an alternative to MarkowitzMarkowitz model tomodel to determine the efficient frontiers with much fewer calculations,determine the efficient frontiers with much fewer calculations, 3n+2 calculations, instead of n(n3n+2 calculations, instead of n(n--1)/2 calculations. For 201)/2 calculations. For 20 securities, it requires 62 inputs instead of 190 insecurities, it requires 62 inputs instead of 190 in MarkowitzMarkowitz model.model.
- 39. MultiMulti--Index ModelIndex Model Someresearchers have attempted to capture someSome researchers have attempted to capture some nonnon--market influences on stock price bymarket influences on stock price by constructing Multiconstructing Multi--Index model. Probably the mostIndex model. Probably the most obvious nonobvious non--market influence is the industrymarket influence is the industry factor. Multifactor. Multi--index model is given by the equation:index model is given by the equation: E(E(RRii)=)=aaii++bbiiRRMM++cciiNFNF ++ eeii, where NF=non, where NF=non--market factormarket factor
- 40. Capital Market Theory(CMT)CapitalMarket Theory(CMT) Capital market theory hypothesizes how investors behave rather tCapital market theory hypothesizes how investors behave rather than how theyhan how they should behave as inshould behave as in MarkowitzMarkowitz portfolio theory. CMT is based onportfolio theory. CMT is based on MarkowitzMarkowitz theory and but it is an extension of that.theory and but it is an extension of that. The more the risk is involved in an investment, the more the retThe more the risk is involved in an investment, the more the return is requiredurn is required to motivate the investorsto motivate the investors. It plays a central role in asset pricing, because it is the ri. It plays a central role in asset pricing, because it is the risksk that investors undertake with expectation to be rewarded.that investors undertake with expectation to be rewarded. CMT is build onCMT is build on MarkowitzMarkowitz Portfolio theory and extended with introduction ofPortfolio theory and extended with introduction of riskrisk--free asset that allows investors borrowing and lending at riskfree asset that allows investors borrowing and lending at risk--free rate andfree rate and at this, the efficient frontier is completely changed, which inat this, the efficient frontier is completely changed, which in tern leads to atern leads to a general theory for pricing asset under uncertaintygeneral theory for pricing asset under uncertainty. Borrowing additional ingestible. Borrowing additional ingestible fund and investing together with investor’s wealth allows investfund and investing together with investor’s wealth allows investors to seek higherors to seek higher expected return, while assuming greater risk. Likewise, lendingexpected return, while assuming greater risk. Likewise, lending part of investor’s wealthpart of investor’s wealth at riskat risk--free rate, investors can reduce risk at the expense of reduced efree rate, investors can reduce risk at the expense of reduced expected return.xpected return.
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- 42. CAPM and ItsTwo Specifications:CAPM and Its Two Specifications: CML, SMLCML, SML CAPM(Capital Asset Pricing Model)CAPM(Capital Asset Pricing Model) This is a form of CMT, and it is an equilibriumThis is a form of CMT, and it is an equilibrium model, allows us to measure the relevant risk of anmodel, allows us to measure the relevant risk of an individual security as well as to assess the relationshipindividual security as well as to assess the relationship between risk and the returns expected from investing.between risk and the returns expected from investing. It has two specifications: CML & SMLIt has two specifications: CML & SML
- 43. CML:CML: CML(Capital Market Line):CML(CapitalMarket Line): A straight line, depicts equilibriumA straight line, depicts equilibrium conditions that prevails in the market for efficient portfoliosconditions that prevails in the market for efficient portfolios consistingconsisting of the optimal portfolio risky assets and the riskof the optimal portfolio risky assets and the risk--free asset. Allfree asset. All combinations of the riskcombinations of the risk--free asset and risky portfolio M are on CML,free asset and risky portfolio M are on CML, and in equilibrium, all investors will end up with portfolios soand in equilibrium, all investors will end up with portfolios somewheremewhere on the CML.on the CML. Risk of marketRisk of market portfolio M,portfolio M, σσMM RFRF RiskRisk E(R)E(R) MM Risk premium for market portfolioRisk premium for market portfolio E(RE(RMM)) E(E(RpRp)=RF+(E(R)=RF+(E(RMM))--RF)RF)ρρpp//σσMM22
- 44. SML:SML: SML (Security MarketLine):SML (Security Market Line): It says that the expected rate of return from anIt says that the expected rate of return from an asset is function of the two components of the required rate ofasset is function of the two components of the required rate of returnreturn-- the riskthe risk free rate and risk premium, and can be written by, k=RF+free rate and risk premium, and can be written by, k=RF+ββ(E(R(E(RMM))--RF). AtRF). At market portfolio M,market portfolio M, ββ=1.=1. RequiredrateofreturnRequiredrateofreturn MM 11 RFRF ββ ββMM Assets less riskyAssets less risky than market portfoliothan market portfolio Assets more riskyAssets more risky than market portfoliothan market portfolio XX YY OvervaluedOvervaluedundervaluedundervalued
- 45. SML…..SML….. CAPM formally relatesthe expected rate of return for anyCAPM formally relates the expected rate of return for any security of portfolio with the relevant risk measure. This issecurity of portfolio with the relevant risk measure. This is the most cited form of relationship and graphicalthe most cited form of relationship and graphical representation of CAPM.representation of CAPM. BetaBeta is the change in risk on an individual securityis the change in risk on an individual security influenced by 1 percent change in market portfolio return.influenced by 1 percent change in market portfolio return. Beta is the relevant measure of risk that can not beBeta is the relevant measure of risk that can not be diversified away in a portfolio of securities and, as such, isdiversified away in a portfolio of securities and, as such, is the measure that investors should consider in their portfoliothe measure that investors should consider in their portfolio management decision process.management decision process.
- 46. Portfolio PerformancePortfolio PerformanceMeasurementMeasurement Sharpe’s measure(Reward to Variability Ratio, RVAR):Sharpe’s measure(Reward to Variability Ratio, RVAR): The performance of portfolio is calculated in Sharpe’s measure aThe performance of portfolio is calculated in Sharpe’s measure as thes the ratio of excess portfolio return to the standard deviation of reratio of excess portfolio return to the standard deviation of return forturn for the portfolio.the portfolio. RVAR=(RVAR=( TRpTRp ––RF)/RF)/SDpSDp Note about RVAR:Note about RVAR: It measures the excess return per unit of total risk(It measures the excess return per unit of total risk(SDpSDp) of the portfolio) of the portfolio The higher the RVAR, the better the portfolio performanceThe higher the RVAR, the better the portfolio performance Portfolios can be ranked by RVAR and best performing one can bePortfolios can be ranked by RVAR and best performing one can be determineddetermined Appropriate benchmark is used for relative comparisons in perforAppropriate benchmark is used for relative comparisons in performance measurementmance measurement CML ofCML of appropriateappropriate benchmarksbenchmarks XX YY ZZ SDpSDp RateofreturnRateofreturnRFRF Efficient portfolios lie on CMLEfficient portfolios lie on CML OutperformersOutperformers lie above CMLlie above CML Underperformers lie under CMLUnderperformers lie under CML
- 47. Portfolio PerformancePortfolio Performance Measurement…………Measurement………… Treynor’sTreynor’smeasure(Reward to Volatility Ratio, RVOR)measure(Reward to Volatility Ratio, RVOR) The performance of portfolio is calculated inThe performance of portfolio is calculated in Treynor’sTreynor’s measure as the ratio ofmeasure as the ratio of excess portfolio return to the beta of the portfolio which is syexcess portfolio return to the beta of the portfolio which is systematic risk.stematic risk. RVOR=(RVOR=( TRpTRp ––RF)/RF)/ βpβp Note about RVOL:Note about RVOL: It measures the excess return per unit of systematic risk (It measures the excess return per unit of systematic risk (βpβp) of the portfolio) of the portfolio The higher the RVOR, the better the portfolio performanceThe higher the RVOR, the better the portfolio performance Portfolios can be ranked by RVOR and best performing one can bePortfolios can be ranked by RVOR and best performing one can be determineddetermined RateofreturnRateofreturn RFRF SML ofSML of appropriateappropriate benchmarksbenchmarks XX YY ZZ βpβp Efficient portfolios lie on SMLEfficient portfolios lie on SML OutperformersOutperformers lie above SMLlie above SML Underperformers lie under SMLUnderperformers lie under SML
- 48. Portfolio PerformancePortfolio Performance Measurement…………Measurement………… Jensen’sDifferential Return MeasureJensen’s Differential Return Measure, α:, α: It is calculated as the difference between what theIt is calculated as the difference between what the portfolio actually earned and what it was expectedportfolio actually earned and what it was expected to earn given the portfolio’s level of systematic risk.to earn given the portfolio’s level of systematic risk. ααpp=(=(RpRp –– RF)RF) –– [[βpβp (R(RMM –– RF)]RF)] =Actual return=Actual return ––required returnrequired return RRMM -- RFRF RpRp -- RFRF 00 XX YY ZZ
- 49. Portfolio monitoring andPortfoliomonitoring and rebalancingrebalancing It is important to monitor market conditions,It is important to monitor market conditions, relative asset mix and investors’ circumstances.relative asset mix and investors’ circumstances. These changes dynamically and frequently andThese changes dynamically and frequently and so there is need for rebalancing the portfolioso there is need for rebalancing the portfolio towards optimal point.towards optimal point.
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