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Portfolio theory

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Portfolio Diversification

Portfolio Diversification

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Portfolio theory Portfolio theory Presentation Transcript

  • Module 4 : Investment AvenuesMutual funds, Investor life cycle, Personal investment, PersonalFinance, Portfolio Management of funds in banks, insurancecompanies, pension funds, International investing, internationalfunds management, emerging opportunities.Module 1: Introduction to portfolio ManagementMeaning of portfolio management, portfolio analysis, whyportfolios, Portfolio objectives, portfolio management process,selection of securities.
  • Module II Mohammed Umair: Dept of Commerce- Kristu Jayanti College
  • Company Name High Low Previous (LTP)Hero Motocorp 2600 2400 2500HDFC Bank 520 499 500State Bank of India 2100 2029 2000TCS 1020 998 1000Tech Mahindra 108 105 100Budget: Rs. 5000
  • Company Name High Low Previous (LTP)Hero Motocorp 2600 2400 2600HDFC Bank 520 499 550State Bank of India 2100 2029 2000TCS 1020 998 1050Tech Mahindra 108 105 150Situation A: Bullish Market
  • Company Name High Low Previous (LTP)Hero Motocorp 2600 2400 2200HDFC Bank 520 499 300State Bank of India 2100 2029 1750TCS 1020 998 850Tech Mahindra 108 105 050Situation B: Bearish Market
  • Portfolio Management Security Portfolio Portfolio Portfolio Portfolio Analysis Analysis Selection Revision Evaluation1. Fundamental Diversification 1. Markowitz 1. Formula 1. Sharpe’s Analysis Model Plans index2. Technical Analysis 2. Sharpe’s 2. Rupee 2. Treynor’s3. Efficient Single cost measure Market index Averaging 3. Jenson’s Hypothesis model measure 3. CAPM 4. APT
  • • Harry Max Markowitz (born August 24, 1927) is an American economist. • He is best known for his pioneering work in Modern Portfolio Theory. • Harry Markowitz put forward this model in 1952. • Studied the effects of asset risk, return, correlation and diversification on probable investment portfolio Harry Max Markowitz returns. Essence of Markowitz Model “Do not put all your eggs in one basket”1. An investor has a certain amount of capital he wants to invest over a single time horizon.2. He can choose between different investment instruments, like stocks, bonds, options, currency, or portfolio. The investment decision depends on the future risk and return.3. The decision also depends on if he or she wants to either maximize the yield or minimize the risk
  • Essence of Markowitz Model1. Markowitz model assists in the selection of the most efficient by analysing various possible portfolios of the given securities.2. By choosing securities that do not move exactly together, the HM model shows investors how to reduce their risk.3. The HM model is also called Mean-Variance Model due to the fact that it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios.Diversification and Portfolio Risk p p the standard deviation SR: Systematic Risk USR: Unsystematic Risk Portfolio Risk SR USR Total Risk 5 10 15 20 Number of Shares
  • • An investor has a certain amount of capital he wants to invest over a single time horizon.• He can choose between different investment instruments, like stocks, bonds, options, currency, or portfolio.• The investment decision depends on the future risk and return.• The decision also depends on if he or she wants to either maximize the yield or minimize the risk.• The investor is only willing to accept a higher risk if he or she gets a higher expected return.
  • Tools for selection of portfolio- Markowitz Model1. Expected return (Mean)Mean and average to refer to the sum of all values divided bythe total number of values.The mean is the usual average, so:(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15 n 1. Expected return (Mean) W 2. Standard deviation (variance)Expected Return (ER)  i  E ( Ri ) 3. Co-efficient of Correlation Where: i 1 ER = the expected return on Portfolio E(Ri) = the estimated return in scenario i Wi= weight of security i occurring in the port folioRp=R1W1+R2W2………..n Where: Rp = the expected return on Portfolio R1 = the estimated return in Security 1 R2 = the estimated return in Security 1 W1= Proportion of security 1 occurring in the port folio W2= Proportion of security 1 occurring in the port folio
  • Tools for selection of portfolio- Markowitz Model2. Variance & Co-variance n _ _ V ariance   Prob i ( R A  R A )  (R 2 2 B - RB ) i 1The variance is a measure of how far a set of numbers is spread out.It is one of several descriptors of a probability distribution,describing how far the numbers lie from the mean (expected value).Co-variance1. Covariance reflects the degree to which the returns of the two securities vary or change together.2. A positive covariance means that the returns of the two securities move in the same direction.3. A negative covariance implies that the returns of the two securities move in opposite direction. n _ _ _ 1 COV AB  N  Prob i ( R A  R A )(R B - RB ) R A =Expected Return on security A i 1 _ R B =Expected Return on security B CovAB=Covariance between security A and B RA=Return on security A RB=Return on Security B
  • Tools for selection of portfolio- Markowitz Model3. Co-efficient of CorrelationCovariance & Correlation are conceptually analogous in the sensethat of them reflect the degree of Variation between two variables.1. The Correlation coefficient is simply covariance divided the product of standard deviations.2. The correlation coefficient can vary between -1.0 and +1.0 -1.0 0 1.0 Perfectly negative No Perfectly Positive Opposite direction Correlation Opposite direction Cov r AB  AB  Standard deviation of A and B   A B security CovAB=Covariance between security A and B rAB=Co-efficient correlation between security A and B
  • Returns If returns of A and B are % 20% perfectly negatively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be riskless. There would 15% be no variability of the portfolios returns over time. 10% Returns on Stock A Returns on Stock B 5% Returns on Portfolio Time 0 1 2 CHAPTER 8 – Risk, Return and Portfolio Theory
  • Returns If returns of A and B are % 20% perfectly positively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be risky. There would be 15% no diversification (reduction of portfolio risk). 10% Returns on Stock A Returns on Stock B 5% Returns on Portfolio Time 0 1 2 CHAPTER 8 – Risk, Return and Portfolio Theory
  • • The riskiness of a portfolio that is made of different risky assets is a function of three different factors: • the riskiness of the individual assets that make up the portfolio • the relative weights of the assets in the portfolio • the degree of variation of returns of the assets making up the portfolio• The standard deviation of a two-asset portfolio may be measured using the Markowitz model:    w   w  2 w A w B rAB  A B 2 2 2 2 p A A B B A The data requirements for a three-asset portfolio grows dramatically if we are using Markowitz Portfolio selection formulae. ρa,b ρa,c B C ρb,c We need 3 (three) correlation coefficients between A and B; A and C; and B and C.    A w A   B w B   C w C  2 w A w B rA , B  A B  2 w B w C rB , C  B  C  2 w A w C rA , C  A C 2 2 2 2 2 2 p
  • • Assets differ in terms of expected rates of return, standard deviations, and correlations with one another • While portfolios give average returns, they give lower risk • Diversification works!• Even for assets that are positively correlated, the portfolio standard deviation tends to fall as assets are added to the portfolio
  • • Combining assets together with low correlations reduces portfolio risk more • The lower the correlation, the lower the portfolio standard deviation • Negative correlation reduces portfolio risk greatly • Combining two assets with perfect negative correlation reduces the portfolio standard deviation to nearly zero
  • n Expected Return (ER)  W i  E ( Ri ) i 1Portfolio Rp IN % Return on Portfolio Risk  p Any portfolio which gives moreA 17 13 return for the same level of risk.B 15 08 OrC 10 03D 7 02 Same return with Lower risk.E 7 04 Is more preferable then anyF 10 12 other portfolio.G 10 12H 09 08J 06 7.5Amongst all the portfolios which offers the highestreturn at a particular level of risk are calledefficient portfolios.
  • ABCD line is the efficient frontier along which attainable and efficient portfolios are available. 18 Which portfolio investor should choose? 16 14 13 12 12 12Risk and Return 10 Return 8 Risk 8 8 7.5 6 4 4 3 2 2 0 A B C D E F G H I Portfolios
  • Utility of Investor Risk Lover Risk Neutral Risk Averse Description Property Risk Seeker Accepts a fair Gamble Risk Neutral Indifferent to a fair gamble Risk Averse Rejects a fair gamble A BMarginal utility of different Utilityclass of investors. C Return
  • Rp Rp Indifference curves of the risk Indifference curves of the risk Loving I4 Fearing I I3 4 I3 I2 I2 I1 I1 Risk RiskRp Indifference curves of the less Rp risk Fearing Indifference curves & Efficient I4 frontier. I4 I3 I3 I2 I2 I1 I1 R Risk Risk 2 4 6 8 10 12 14 14 18
  • • The optimal portfolio concept falls under the modern portfolio theory. The theory assumes that investors fanatically try to minimize risk while striving for the highest return possible.
  • • WHAT IS A RISK FREE ASSET? • DEFINITION: an asset whose terminal value is certain • variance of returns = 0, • covariance with other assets = 0 If i  0then  ij   ij  i j  0
  • • DOES A RISK FREE ASSET EXIST? • CONDITIONS FOR EXISTENCE: • Fixed-income security • No possibility of default • No interest-rate risk • no reinvestment risk 24
  • • DOES A RISK FREE ASSET EXIST? • Given the conditions, what qualifies? • a U.S. Treasury security with a maturity matching the investor’s horizon• DOES A RISK FREE ASSET EXIST? • Given the conditions, what qualifies? • a U.S. Treasury security with a maturity matching the investor’s horizon
  • • ALLOWING FOR RISK FREE LENDING • investor now able to invest in either or both, • a risk free and a risky asset
  • • ALLOWING FOR RISK FREE LENDING • the addition expands the feasible set • changes the location of the efficient frontier • assume 5 hypothetical portfolios 27
  • • INVESTING IN BOTH: RISKFREE AND RISKY ASSETPORTFOLIOS X1 X2 ri di A .00 1.0 4 0 B .25 .75 7.05 3.02 C .50 .50 10.10 6.04 D .75 .25 13.15 9.06 E 1.00 .00 16.20 12.08 28
  • • RISKY AND RISK FREE PORTFOLIOS rP E D C B A rRF = 4% P 0 29
  • • IN RISKY AND RISK FREE PORTFOLIOS • All portfolios lie on a straight line • Any combination of the two assets lies on a straight line connecting the risk free asset and the efficient set of the risky assets rP • The Connection to the Risky Portfolio 0 P
  • • The Connection to the Risky Portfolio rP S R P P 0 31