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- 1. Portfolio Management
- 2. Portfolio is a combination of securities such as stocks, bonds and money market instruments. The process of blending together the broad asset classes so as to obtain optimum return with minimum risk is called portfolio management. Diversification of investments helps to spread risk over many assets.
- 3. WHY PORTFOLIOS? The simple fact that securities carry differing degrees of expected risk leads most investors to the notion of holding more than one security at a time, in an attempt to spread risks by not putting all their eggs into one basket. Most investors hope that if they hold several assets, even if one goes bad, the others will provide some protection from an extreme loss.
- 4. Diversification Efforts to spread and minimize risk take the form of diversification. The more traditional forms of diversification have concentrated upon holding a number of security types( shares, bonds) across industry lines( mining , manufacturing , steel). Most people would agree that a portfolio consisting of two stocks is probably less risk than one holding either stock alone.
- 5. Approaches in Portfolio Construction 1.Traditional approach 2.Markowitz efficient frontier approach
- 6. Traditional approach evaluates the entire financial plan of the individual. In the modern approach, portfolios are constructed to maximise the expected return for a given level of risk.
- 7. Traditional Approach The traditional approach basically deals with two major decisions: Determining the objectives of the portfolio. Selection of securities to be included in the portfolio.
- 8. Steps in Traditional Approach A n a ly s is o f C o n s tr a in ts D e te r m in a tio n o f O b je c t iv e s S e le c tio n o f P r o tfo lio B o n d a n d C o m m o n s to c k Bond C o m m o n s to c k A s s e s s m e n t o f r is k a n d r e t u r n D iv e r s if ic a tio n
- 9. Analysis of Constraints Income needs Need for current income Need for constant income Liquidity Safety of the principal Time horizon Tax consideration Temperament
- 10. Determination of Objectives The common objectives are stated below: Current income Growth in income Capital appreciation Preservation of capital
- 11. Selection of Portfolio Objectives Growth of income Capital appreciation Safety of principal Risk and return analysis
- 12. Diversification According to the investor’s need for income and risk tolerance level portfolio is diversified. In the bond portfolio, the investor has to strike a balance between the short term and long term bonds.
- 13. Stock Portfolio Following steps as shown in the figure are adopted S e le c t io n o f I n d u s t r ie s S e le c t io n o f C o m p a n ie s in t h e In d u s t r y D e t e r m in in g t h e s iz e o f p a r t ic ip a t io n
- 14. Modern Approach Modern approach gives more attention to the process of selecting the portfolio. The selection is based on the risk and return analysis. Return includes the market return and dividend. Investors are assumed to be indifferent towards the form of return. The final step is asset allocation process that is to choose the portfolio that meets the requirement of the investor.
- 15. Managing the Portfolio Investor can adopt passive approach or active approach towards the management of the portfolio. In the passive approach the investor would maintain the percentage allocation of asset classes and keep the security holdings within its place over the established holding period. In the active approach the investor continuously assess the risk and return of the securities within the asset classes and changes them accordingly.
- 16. Simple Diversification Portfolio risk can be reduced by the simplest kind of diversification. In the case of common stocks, diversification reduces the unsystematic risk or unique risk. Analysts says that if 15 stocks are added in a portfolio of the investor , the unsystematic risk can be reduced to zero. But at the same time if the number exceeds 15, additional risk reduction cannot be gained. But diversification cannot reduce systematic or undiversifiable risk.
- 17. Diversification and Portfolio Risk σp U n iq u e R is k T o t a l R is k M a rk e t R is k 5 10 15 N u m b e r o f S to c k s 20
- 18. The standard deviations of the portfolios are given in y axis and the number of randomly selected portfolio securities in the X axis. The S.D was calculated for each portfolio and plotted. As the portfolio size increases, the total risk line starts declining. It flattens out after a certain point. Beyond that limit, risk cannot be reduced. This indicates that spreading out the assets beyond certain level cannot be expected to reduce the portfolio’s total risk below the level of undiversifiable risk.
- 19. Problems of Vast Diversification Information inadequacy Purchase of poor performers High research cost High transaction
- 20. The Markowitz Model Harry Markowitz published an article on portfolio selection in the Journal of Finance in March 1952. His publication indicated the importance of correlation among the different stocks’ returns in the construction of a stock portfolio. After the publication of this paper, numerous investment firms and portfolio managers developed ‘Markowitz algorithms’ to minimise risk.
- 21. Assumptions The individual investor estimates risk on the basis of variability of returns i.e the variance of returns. Investor’s decision is solely based on the expected return and variance of returns only. For a given level of risk, investor prefers higher return to lower return. Likewise, for a given level of return investor prefers lower risk than higher risk.
- 22. Example Stock ABC Return % Probability Expected return Variance Standard deviation 11 or 17 .5 each return 14 9 3 Stock XYZ 20 or 8 .5 each return 14 36 6
- 23. ABC Expected return = (.5 x 11) + (.5 x 17) =14 XYZ Expected return = (.5 x 20) + (.5 x 8) =14 ABC variance = .5( 11 -14 )2 + .5( 17 -14)2 = 9 XYZ variance = .5( 20 -14 )2 + .5( 8 -14)2 = 36 ABC S. D = 3 XYZ S . D = 6
- 24. Portfolio Return N R p = ∑ 1R 1 X t =1
- 25. Rp = return on the portfolio X1 = proportion of total portfolio invested in security 1 R1 = expected return of security 1
- 26. Suppose the investor holds two thirds of ABC and one third of XYZ , the return is Possibility 1 =( 2/3 x 11) + (1/3 x 20) = 14 Possibility 2 =( 2/3 x 17) + (1/3 x 8 ) = 14 In both the situations, the investor stands to gain if the worst occurs, than by holding either of the security individually.
- 27. Portfolio Risk Ã p = X Ã + X σ + 2X1 X 2 (r12 Ã 1 Ã 2) 2 1 2 1 2 2 2 2
- 28. σp = portfolio standard deviation X1 = percentage of total portfolio value in stock X1 X2 = percentage of total portfolio value in stock X2 σ1 = standard deviation of stock X1 σ2 = standard deviation of stock X2 r12 = correlation co-efficient of X1 and X2
- 29. covariance of X12 r12 = σ1 σ 2
- 30. Covariance of X12 Using the same example given in the return analysis, the portfolio risk can be estimated. Let us assume ABC as X1 and XYZ as X2. N Cov of X12 = 1/ N ∑ ( R1- R1*) (R2 – R2*) I=1 Where R1, R2 – Actual return R1 *, R2* - Expected return
- 31. Cov of X12 =( ½)[ ( 11- 14)( 20-14) + ( 17-14)( 8 – 14)] = 1/2 [ ( -18) + ( -18 )] = -36 / 2 = -18 r = (Covariance of X12 / σ1 σ2 ) = -18/ (3 x 6) = -1
- 32. Here the correlation co-efficient is -1.0 , which indicates that there is a perfect negative correlation and the returns move in the opposite direction. If the correlation is 1, perfect positive correlation exists between the securities and they tend to move in the same direction. If the correlation co-efficient is zero, the securities’ returns are independent. Thus, the correlation between two securities depends upon the covariance between the two securities and the standard deviation of each security.
- 33. If the investor holds two thirds of ABC and one third of XYZ the portfolio risk is σ p = √( 2/3)2 x 9 + ( 1/3)2 x 36 + 2 x 2/3 x 1/3 ( -1 x 3 x 6) = √ 4 + 4 + ( -8) =√0
- 34. Proportion X1 = σ2 ÷ (σ1 + σ2) the precondition is that the correlation coefficient should be –1.0, Otherwise it is σ 2 − (r12 σ 1 σ 2 ) X1 = 2 2 2 σ 1 + σ 2 − (2r12 σ 1 σ 2 )
- 35. Rp and σ p for varying degrees of correlation co-efficients Proportion of X security in portfolio X Proportion of Y security in portfolio 1–X Rp rxy 1.00 0.75 0.50 0.25 0.00 0.00 0.25 0.50 0.75 1.00 5.00 5.75 6.50 7.25 8.00 σp rxy σp rxy σp rxy σp +1 –1 0 + .5 4.0 5.5 7.0 8.5 10.0 4.0 0.5 3.0 6.5 10.0 4.0 3.9 5.4 7.6 10.0 4.0 4.8 6.25 8.1 10.0
- 36. Two Security Portfolios with Different Correlation Coefficients R p 10 B r = – 1 r = +1 K D 5 r = 0 C r = + .5 J A r = – 1 5 10 σp
- 37. In the above figure, portfolio return is given on the vertical axis and portfolio risk on the horizontal axis. Point A represents 100% holdings of X and point B represents 100% holdings of y. The intermediate points along the line segment AB represent portfolios containing various combinations of two securities. The straight line r=+1 shows that the portfolio risk increases with the increase in portfolio return. Here the combination of two securities could not reduce the portfolio risk because of their positive correlation.
- 38. Along the line segment ACB, the r=0 . CB contains portfolios that are superior to those along the line segment AC. Markowitz says that all portfolios along the ACB line segment are feasible but some are more efficient than others. The line segment ADB indicates ( r = -1 ) perfect inverse correlation and it is possible to reduce portfolio risk to zero. Portfolios on the line segment DB provides superior returns than on the line segment AD.
- 39. For example, take two points on both the line segments K and J. The point K is superior to the point J because with the same level of risk the investor earns more return on point K than on point J. Thus, Markowitz diversification can lower the risk if the securities in the portfolio have low correlation coefficients.
- 40. Markowitz Efficient Frontier Among all the portfolios, the portfolios which offer the highest return at a particular level of risk are called efficient portfolios. The risk and return of all portfolios plotted in risk-return space would be dominated by efficient portfolios. Portfolios may be constructed from available securities. All the possible combination of expected return and risk compose the attainable set.
- 41. Example: Portfolio risk and return Portfolio A B C D E F G H J Expected return (Rp)% 17 15 10 7 7 7 10 9 6 Risk( S.Dp) 13 8 3 2 4 8 12 8 7.5
- 42. Efficient Frontier R p A 15 B 10 C H E G F D 5 I 5 10 15 σp
- 43. Each of the portfolio along the line or within the line ABCDEFGHI is possible. When the attainable sets are examined, some are more attractive than others. Portfolio B is more attractive than portfolios F and H because B offers more return on the same level of risk. Likewise, c is more attractive than portfolio G even though same level of return is got in both the points, the risk level is lower at point C.
- 44. In other words, any portfolio which gives more return for the same level of risk or same return with lower risk is more preferable than any other portfolio. Here the efficient portfolios are A, B, C and D. The ABCD line is the efficient frontier along which all attainable and efficient portfolios are available.
- 45. Now the question raised is which portfolio the investor should choose? He would choose a portfolio that maximizes his utility. For that utility analysis has to be done.
- 46. Utility Analysis Utility is the satisfaction the investor enjoys from the portfolio return. The investor gets more satisfaction of more utility in X + 1 rupees than from X rupee. Utility increases with increase in return. The utility function makes certain assumptions about an investors’ taste for risk. The investors are categorised into risk averse, risk neutral and risk seeking investor.
- 47. Indifference Curve and the Efficient Frontier Each investor has a series of indifference curves or utility curves. His final choice out of the efficient set depends on his attitude towards risk.
- 48. Indifference Curve and Efficient Frontier R p I4 I3 S R I2 I1 T 0 σp
- 49. The utility of the investor or portfolio manager increases when he moves up the indifference map from I1 to I4. He can achieve higher expected return without an increase in risk. Even though the points T and S are in the I2 curve, R is the only attainable portfolio which maximises the utility of the investor.
- 50. Thus, the point at which the efficient frontier tangentially touches the indifference curve determines the most attractive portfolio for the investor.

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