Portfolio Evaluation and Revision

Portfolio Theories , single index , multi index , Sharp Ratio, Treynor Ratio ,Jensen’s Alpha and Formulation Plan.

1. PORTFOLIO MANAGEMENT Portfolio E valuation and Revision BY JIBUMON K G

2. Portfolio of Investment What is portfolio ..? A portfolio is a collection of financial investments by an individual or organization like stocks, bonds, commodities, cash, and cash equivalents

3. Portfolio management What is portfolio management …? The art of selecting the right investment policy for the individuals in terms of minimum risk and maximum return is called as portfolio management. Portfolio Management basically deals with three critical questions of investment planning. Where to invest ? When to invest? How much to invest ?

4. Types of Portfolio Management Aggressive Portfolio An aggressive portfolio, as the name suggests, is one of the common types of portfolio that takes a greater risk in search of high returns. Stocks in an aggressive portfolio have high beta and therefore experience a higher fluctuation in price. Defensive Portfolio A defensive portfolio is one comprising stocks that don’t have a high beta. Stocks in this portfolio are relatively isolated from broad market movements. In this type of portfolio, the strategy is to bring down the risk of losing the principal. Income Portfolio This is another common type of portfolio that focuses on investments making money from dividends or other types of distributions.

5. Hybrid Portfolio It is combined form of active and passive portfolio. Mixing stocks and bonds in a fixed proportion, a hybrid portfolio offers diversification across several asset classes.

6. Factors Considering Portfolio

7. Diversity When you invest in the stock market, a good approach is to spread your investments across various market categories. Diversity helps to minimize risk. Minimize investment costs When your are regularly buy or sell securities you may bear transaction cost and commission to brokers and other intermediaries. Therefore avoid unnecessary transfer of securities Regular investment In order to strengthen your portfolio, it is important to invest regularly. Follow-up buying When you are investing in a new stock, you may not know how it is going to perform. So to be on the safe side, it is a good idea to avoid committing your full position in one single investment. Instead, try to invest through a follow-up strategy.

8. Portfolio Analysis Portfolio analysis is the process of studying an investment portfolio to see if it meets a given investor's needs, preferences, and resources. It also measures how likely it is of meeting the goals and objectives of a given investment mandate. This is done on a risk-adjusted basis, looking at factors such as how the asset class performed in the past, as well as inflation.

9. Portfolio Construction & Selection Portfolio Construction refers to a process of selecting the optimum mix of securities such as stocks, bonds, mutual funds, and money market instruments, for the purpose of achieving maximum returns by making minimum risk or loss. Approaches of Portfolio Constructions Traditional Approach Modern Approach or Markowitz efficient frontier approach

10. Portfolio Theory

11. Traditional Approach In the traditional approach, investor’s needs in terms of income and capital appreciation are evaluated and appropriate securities are selected to meet the needs of the investor. The common practice in the traditional approach is to evaluate the entire financial plan of the individual. The traditional approach basically deals with two major decisions. Determining the objectives of the portfolio. Selection of securities to be included in the portfolio.

12. Steps in traditional approach

13. Analysis of constraints Income needs (current income and constant income) Income needs –  Investors need for current income (to meet living expenses) and constant income (to offset the effect of inflation) Liquidity needs –  Investors preference for liquid assets Safety of Principal –  Safety of principal value at the time of liquidation Time Horizon –  Life cycle stage and investment planning period of the investor Tax Consideration – Tax benefits of investing in a particular asset Temperament – Risk  bearing capacity of the investor

14. Determination of objectives Current income Growth in income Capital appreciation Preservation of capital Selection of portfolio. Selection of portfolio depends upon various objectives of investors. A Objective and asset mix. Growth of income and asset mix. Capital appreciation and asset mix. Safety of principal and asset mix.

15. Risk & Return Analysis : It involves analysis of risk and returns involved in following a particular course of action. Major risk  categories that an investor can tolerate are determined and efforts are made to minimize these risks to get expected returns. Diversification: It involves assigning relative portfolio weights to different securities  on the basis of which the portfolio is diversified.  Diversification is done on the basis of investors need of income and his risk bearing capacity

16. Formula Plans It is a portfolio revision techniques or procedures have been developed to enable investors to benefit from price fluctuations in the market. It is a plan for buying stocks when prices are low and selling them when prices are high. Formula plans are primarily oriented to achieve loss minimization rather than return maximization.

17. Features of Formula plans The amount available for investment is predetermined The investor would construct two portfolios, one aggressive (equities) and the other defensive (bonds, debentures) with his investment funds. The ratio between the investments in the aggressive portfolio and the defensive portfolio would be predetermined such as 1:1 or 2:1. The portfolios are periodically monitored and adjusted accordingly

18. Modern Portfolio Theory or Markowitz Theory The model was developed by Harry Markowitz in 1952 and he was later awarded a Nobel Prize for his work on modern portfolio theory It is a theoretical framework for analysis of risk and return and their inter relationship According to Markowitz identifying the portfolio which give the highest return for a particular level of risk. The model is also called mean-variance model because it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios.

19. Markowitz Theory…….. He studied the effect of asset risk, return, correlation and diversification on probable investment portfolio returns. Total risk of the portfolio can be reduced by diversification this can be achieved by investing in assets that have no correlation, or negative correlation. Which means that assets or securities whose return are not correlated and whose risk are mutually offsetting will reduce the overall risk. The covariance have negative interactive effect among the securities with in the portfolio and coefficient of correlation to have -1 so that the over all risk of the portfolio is nill or negligible.

20. Assumptions Investors are rational and behave in a manner as to maximise their utility with a given level of income or money. Investors have free access to fair and correct information on the returns and risk. The markets are efficient and absorb the information quickly and perfectly. Investors are risk averse and try to minimise the risk and maximise return. Investors base decisions on expected returns and variance or standard deviation of these returns from the mean. Investors choose higher returns to lower returns for a given level of risk.

21. Limitations of Markowitz Theory The portfolio returns are not normally distributed but are heavily skewed on the tails. The investors are irrational. They believe in risk taking, expecting that higher the risk, higher the returns. In reality, the investors in the market have limited access to borrowing or lending of money at risk free rate.

22. Markowitch - Efficient frontier An efficient frontier is a set of investment portfolios that are expected to provide the highest returns at a given level of risk. A portfolio is said to be efficient if there is no other portfolio that offers higher returns for a lower or equal amount of risk. Where portfolios are located on the efficient frontier depends on the investor’s degree of risk tolerance.

23. Efficient Frontier………… The efficient frontier is a curved line. This frontier is formed by plotting the expected return on the y-axis and the standard deviation as a measure of risk on the x-axis. It evinces the risk-and return trade-off of a portfolio.  For building the frontier, there are three important factors to be taken into consideration: Expected return Variance Standard deviation

24. Efficient Frontier……..

25. Efficient Frontier……….. All portfolios that lie below the Efficient Frontier are not good enough because the return would be lower for the given risk. Portfolios that lie to the right of the Efficient Frontier would not be good enough, as there is higher risk for a given rate of return. All portfolios lying on the boundary of efficient frontier are called Efficient Portfolios. The Efficient Frontier is the same for all investors, as all investors want maximum return with the lowest possible risk and they are risk averse.

26. The capital allocation line (CAL), also known as the capital market link (CML), is a line created on a graph of all possible combinations of risk-free and risky assets.

27. Single Index Model The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. William Sharpe simplify the mathematical calculations of Markowitch theory and develop a new model that is single index model. According to Sharp model the theory estimate , the expected return and variance indices which may be one or more are related to economic activity. Sharp assumed that the return of a security is linearly related to a single Index ( NIFTY, SENSEX) eg market index. The market index represent all securities traded in the market

28. Single Index Model…….. In simple terms The Sharpe ratio is an investment measurement that is used to calculate the average return beyond the risk free rate of return. Risk free return means returns from government securities. Assumptions of Single Index Model; The security return are related to each other The expected return and variance of the index are same The return on individual security is determined by unpredictable sources

29. Single Index Model…….. Stock prices are related to the market index and this relationship could be used to estimate the return on stock. Towards this purpose, them following equation can be used Ri - expected return on security i αi - intercept of the straight line or alpha co-efficient βi - slope of straight line or beta co-efficient Rm - the rate of return on market index ei - error term Ri = α i + β iRm + ei

30. Calculation of Alpha( α) R represents the portfolio return Rf represents the risk-free rate of return Beta represents the systematic risk of a portfolio Rm represents the market return, per a benchmark Alpha ( α )= R – Rf – beta ( Rm-Rf )

31. Multi Index Model Multi-index models attempt to identify and incorporate these nonmarket or extra-market factors that cause securities to move together also into the model. These extra-market factors are a set of economic factors that account for common movement in stock prices beyond that accounted for by the market index itself. Fundamental economic variables such as inflation, real economic growth, interest rates, exchange rates, etc. would have a significant impact in determining security returns and hence, their co-movement.

32. A multi-index model augments the single index model by incorporating these extra market factors as additional independent variables. The model says that the return of an individual security is a function of four factors – the general market factor Rm and three extra-market factors R1, R2, R3 . Multi-factor models also help explain the weight of the different factors used in the models, indicating which factor has more of an impact on the price of an asset.

33. Multi-Factor Model Formula Ri is the return of security Rm is the market return F (1, 2, 3 ... N) is each of the factors used _ is the beta with respect to each factor including the market (m) e is the error term a is the intercept Ri = ai + _i(m) * Rm + _i(1) * F1 + _i(2) * F2 +...+_i(N) * FN + ei

34. Portfolio Performance Evaluation Portfolio performance measures are a key factor in the investment decision . The portfolio performance evaluation can be made based on the following methods. Sharpe Ratio Treynor Ratio Jensen’s Alpha

35. Sharp Ratio The Sharpe Ratio is defined as the portfolio risk premium divided by the portfolio risk: Rp = Portfolio Return Rf = Risk free return SD = Standard deviation or Beta The Sharpe ratio, or reward-to-variability ratio, is the slope of the capital allocation line (CAL). The greater the slope (higher number) the better the asset.

36. Usually the Sharpe Ratio is stated in annual terms (to do so multiply it by the square root of the number of periods in a year). A higher Sharpe Ratio is better – reflecting higher returns and a lower standard deviation. Sharpe Ratio Grading Thresholds <1: Not Good 1 – 1.99: Ok 2 – 2.99: Really Good >3: Exceptional

37. Treynor Ratio The Treynor's measure related a portfolio's excess return to non-diversifiable or Systematic risk. The Treynor ratio is an extension of the Sharpe ratio that, instead of using total risk, uses beta or systematic risk in the denominator. As such, this is better suited to investors who hold diversified portfolios.

38. The Treynor based his formula on the concept of characteristic line. It is the risk measure of standard deviation, namely the total risk of the portfolio is replaced by beta. The equation can be presented as follow:

39. Treynor ratio does not work for negative beta assets. Also. Do not provide information on whether the portfolios are better than the market portfolio. Do not information about the degree of superiority of a higher ratio portfolio over a lower ratio portfolio. A higher Treynor Ratio is better. The Treynor Ratio does account for leverage.

40. Jensen’s Alpha Measure Jensen’s Alpha is based on systematic risk. The daily returns of the portfolio are regressed against the daily returns of the market in order to compute a measure of this systematic risk in the same manner as the CAPM. The difference between the actual return of the portfolio and the calculated or modeled risk-adjusted return is a measure of performance relative to the market. Jensen’s Alpha is the expected return on the portfolio adjusted for the return earned for taking market risk. In other words, it is the return on a portfolio is excess of what the CAPM expects it to be:

41. Return on Portfolio = Rf + ( Rm – Rf ) x ß Rf = Risk free return Rm = Market return ß = systematic risk It measures the portfolio manager's predictive ability to achieve higher return than expected for the accepted riskiness. The ability to earn returns through sucessful prediction of security prices on a standard measurement. The larger the alpha the better. The CAPM predicts a zero alpha.

42. Which Measure Should I Use? A well-diversified portfolios (with no firm-specific risk), the Sharpe Ratio is the preferred measure. If the portfolio contains leverage, or firm-specific risks that can be diversified away, then the Treynor Ratio and Jensen’s Alpha ratios are preferable. Aalpha -based measures are popular measures of hedge fund performance.

43. Portfolio Revision Portfolio revision involves changing the existing mix of securities. The objective of portfolio revision is maximizing the return for a given level of risk or minimizing the risk for a given level of return. The process of addition and withdrawal of assets from the existing portfolio or changing the ratio of funds invested is called as portfolio revision.

44. Portfolio Revision Strategies Active revision strategy Active revision strategy involves frequent and sometimes substantial adjustments to the portfolio. Investors who undertake active revision strategy believe that security markets are not continuously efficient. They believe that securities can be mispriced at times giving an opportunity for earning excess returns through trading in them. Example Buying railway related securities before railway budget and selling the security on the budget day or day after the budget

45. Passive revision strategy In passive portfolio revision, the primary aim is to keep earning market returns by executing a buy-and-hold strategy for the most part. The believers in passive portfolio revision subscribe to Efficient Market Hypothesis which holds that financial markets are efficient as all available information about a security is available throughout the market and is priced into the security. Portfolio changes in this strategy usually take place at a pre-determined duration and a smaller number of changes, the costs associated with this strategy are low.

46. There are rules associated with the portfolio revision strategy, specifically that which is passive in approach, which decides the changes that will need to be made to a portfolio. These rules are known as formula plans. Formula Plans Formula Plans are certain predefined rules and regulations deciding when and how much assets an individual can purchase or sell for portfolio revision. Securities can be purchased and sold only when there are changes or fluctuations in the financial market.

47. Why formula plan? Formula plans help an investor to make the best possible use of fluctuations in the financial market. Formula plans help an investor to make the best possible use of fluctuations in the financial market. There are three types of formula plans Dollar or Rupee cost average Plan Constant Ratio Plan Variable Ratio Plan

48. Dollar or Rupee C ost A veraging The plan stipulates that the investor invest a constant sum, in a specified share or portfolio of shares regularly at periodical intervals. This periodic investment is to be continued over a fairly long period to cover a complete cycle of share price movements. The investor will obtain his shares at a lower average cost per share than the average price prevailing in the market over the period. When a large portfolio has been built up over a complete cycle of share price movements, the investor may switch over to one of the other formula plans for its subsequent revision. The dollar cost averaging is specially suited to investors who have periodic sums to invest.

49. Constant Ratio Plan The investor would construct two portfolios, one aggressive and the other defensive with his investment funds. The ratio between the investments in aggressive portfolio and the defensive portfolio would be predetermined such as 1:1 or 1.5:1 etc. The purpose of this plan is to keep this ratio constant by readjusting the two portfolios when share prices fluctuate from time to time. For this purpose, a revision point will also have to be predetermined. Suppose the revision points may be fixed as +/- 0.10. This means that when the ratio between the values of the aggressive portfolio and the defensive portfolio moves up by 0.10 points or moves down by 0.10 points, the portfolios would be adjusted by transfer of funds from one to the other.

50. Variable Ratio Plan The variable ratio plan allows the ratio between the aggressive and defensive portions of a portfolio to change either based on market movement or on some pre-set factors. For instance, a variable ratio plan can allow for a higher ratio of the aggressive portion vis-à-vis the conservative portion when equities are doing well in order to benefit from the bull-run. The plan can also allow for a higher ratio in favor of the defensive portion as an investor grows old and his life cycle demands a more conservative approach to investments

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