53
KARISHMA SIROHI 2
KARISHMA SIROHI
KARISHMA SIROHI 3
UNIT 1
PORTFOLIO:
Portfolio is the combination of securities such as stocks, bonds and money market instruments. Investment portfolio is the set of investment vehicles, formed by the investor seeking to realize its’ defined investment objectives. In other words, Portfolio - an appropriate mix of or collection of investments held by an institution or a private individual. The process of blending together the broad asset classes so as to obtain optimum return with minimum risk is called portfolio construction. Diversification of investments helps to spread risk over many assets.
Portfolio management:
Portfolio Management - the art and science of making decisions about investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions, and balancing risk vs. performance. Portfolio Management Involves,-Investing and divesting different, -investment Risk management,- Monitoring and analyzing returns
Portfolio management is a process encompassing many activities aimed at optimizing the investment of one’s funds.
Objective of make portfolio:
The portfolio construction and management can satisfy the following objectives:
WHY PORTFOLIO:
1) Performance measurement2) Improvement – learning loop3) Discipline4) Risk control5) Consistency6) Continuity7) Selling tool,
The objectives of portfolio management is to maximize the return and minimize the risk. These objectives are categorized into:
Basic Objectives§ Maximize yield,§ Minimize risk.
Subsidiary Objectives§ Reasonable income on investment§ Appreciation of capital§ Safety of the investment and liquidity§ Termination and marketable facility
KARISHMA SIROHI
security analysis
portfolio analysis
portfolio selection
portfolio revision
portfolio evaluation
KARISHMA SIROHI 4
Scope of portfolio management:portfolio management is a continues process. It is a dynamic activity. The following are the basic operation of a portfolio management:
1. Monitoring the performance of portfolio by incorporating the latest market conditions.2. Identification of the investor’s objectives, constraints and preferences.3. Making an evaluation of portfolio income (comparison with targets and achievement).4. Making revision in the portfolio.5. Implementation of the strategies in tune with investment objectives.
Nature of Portfolio Management:
1. Portfolio should be constructed according to the investor’s objectives.2. Constructed portfolio shall be reviewed from time to time in view of latest market
developments.3. The portfolio evaluation should be done according to risk and return.4. Portfolio management is a dynamic concept. 5. It involves a regular, scientific analysis, right judgment and timely action.
Importance/ Benefits of Portfolio:
It helps to spread risk over many assets. It gives the assurance of obtaining the anticipated return on the portfolio. It helps in improving the return through time to time control and portfolio revision. It helps in risk control.
Phases of Portfolio Management:
Portfolio management is a process encompassing many activities aimed at optimizing the investment of one’s funds. Five phases can be identified as this process:-1. Security analysis2. Portfolio Analysis3. Portfolio Selection
KARISHMA SIROHI
KARISHMA SIROHI 5
4. Portfolio revision5. Portfolio Evaluation
Portfolio construction process:
The diagram shows the process of portfolio construction:
KARISHMA SIROHI
Portfolio Construction
Diversification
Selection and Allocation
Portfolio Evaluation
Appraisal
Revision
KARISHMA SIROHI 6
Approaches in portfolio construction:
Commonly, there are two approaches in the construction of the portfolio of securities viz, traditional approach and Markowitz efficient frontier approach.
In the tradition 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. In the modern approach, portfolios are constructed to maximize the expected return for a given level of risk. It views portfolio construction in terms of the expected return and the risk associated with obtaining the expected return.
Tradition Approach:
The traditional approach basically deals with two major decisions. They are:
1) Determining the objectives of the portfolio2) Selection of securities to be included in the portfolio.
Normally, this is carried out in four to six steps:
1. Analysis of Constraints:The constraints normally discussed are: income needs, liquidity, time horizon, safety, tax consideration and the temperament.
a) Income Needs: the income needs depend on the need for income in constant rupees and current rupees. The need for income in current rupees arises from the investor’s need to meet all or part of the living expenses. At the same time inflation may erode the purchasing power, the investor may like to offset the effect of the inflation and so, needs income in constant rupees.
Need for current income: the investor should establish the income which the portfolio should generate. The current income need depends upon the entire current financial plan of the investor. The expenditure required to maintain a certain level of standard of living and all the other income generating sources should be determined. Once this info. Is arrived at, it is possible to decide how much income must be provided for the portfolio of securities.
KARISHMA SIROHI
Analysis of constraints
Determination of objectives
Selection of portfolioBond and common stock
Bond
common stock
Assessment of risk and return
Evaluation/ Diversification
KARISHMA SIROHI 7
Need for constant income: funds should be invested in such securities where income from them might increase at a rate that would offset the effect of inflation. The inflation or purchasing power risk must be recognized but this does not pose a serious constraint on portfolio if growth stocks are selected.
b) Liquidity: if the investor prefer to high liquidity, then funds should be invested in high quality short term debt maturity issues such as money market funds, commercial papers and shares that are widely traded. Keeping the funds in shares that are poorly traded or stocks in closely held business and real estate lack liquidity. The investor should plan his cash drain and the need for net cash inflows during the investment period.
c) Safety of the principal: investing in bonds and debentures is safer than investing in the stocks. Even among the stocks, the money should be invested in regularly traded companies of longstanding. Investing money in the unregistered finance companies may not provide adequate safety.
d) Time horizon: is the investment planning period of the individuals. This varies from individual to individual. The first stage is the early career stage; at this stage his assets are lesser than their liabilities. His priority towards investments may be in the form of savings for liquidity purposes. The investor is young at this stage and has long horizon of life expectancy with possibilities of growth in income, he can invest in high-risk and growth oriented investments.The other stage of the time horizon is the mid career individual. At this stage, his assets are larger than his liabilities. He may wish to reduce the overall risk exposure of the portfolio but, he may continue to invest in high risk and high return securities. The final stage is the late career or the retirement stage. In this stage, he shifts his investment to low return and low risk category investment.
e) Tax consideration: investors in the income tax paying group consider the tax concessions they could get from their investment.
f) Temperament: Some investors are risk lovers or takers who would like to take up higher risk even for low return. While some investors are risk averse, who may not be willing to undertake higher level of risk even for higher level of return. The risk neutral investors match the return and the risk. Hence, the temperament of the investor plays an important role in setting the objectives.
2. Determination of objectives: portfolios have the common objectives: Current income Growth in income Capital appreciation Preservation of capital
3. Selection of portfolio: the selection of portfolio depends on the various obejectives of the investors.
Objectives and asset mix: if the main objective if getting adequate amount of current income, sixty per cent of the investment is made on debts and forty per
KARISHMA SIROHI
Selection of industri es
Selection of companies in the industry
Determining the size of participation.
KARISHMA SIROHI 8
cent on equities. The proportions of investment on debts and equity differ according to the individual’s preferences.
Growth of income and asset mix: the investor’s portfolio may consist of 60 to 100 % equities and 0 to 40 % debt instrument.
Capital appreciation and asset mix: for this the investor’s portfolio may consist of 90 to 100 % equities and 0-10% of debts.
Safety of principal and asset mix: the investor’s portfolio may consist more of debt instruments and within the debt portfolio more would be on short term debts.
4. Risk and return analysis: the traditional approach to portfolio building has some basic assumptions. First, the individual prefers larger to smaller returns from securities. To achieve this goal, the investor has to take more risk. The ability to achieve higher returns is dependent upon his ability to judge risk and his ability to take specific risks. The investors make a series of compromises on risk and non-risk factors like taxation and marketability after he has assessed the major risk categories, which he is trying or minimize.
5. Diversification: according to the investor’s need for income and risk tolerance level portfolio is diversified. In the stock portfolio, he has to adopt the following steps which are shown in the following figure:
KARISHMA SIROHI
KARISHMA SIROHI 9
Assumptions:
The traditional theory is based on the following assumptions:
1. It assumes that the market is inefficient.2. It also thinks that the fundamentalists can take advantage of market inefficiency
situation.3. It felt that the fundamentalists can earn quick profits.4. It considers that the fundamentalists will expect the potential growth of a particular
company for predicting the future trend of the share prices.
Modern approach:
KARISHMA SIROHI
Select group of shares
Calculates risk and return
Asset allocation
KARISHMA SIROHI 10
In the modern approach Markowitz model is used. Markowitz gives more attention to the process of selecting the portfolio. His planning can be applied more in the selection of common stocks portfolio than the bond portfolio. The stocks are not selected on the basis of need for income or appreciation but the selection is based on the risk and return analysis. This approach follows the following steps:
From the list of stocks quoted at the Bombay Stock Exchange or at any other regional stock exchange, the investor selects roughly some group of shares. For these stocks expected return and risk would be calculated. The investor is assumed to have the objectives of maximizing the expected return and minimizing the risk. Further, it is assumed that investors would take up risk in a situation when adequately rewarded for it. This implies that individuals would prefer the portfolio of highest expected return for a given level of risk. The final step is asset allocation process that is to choose the portfolio that meets the requirements of the investor. The risk taker would choose high risk portfolio. Investor with lower tolerance for risk would choose low level risk portfolio. The risk neutral investor would choose the medium level risk portfolio.
Assumptions:
Modern portfolio theory is based on the following assumptions:
1. It is based on assumption of free and perfect flow of information.2. It believes that markets are perfect and absorbs all information quickly.3. The riskiness of a financial asset in portfolio is to be seen in the context of market
related risk or portfolio risk, but not in isolation.
It also indicates that the returns are the same whenever you enter the market. This theory uses of Beta for measuring the market risk.
The difference between Traditional Portfolio Theory and Modern Portfolio Theory.
Traditional Portfolio Theory Modern Portfolio Theory§ It deals with the evaluation of return
and risk conditions in each security.
§ It is based on measurement of standard deviation of particular scrip.
§ It assumes that market is inefficient.
§ It deals with the maximization of returns through a combination of different types of financial assets.
§ It is based on mainly diversification process.
§ It assumes that market is perfect and
KARISHMA SIROHI
KARISHMA SIROHI 11
§ It gives more importance to standard deviation.
all information is known to public.§ It gives more importance to Beta.
The following are some of the important Modern Portfolio theories:
1. Markowitz Theory of Portfolio Management.2. Sharpe’s Theory of Portfolio Management.3. Capital Asset Pricing Model.
Managing the Portfolio:
There are two approaches to manage the portfolio:
1. Passive Approach: in the passive approach the investor would maintain the percentage allocation for asset classes and keep the security holdings within its place over the establishes holding period.
2. Active Approach: in this the investors continuously assess the risk and return of the securities within the asset classes and changes them accordingly.
UNIT 2
MARKOWITZ PORTFOLIO THEORY
Harry Markowitz opened new vistas to modern portfolio selection by publishing an article in the Journal of Finance in March 1952. His publication indicated the importance of correlation among the different stocks’ return in the construction of a stock portfolio.
Simple Diversification
KARISHMA SIROHI
KARISHMA SIROHI 12
Portfolio means the group of assets investor owns. The assets may vary from stocks to different types of bonds. When different assets are added to the portfolio, the total risk tends to decrease. In the case of common stocks, diversification reduces the unsystematic risk or unique risk.
The naïve kind of diversification is known as simple diversification. In the case of simple diversification, securities are selected at random and no analytical procedure is used. Total risk of the portfolio consists of systematic and unsystematic risk and this total risk is measured by the variance of the rates of return over time. The simple random diversification reduces the total risk. The reason behind this is that the unsystematic price fluctuations are not correlated with the market’s systematic fluctuation.
The standard deviation was calculated for each portfolio and plotted. As the portfolio size increases, the total risk line starts declining. It flatters 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.
The Markowitz Model
Concept
Markowitz Model is also known as Risk Variance Theory. Most people agree that holding two stocks is less risky than holding one stock. In developing his model, Markowitz had given up the single stock portfolio and introduced diversification. The single security portfolio would be preferable if the investor is perfectly certain that his expectation of highest return would turn out to the real. In the world of uncertainty, most of the risk averse investors would like to join Markowitz rather than keeping a single stock, because diversification reduces the risk.
Assumption:
The assumption: Markowitz theory is based on the following assumption:
§ Investor behave rationally
§ Investors know all the information about the market situation.
KARISHMA SIROHI
Diversification and portfolio risk
Unique risk
Market risk
Total risk
Number of stocks
Risk
KARISHMA SIROHI 13
§ Investors choose higher returns to lower level of risk.
§ The markets are higher return to lower level of risk.
§ The markets are efficient and they absorb information quickly and perfectly.
§ Investors are risk averse.
§ Investors can reduce their risk by adding new investments in the portfolio.
§ Investors will get a higher rate of return if they adopt the efficient portfolio model.
§ By combining all the financial assets, the return on various securities as to be correlated to each other.
§ Investor decisions are based on expected return and their variance.
Explanation
Holding two securities is probably less risky than holding either security alone. It is possible to reduce the risk of a portfolio by incorporating into it a security whose risk is greater than that of any of the investments held initially. But it will depend upon the quantum of ratio of two securities.
1. Measurement of expected return on portfolio:Markowitz developed algorithms to minimize portfolio risk. The level of risk exposure is measured with the help of the standard deviation of the returns. The expected return is the weighted sum of the expected return of the portfolio, the weights being the probabilities of their occurrence.
RP= ∑t=1 N Xi Ri
Rp= return from portfolio
N= number of securities
T= time
X= security
R= return
2. Co-variance of two securities:The interactive risk of two securities is called as “co-variance”. If the rates of return of two securities move together, then their interactive risk is called as co-variance is positive. If the rates of returns are independent co-variance is zero. Inverse movements results in negative co-variance.
The portfolio risk can be calculated with the help of the following formula:
σ p=√X12 σ1
2+ X 22σ2
2 +2X1 X2( r12σ1σ2)
KARISHMA SIROHI
R= +1 R= -1
RpRp
σpσp
Rp
KARISHMA SIROHI 14
The correction co-efficient indicates the similarity or dissimilarity in the behavior of X1 and X2 stocks. In correlation, co-variance in not taken as an absolute value but the relative to the standard deviation of individual securities.
Co-variance Model:
All the graphs show the portfolio risks under varying levels of correlation co-efficient.
KARISHMA SIROHI
Rp
r=-1r=+1
r=0
r=-0.5
B
AD
σp
KARISHMA SIROHI 15
In this figure, portfolio return is given on the vertical axis and on the horizontal axis. Point A represents 100 % holding of X and Point B represents 100 % holding of Y. The intermediate points along the line segment AB represents 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. Again, the ratio of smaller standard deviation to larger deviation is less than the correlation coefficient. The r=0 is hyperbola. CB contain 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 other. The line segment ADB indicates (r=-1) represents inverse correlation and it is possible to reduce portfolio risk to zero.
Thus, Markowitz diversification can lower the risk if the securities in the portfolio have lox correlation coefficients.
Markowitz efficient Frontier
The risk and return of all portfolios plotted in risk-return space would be dominated by efficient portfolios. It also reveals the least portfolio risk at a particular level of return and his analysis is depicted in the form of diagram of securities as presented below:
KARISHMA SIROHI
Rp
σp
A
B
C
D
E
F
Efficient Frontier
E
Attainable Portfolio
E
S1 S2 S3 S4
utility
return
marginal utility and return
utility
return
Indifference curves of the risk Fearing
I1
I2
I3I4
AB
C
utility
Indifference curves of the risk loving
KARISHMA SIROHI 16
The shaded portion of area indicates attainable set of portfolio combination it can be constructed from a given number of securities. According to the diagram the securities BCD stands on the efficient line AD are treated as the portfolios on the efficient frontier ABCD is a boundary of the attainable set. The efficient frontier appears as a budge or Arc. Only those assets which perfectly positively correlated will generate an efficient frontier. The diagram further reveals that the portfolio B dominates portfolio F and C dominates E because the return is the same but the risk greater at F and E.
Investor’s Utility Analysis:
Utility is the satisfaction the investor enjoys from the portfolio return. The investor gets mire satisfaction or more utility in X+1 rupees than from X rupees. The utility function makes certain assumption about an investors’ taste for risk. The investors are categorized into three category:
KARISHMA SIROHI
utility
return
I1
I2I3
I4
RS
I4
KARISHMA SIROHI 17
The curve ABC are three different slopes of utility curves. The upward sloping curve A shows increasing marginal utility. The straight line B shows constant utility, and curve C shows diminishing marginal utility. The constant utility, a linear function means doubling of returns would double the utility and it indicates risk neutral situation. The increasing marginal utility suggests that the utility increases more than proportion to increase in return and shows the risk. The curve C shows risk averse investor. Investors generally, like to get more returns for additional risks assumed and lines would be positively sloped. The risk lover’s utility curves are negatively sloped and coverage towards the origin. For the risk fearing, lower the risk of the portfolio, happier he would be. The degree of the slopes of indifference curve indicates the degree of risk aversion. The conservative investor needs larger return to undertake small increase in risk. The aggressive investor would be willing to undertake greater risk for smaller return.
Indifference map and the efficient frontier
Each investor has a series of indifferent curves. 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
KARISHMA SIROHI
KARISHMA SIROHI 18
risk. I2 touches the efficient frontier at point R. even though the points T and S are in the I2 curve, R is the only attainable portfolio which maximizes the utility of the investor. Thus, the point at which the efficient frontier tangentially touches the highest indifference curve determines the most attractive portfolio for the investor.
Assumptions:
1. Risk: variability in return is risk. In this theory main focus is on correlation coefficient. Under this model invest decision is based on expected return and variance of return.
2. For a given level of risk investor prefer higher return to lower return or for a given level of return investor prefer lower risk than the highest risk.
SHARPE SINGLE INDEX MODEL
The Markowitz model is adequate and conceptually sound in analyzing the risk and return of the portfolio. The problem with Markowitz model is that a number of co-variances have to be estimated. If a financial institution buys 150 stocks, it has to estimate 11,175 (N2-N)/2 correlation co-efficient. Sharpe had developed a simplified model to analyze the portfolio.
Concept:
This model was developed by William Sharpe. He simplified the method of diversification of portfolios. Sharpe published a model simplifying the mathematical calculations done by the Markowitz model. According to Sharpe’s model, the theory estimate, the expected return and variance of indices which may be one or more and are related to economic activity. This theory has come to be known as market model. He assumed that the return of a security is linearly related to a single index like the market index. The market index should consist of all the securities trading on the exchange. In the absence of it, a popular index can be treated as a surrogate for the market index.
Assumptions:
Sharpe’s portfolio theory is based on the following assumptions:
1. The securities returns are related to each other.2. The expected return and variance of indices are the same.3. The return on individual securities is determined by unpredictable factors.
Single index model:
Casual observation of the stock prices over a period of time reveals that most of the stock prices move with the market index. When the Sensex increases, stock prices also tend to increase and vice-versa. This indicates that some underlying factors affect the market index as well as the stock prices. Stock prices are related to the market index and this relationship could be used to estimate the return on stock. For this following equation can be used:
KARISHMA SIROHI
KARISHMA SIROHI 19
Ri= αi+βiRm+ei
Where 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
Beta is a measure of volatility faced by a financial asset between actual earned or a project returns.
Alpha is the measurement of difference between actual earned return and expected return at a level of systematic risk.
The single index model is based on the assumption that stocks vary together because of the common movement in the stock market and there are no effect beyond the market. The variance of the security has two components systematic risk and unsystematic risk.
Total risk= systematic risk + unsystematic risk
Total risk= βi2σ 2
m+e2i
Systematic risk= β2i * variance of market index
Unsystematic risk = total variance – systematic risk.
e2i = σ i
2−β i2σ m
2
Corner portfolio:
In a two stocks portfolio, the minimum attainable risk (variance) and the lowest return would be the corner portfolio. As the number of stocks increases in a portfolio, the corner portfolio would be the one with lowest return and risk combination.
KARISHMA SIROHI
Rp
RB
0S
----15
---10
---5
Corner portfolio
KARISHMA SIROHI 20
In the above diagram, AB shows the risk-return combination of several portfolios. Each number indicates the number of stocks in the portfolio. When the number of stock increases, the risk and return decline. Tracing the AB line shows the corner portfolio. An efficient frontier may have one or two security portfolio at the low or high extremes, if the percentages of allocations to stocks are free to take any value.
Sharpe’s Optimal Portfolio:
Sharpe had provided a model for the selection of appropriate securities in a portfolio. The selection of any stock is directly related to its excess return- beta ratio.
Ri-Rf / βi
Where, Ri= the expected return on stock i
Rf= the return on a riskless asset
βi= the expected change in the rate of return on stock i associated with one unit change in the market return
the excess return is the difference between the expected return on the stock and the riskless rate of interest such as the rate offered on the govt security or treasury bill. The steps for finding out the stocks to be included in the optimal portfolio are given below:
1. Find out excess return to beta ratio for each stock under consideration.2. Rank them from the highest to the lowest.3. Proceed to calculate Ci for all the stocks according to the ranked order using the
following formula:
KARISHMA SIROHI
KARISHMA SIROHI 21
Ci=σm2 ∑
i=1
N
( R i−Rf ) β i /σ ei2
1+σ m2 ∑
i=1
N
β i2/σ ei
2
4. The cumulated values Ci starts declining after a particular Ci and that point is taken as the cut off and that stock ratio is the cut off ratio C.
Construction of the optimal portfolio:
After determining the securities to be selected, the portfolio manager should find out how much should be invested in each security. The percentage of funds to be invested in each security can be estimated as follows:
Xi= Z i
∑i=1
N
Z i
Zi= βi
σei2 ¿
Thus, the proportion to be invested in different securities are obtained.
Optimum portfolio with short sales: the procedure used to calculate the optimal portfolio when short sales are allowed is, more or less similar to the procedure adopted for no short sales, except the cut off point concept. At first, the stocks have to be ranked by excess return to beta. Here, all the stocks are added to the portfolio. They are either held long or short. All the stocks affect the curt off point. The Z value has to be calculated for each stock. If the Z value is positive, the stock will be held long and if negative, will be sold short. Stocks which are having excess return to beta above C* are sold short.
KARISHMA SIROHI
KARISHMA SIROHI 22
UNIT 3
CAPM
Capital asset pricing model:
In the portfolio diversification risk can be eliminated by diversification. The remaining risk portion is the undiversifiable risk i.e. market risk. Investors are knowing the systematic risk when they search for efficient portfolios. They would like to have assets with low beta co-efficient i.e. systematic risk. Investors would opt for high beta co-efficient only if they provide high rate of return.
CAPM theory helps the investors to understand the risk and return relationship of the securities. It also explains how assets should be priced in the capital market.
The CAPM Theory:
Markowitz, William Sharpe, John Lintner and John Mossin provided the basic structure for the CAPM Model. This theory is concerned with the analysis of risk and return and the process by which an efficient portfolio can be achieved. The CAPM was developed by Sharpe and Lintener in 190. It is based on economic model. It reveals the relationship between the expected return, unavoidable risk and the valuation of securities.
In this model the company’s risk is eliminated and only the market risk remains. This model reveals that the company risk and the market risk are related by a variable called “Beta”.
Assumptions of CAPM:
The capital asset pricing model is based on certain explicit assumptions regarding the behavior of investors. The assumptions are listed below:
1. Investor make their investment decisions on the basis of risk-return assessments measured in terms of expected returns and standard deviation of return.
2. The purchase or sale of a security can be undertaken in infinitely divisible unit.3. Purchase and sale by a single investor cannot affect prices. This means that there is
perfect competition where investors in total determine prices by their action.4. There are no transaction costs. Given the fact that transaction costs are small, they are
probably of minor importance in investment decision-making, and hence they are ignored.
5. There are no personal income taxes. Alternatively, the tax rate on dividend income and capital gains are the same, thereby making the investor indifferent to the form in which the return on the investment is received (dividends or capital gains).
6. The investor can lend or borrow any amount of fund desired at a rate of interest equal to the rate of risk less securities.
7. The investor can sell short any amount of any shares.
KARISHMA SIROHI
KARISHMA SIROHI 23
8. Investors share homogeneity of expectations. This implies that investors have identical expectations with regard to the decision period and decision inputs. Investors are presumed to have identical expectations regarding expected returns, variance of expected returns and covariance of all pairs of securities.
Lending and Borrowing:
Here, it is assumed that the investor could borrow or lend any amount of money at riskless rate of interest. Investors can mix risk free assets with the risky assets in a portfolio to obtain a desired rate of risk return combination. The expected return on the combination of risky is
Rp=R f X f +Rm(1−X f )
R p= portfolio return
X p= the proportion of funds invested in risk free assets
1-Xp= the proportion of funds invested in risky assets.
R f =risk free rate of return
R m= return on risky assets.
This formula can be used to calculate the expected returns for different situations, like mixing riskless assets with risky assets, investing only in the risky assets and maximising the borrowings with risky assets.
Variance of the portfolio can be calculated by using the equation.
σ p2=σ1
2 x f2+σm
2 ¿
Concept:
According to CAPM, all investor hold only the market portfolio and riskless securities. The market portfolio is a portfolio comprised of all stocks in the market. Each asset is held in proportion to its market value to the total value of all risky assets.
KARISHMA SIROHI
R p
σ p0
C
B
A
Efficient Frontier
KARISHMA SIROHI 24
The investor prefers any point B and C because, with the same level of risk they face on line BA, they are able to get superior profits. The ABC line shows the investor’s , portfolio of risky assets. The investors can combine riskless assets either by lending and borrowing.
The line R f S represents all possible combinations of riskless and risky assets. The ‘S’ portfolio does not represent any riskless asset but the line RSf gives the combination of both. The portfolio along the path RfS is called lending portfolio that is some money is invested in the riskless asset or may be deposited in the bank for a fixed rate of interest. If it crosses the point S, it becomes borrowing portfolio. Money is borrowed and invested in the risky asset. The straight line is called capital market line (CML). It gives the desirable set of investment opportunities between risk free and risky investments.
E(Rp) = Rf+ (Rm-Rf/σ m) σ p
E (Rp) = portfolio’s expectations of return
Rm= expected return on market portfolio
σ p= standard deviation of the portfolio
σ m= standard deviation of market portfolio
Security market line:
The risk return relationship of an efficient portfolio is measured by the capital market line. But, it does not show the risk return trade off for other portfolios and individual securities.
Inefficient portfolio lies below the CML and the risk return relationship cannot be established with the help of CML. Unsystematic risk can be diversified then the remaining risk i.e. systematic risk, could be measured by beta. The beta analysis is useful for individual securities and portfolios whether efficient or inefficient.
When betas are given, investor can generate expected return for the given securities.
KARISHMA SIROHI
R p
0 σ p
R f
SLending
portfolio
Borrowing
portfolioThe capital market line
KARISHMA SIROHI 25
If we assume the expected market risk premium to be 8% and the risk of return to be 7%, we can calculate expected return for A,B,C, and D securities.
E(Ri)= Rf+βi (E(Rm)-Rf)
If beta is =1
=7+1(8)
=15%
Security A
Beta= 1.10
E(R)=7+1.10(8)
=15.8
Security B, Beta= 1.20, E(R)= 7+1.20(8)
=16.8=16.6
Security C, Beta= 0.7, E(R)= 7+0.7(8)
=12.6
The securities A and B are aggressive securities, because their beta values are greater than one.
β>1= security is aggressive means highly volatile
β=1= constant
β<1= less volatile
KARISHMA SIROHI
KARISHMA SIROHI 26
UNIT 4
APT :
Arbitrage pricing theory is one of the tools used by the investor and portfolio managers. The CAPM explains the return of the securities on the basis of their respective betas.
The APT is developed by Stephen Ross. The APT model explains the nature of equilibrium in the asset pricing in a less complicated manner with fewer assumptions compared to CAPM.
Arbitrage: arbitrage is a process of earning profit by taking advantage of differential pricing for the same asset. The process generates riskless profit. In security market, it is of selling security at a high price and the simultaneous purchase of the same security at a relatively lower price. Since the profit earned through arbitrage is riskless, the investors have the incentive to undertake this whenever an opportunity arises.
However, the buying and selling activities of the arbitrageur reduces and eliminates the profit margins, bringing the market price to the equilibrium level.
Assumptions:
§ The investors have homogenous expectations.
§ The investor’s utility is risk averse and utility maximizes.
§ Perfect competition prevails in the market and there is no transaction cost.
The APT theory does not assume (1) single period investment horizon, (2) no taxes, (3) investors can borrow and lend at risk free rate of interest and (4) the selection of the portfolio is based on the mean and variance analysis. This assumption is present in the CAPM model.
Arbitrage portfolio: according to APT theory an investor tries to find out the possibility to increase returns from his portfolio without increasing the funds in the portfolio. He also likes to keep the risk at the same level.
For example, the investor holds A,B, and C securities and he wants to change the proportion of the securities without any additional financial commitment. Now the change in proportion of securities can be denoted by XA,XB, XC. the increase in the investment in security A could be carried out only if he reduces the proportion of investment either in B or C because it has already states that the investor tries to earn more income without increasing his financial commitment. Thus, the changes in different securities will add up to zero. This is the basic requirement if an arbitrage portfolio. If X indicates change in proportion.
∆ X A+∆ XB+∆ XC=0
the factor sensitivity indicates the responsive of security’s return to a particular factor. The sensitiveness of the securities to any factor is the weighted average of the sensitivities of the securities, weights being the changes made in the proportion. For example, bA, bB, and bC are
the sensitivities, in an arbitrage portfolio the sensitivities become zero.
KARISHMA SIROHI
KARISHMA SIROHI 27
bA∆ X A+b B ∆ X B+bC ∆ XC=0
The variance of the new portfolio’s change is only due to the changes in its non factor risk. Hence, the change in the risk factor is negligible. From the analysis it can be concluded that-
§ The return in the arbitrage portfolio is higher than the old portfolio.
§ The arbitrage and old portfolio sensitivity remains the same.
§ The non factor risk is small enough to be ignored in an arbitrage portfolio.
Effect on price
The APT Model: according to Stephen Ross, returns of the securities are influenced by a number of macroeconomic factors. The macro economic factors are growth rate of industrial production, rate of inflation, spread between long term and short term and short term interest rates and spread between low grade and high grade bonds. The arbitrage theory is represented by the equation-
Ri=¿ ⋋1 bi1+⋋2 bi2…………+⋋ j bi j
Ri= average expected return
⋋=¿ sensitivity of return of bi1
bi1= the beta co-efficient relevant to the particular factor
Arbitrage Pricing Equation: in a single factor model, the linear relationship between the return and sensitivity bi can be given in the following form-
Ri=¿ ⋋0+⋋i bi
Ri= return form stock A
⋋0=¿riskless rate of return
b i=the sensitivity related to the factor
⋋1=¿slope of the arbitrage pricing line
The above model is known as single factor model since only one factor is considered. Here, the industrial production alone is considered.
The APT one factor model is based on only single factor
Factor affecting the return:
Salmon brothers identified give factor in their fundamental factor model. Inflation is the only common factor identified by others.
The other factor are given below-
KARISHMA SIROHI
KARISHMA SIROHI 28
§ Growth rate in gross national product.
§ Rate of interest
§ Rate of change in oil prices
§ Rate of change in defense spending
PORTFOLIO REVISION:
A portfolio is a mix of securities selected from a vast universe of securities. Two variables determine the composition of a portfolio; the first is the securities included in the portfolio and the second is the proportion of total funds invested in each security.
Portfolio revision involves changing the existing mix of securities. This may be effected either by changing the securities currently included in the portfolio or by altering the proportion of funds invested in the securities. New securities may be added to the portfolio or some of the existing securities may be removed from the portfolio. Portfolio revision thus leads to purchase and sales of securities. The objective of portfolio revision is the same as the objective of portfolio selection i.e. maximizing the return for a given level of risk or minimizing the risk for a given level of return.
Need for portfolio revision:
The primary factor necessitating portfolio revision is changes in the financial markets since the creation of the portfolio. The need for portfolio revision may arise because of some investor related factor also. These factors may be listed as-
§ Availability of additional funds for investment
§ Change in risk tolerance
§ Change in the investment goal
§ Need to liquidate a part of the portfolio to provide funds for some alternative use,
The portfolio needs to be revised to accommodate the changes in the investor’s position.
Constraints in portfolio revision:
Portfolio revision is the process of adjusting the existing portfolio in accordance with the changes in financial market and the investor’s position so as to ensure maximum return from the portfolio with the minimum of risk.
§ Transaction cost: buying and selling of securities involve transaction costs such as commission and brokerage. Frequent buying and selling of securities for portfolio revision may push up transaction costs thereby reducing the gains from portfolio revision. Hence, the transaction costs involved in portfolio revision may act as a constraint to timely revision of portfolio.
§ Taxes: tax is payable on the capital gains arising from sale of securities. Usually, long term capital gains are taxed at a lower rate than short term capital gains. To qualify as long term capital gains, a security must be held by an investor for a period
KARISHMA SIROHI
KARISHMA SIROHI 29
of not less than 12 months before sale. Frequent sales of securities in the course of periodic portfolio revision or adjustment will result in short term capital gain which taxed at a higher rate compared to long term capital gains.
§ Statutory stipulations: the largest portfolios in every country are managed by investment companies and mutual funds. These institutional investors are normally governed by certain statutory stipulations regarding their investment activity. These stipulations often act as constraints in timely portfolio revision.
§ Intrinsic difficulty: portfolio revision is a difficult and time consuming exercise. The methodology to be followed for portfolio revision is also not clearly established. Different approaches may be adopted for the purpose. The difficulty of carrying out portfolio revision itself may act as a constraint to portfolio revision.
Portfolio revision strategies:
1. 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. Moreover, they believe that different investors have divergent or heterogeneous expectations regarding the risk and return of securities in the market.
2. Passive revision strategy: involves only minor and infrequent adjustment to the portfolio over time. Under passive revision strategy, adjustment to the portfolio is carried out according to certain predetermined rules and procedures designated 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.
In the market, the prices of securities fluctuate. Ideally, investors should buy when prices are low and sell when prices are high. If portfolio revision is done according to this principle, investors would be able to benefit from the price fluctuations in the securities market.
In other words, the formula plan provides the basic rules and regulations for the purchase and sale of securities. The amount to be spent on the different types of securities is fixed. The amount may be fixed either in constant and variable ratio.
Formula plan, represents an attempt to explicit the price fluctuations in the market and make them a source of profit to the investor.
Formula plan consists of predetermined rules regarding when to buy and sell and how much to buy or sell.
KARISHMA SIROHI
KARISHMA SIROHI 30
Why formula plan???
§ Formula plan help an investor to make the best possible use of fluctuations in the financial market. One can purchase shares when the prices are less and sell off when market prices are higher.
§ With the help of formula plan an investor can divide his funds into defense portfolio and aggressive and easily transfer from one portfolio to other.
Aggressive portfolio: it consists of funds that appreciate quickly and guarantee maximum returns to the investor.
Defensive portfolio: it consists of securities that do not fluctuate much and remain constant over a period of time.
Assumptions of formula plan:
1. The first assumption is that certain percentage of the investor’s fund is allocated to fixed income securities and common stocks.
2. The second assumption is that if the market moves higher, the proportion of stocks in the portfolio may either decline or remain constant.
3. The third assumption is that the stocks are bought and sold whenever there is a significant change in the price.
4. The fourth assumption requires that the investor should strictly follow the formula plan once he chooses it.
5. The investor should select good stocks that move along with the market. They should reflect the risk and returns features of the market.
Advantages of formula plan:
1. Basic rules and regulations for the purchase and sale of securities are provided.2. The rules and regulations are rigid and help to overcome human emotion.3. The investor can earn higher profits by adopting the plan.4. A course of action is formulated according to the investor’s objective.5. It controls the buying and selling of securities by the investor.6. It is useful for taking decision on the timing of investments.
Disadvantages:
1. The formula plan does not help the selection of the security.2. It is strict and not flexible with the inherent problem of adjustment.3. The formula plan should be applied for long periods, otherwise the transaction cost
may be high.4. Even if the investors adopts the formula plan, he needs forecasting. Market
forecasting helps him to identify the best stocks.
KARISHMA SIROHI
Formula Plan
Rupee Cost Averaging
Constant Rupee Value
Constant Ration Plan
Variable Ratio Plans
KARISHMA SIROHI 31
Types of formula plan:
1. Rupee cost averaging:The simplest and most effective formula plan is rupee cost averaging. First, stocks with good fundamentals and long term growth prospects should be selected. Such stocks’ prices tend to be volatile in the market and provide maximum benefit from rupee cost averaging. Secondly, the investor should make a regular commitment of buying shares at regular intervals. Once he makes a commitment, he should purchase the shares regardless of the stock’s price, the company’s short term performance and the economic factors affecting the stock market.In this plan, the investor buys varying number of shares at various points of the stock market cycle. In a way, it can be called time diversification.Advantages:
§ Reduces the averages cost per share and improves the possibility of gain over a long period.
§ Takes away the pressure of timing the stock purchase from investor.
§ Makes the investors to plan the investment programme thoroughly on the commitment of funds that has to be done periodically.
§ Applicable to both falling and rising market, although it works best if the stocks are acquired in a declining market.
Disadvantages:
§ Extra transaction costs are involved with small and frequent purchase of shares.
§ The plan does not indicate when to sell. It is strictly a strategy for buying.
KARISHMA SIROHI
KARISHMA SIROHI 32
§ It does not eliminate the necessity for selecting the individual stocks that are to be purchased.
§ There is no indication of the appropriate interval between purchases.
§ The averaging advantage does not yield profit if the stock price is in a downward trend.
§ The plan seems to work better when stock prices have cyclical patterns.2. Constant rupee plan: this plan force the investors to sell when the prices rise and
purchase as prices fall. Forecasts are not required to guide buying and selling. The actions suggested by the formula timing plan automatically help the investor to reap the benefits of the fluctuations in the stock prices.The essential feature of the plan is that the portfolio is divided into two parts, which consists of aggressive and defensive or conservative portfolios. The portfolio mix facilitates the automatic selling and buying of bonds and stocks. This plan enables the shift of investment from bonds to stocks and vice-versa by maintain a constant amount investment in the stock portion of the portfolio. The constant rupee plan starts with a fixed amount of money invested in selected stocks and bonds. When the price of the stocks increases, the investor sells sufficient amount of stocks of return to the original amount of the investment in stocks. By keeping the value of aggressive portfolio constant, remainder is invested in the conservative portfolio.The investor must choose action point or revaluation points. The action point is the times at which the investor has to readjust the values of the stocks in the portfolio. Advantages:
§ Purchase and sales are determined automatically.
§ Helps in gaining higher profits.Disadvantage:
§ Investor should have to be very rational while buying and selling the stocks.3. Constant ratio plan:
It attempts to maintain a constant ratio between the aggressive and conservative portfolios. The ratio is fixed by the investor. The investor’s attitude towards risk and return plays a major role in fixing the ratio. The conservative investor may like to have more of bond the aggressive investor, more of stocks. Once the ratio is fixed, it is maintained as the market moves up and down. As usual, action points may be fixed by the investor.Advantages:
§ The automatism with which it forces the manager to counter adjust his portfolio cyclically.
Limitations:
§ The money is shifted from the stock portion to bond portion. 4. Variable ratio plan:
According to this plan, at varying levels of marker prices, the proportions of the stocks and bonds change. Whenever the price of the stock increases, the stocks are
KARISHMA SIROHI
KARISHMA SIROHI 33
sold and new ratio is adopted by increasing the proportion of defensive portfolio. To adopt this plan, the investor is required to estimate a long term trend in the price of the stocks. Forecasting is very essential to this plan.Advantages:
§ Automatically the investor tends to correct his portfolio portions according to the price changes.
§ With accurate forecast the variable ratio plan takes greater advantage of price fluctuations than the constant ratio plan.
Limitations:
§ The investor has to construct the appropriate zones and trend for alterations of the proportions.
§ The selection of security has to be done by the investor by analyzing the merits of the stock. The plan does not help in the selection of scrips.
§ If the zones are too small frequent changes have to be done and it would limit portfolio performance.
KARISHMA SIROHI
KARISHMA SIROHI 34
UNIT 5
PORTFOLIO PERFORMANCE EVALUATION:
Portfolio evaluation is the last step in the process of portfolio management. Portfolio evaluation is the stage where we examine to what extent the objective has been achieved. Through portfolio evaluation the investor tries to find out how well the portfolio has performed. The portfolio of securities held by an investor is the result of his investment decision. Portfolio evaluation is really a study of the impact of such decisions. Without portfolio evaluation portfolio management would be incomplete.
Meaning:
Portfolio evaluation refers to the evaluation of the performance of the portfolio. It is essentially the process of comparing the return earned on a portfolio with the return earned on one or more other portfolios or on a benchmark portfolio.
Portfolio evaluation comprises two functions: performance measurement and performance evaluation.
Performance measurement is an accounting function which measures the return earned on a portfolio during the holding period or investment period.
Performance evaluation addresses such issues as whether the performance was superior or inferior, whether the performance was due to skill or luck, etc.
While evaluating the performance of a portfolio the return earned on the portfolio has to be evaluated in the context of the risk associated with that portfolio. One approach would be to group portfolios into equivalent risk classes and then compare returns of portfolios within each risk category. An alternative approach would be to specifically adjust the return for the riskiness of the portfolio by developing risk adjusted return measure and use these for evaluating portfolios across differing risk levels.
Need for evaluation:
Evaluation is an appraisal of performance. Whether the investment activity is carried out by individual investors themselves or through mutual funds and investment companies, different
KARISHMA SIROHI
KARISHMA SIROHI 35
situations arise where evaluation of performance becomes imperative. These situations are discussed below:
1. Self evaluation: where individual investors undertake the investment activity on their own, the investment decisions are taken by them. They construct and manage their own portfolio of securities. In such a situation, an investor would like to evaluate the performance of his portfolio in order to identify the mistakes committed by him. This self evaluation will enable him to improve his skills and achieve better performance in future.
2. Evaluation of portfolio managers: a mutual fund or investment company usually creates different portfolios with different objectives aimed at different sets of investors. Each such portfolio may be entrusted to different professional portfolio managers who are responsible for the investment decisions regarding the portfolio entrusted to each of them. In such a situation, the organization would like to evaluate the performance of each portfolio so as to compare the performance of different managers.
3. Evaluation of mutual funds: investors and organizations desirous of placing their funds with mutual funds would like to know the comparative performance of each so as to select the best mutual fund or investment company. For this, evaluation of the performance of mutual funds and their portfolios becomes necessary.
Evaluation perspective:
Evaluation may be carried from different perspective or viewpoints such as---
1. Transaction view: an investor may attempt to evaluate every transaction of purchase and sale of securities. Whenever, a security is bought and sold, the transaction is evaluated as regards its correctness and profitability.
2. Security view: each security included in the portfolio has been purchased at a particular price. At the end of the holding period, the market price of the security may be higher or lower than its cost price or purchase price. Further, during the holding period, interest or dividend might have been received in respect of the security. Thus, it may be possible to evaluate the profitability of holding each security separately. This is evaluation from the security viewpoint.
3. Portfolio view: an investor may attempt to evaluate the performance of the portfolio as a whole without examining the performance of individual securities within the portfolio. This is evaluation from the portfolio view.
Measures of portfolio evaluation:
1. Sharpe’s measures: Sharpe’s performance index gives a single value to be used for the performance ranking of various funds or portfolios. Sharpe index measures the risk premium of the portfolio relative to the total amount of risk in the portfolio. This risk
KARISHMA SIROHI
Measures
Sharpe's Measures
Treynor's Measures
Jensen"s Measures
KARISHMA SIROHI 36
premium is the difference between the portfolio’s average rate of return and the riskless rate of return. The standard deviation of the portfolio indicates the risk. The index assigns the highest values to assets that have best risk-adjusted average rate of return.
St=R p−R f
σ p
Sharpe index= p ortfolio average return−risk freerate of interest
standard deviationof the portfolio return
2. Treynor’s Performance index: To understand the Treynor index, an investor should know the concept of characteristic line. The relationship between a given market return and the fund’s return is given by the characteristic line. The fund’s performance is measured in relation to the market performance. The ideal fund’s return rises at a faster rate than the general market performance when the market is moving upwards and its rate of return declines slowly than the market return, in the decline. The ideal fund may place its fund in the treasury bills or short sell the stock during the decline and earn positive return. With the help of charateristics line Treynor measures the performance of the fund. The slope of the line is estimated by:
Rp=α +β Rm+ep
Rp= portfolio returnRm=the market return∨index return
e p=the error term∨the residual
α ,β=coefficients ¿beestimatedBeta co efficient is treated as a measure of undiversifiable systematic risk.
Tn=portfolio averagereturn−riskless rate of interest
betaco efficient of portfolio
Tn=R p−R f
β p
3. Jensen’s Performance Index: the absolute risk adjusted return measure was developed by Micheal Jensen and commonly known as Jensen’s measure. It is mentioned as a measure of absolute performance because a definite standard is set and against that the performance is measured. The standard is based on the manager’s predictive ability. Successful prediction of security price would enable the manager to earn higher return than the ordinary investor expects to earn in given level of risk. The basic model of Jensen is given below:
KARISHMA SIROHI
See example and graph in the book pandian pg 414.
KARISHMA SIROHI 37
Rp=α +β¿¿
Rp= portfolio return
R f=riskless rate of interest
Rm=average market return
α= the interceptβ=a measure of systematic risk
Jensen’s evaluation of portfolio performance involves two steps: Using the equation the expected return should be calculated With the help of β, Rm,Rp, he has to compare the actual return with the
expected return. If the actual return is greater than the expected return, then the portfolio is considered to be functioning in a better manner.
Portfolio management strategies:
Portfolio Management Strategies refer to the approaches that are applied for the efficient portfolio management in order to generate the highest possible returns at lowest possible risks. There are two basic approaches for portfolio management including Active Portfolio Management Strategy and Passive Portfolio Management Strategy.
1. Active Portfolio Management StrategyThe Active portfolio management relies on the fact that particular style of analysis or management can generate returns that can beat the market. It involves higher than average costs and it stresses on taking advantage of market inefficiencies. It is implemented by the advices of analysts and managers who analyze and evaluate market for the presence of inefficiencies.The active management approach of the portfolio management involves the following styles of the stock selection.
§ Top-down Approach: In this approach, managers observe the market as a whole and decide about the industries and sectors that are expected to perform well in the ongoing economic cycle. After the decision is made on the sectors, the specific stocks are selected on the basis of companies that are expected to perform well in that particular sector.
§ Bottom-up: In this approach, the market conditions and expected trends are ignored and the evaluations of the companies are based on the strength of their product pipeline, financial statements, or any other criteria. It stresses the fact that strong companies perform well irrespective of the prevailing market or economic conditions.
2. Passive Portfolio Management StrategyPassive asset management relies on the fact that markets are efficient and it is not possible to beat the market returns regularly over time and best returns are obtained from the low cost investments kept for the long term.
KARISHMA SIROHI
KARISHMA SIROHI 38
The passive management approach of the portfolio management involves the following styles of the stock selection.
§ Efficient market theory: This theory relies on the fact that the information that affects the markets is immediately available and processed by all investors. Thus, such information is always considered in evaluation of the market prices. The portfolio managers who follows this theory, firmly believes that market averages cannot be beaten consistently.
§ Indexing: According to this theory, the index funds are used for taking the advantages of efficient market theory and for creating a portfolio that impersonate a specific index. The index funds can offer benefits over the actively managed funds because they have lower than average expense ratios and transaction costs. Apart from Active and Passive Portfolio Management Strategies, there are three more kinds of portfolios including Patient Portfolio, Aggressive Portfolio and Conservative Portfolio.
§ Patient Portfolio: This type of portfolio involves making investments in well-known stocks. The investors buy and hold stocks for longer periods. In this portfolio, the majority of the stocks represent companies that have classic growth and those expected to generate higher earnings on a regular basis irrespective of financial conditions.
§ Aggressive Portfolio: This type of portfolio involves making investments in “expensive stocks” that provide good returns and big rewards along with carrying big risks. This portfolio is a collection of stocks of companies of different sizes that are rapidly growing and expected to generate rapid annual earnings growth over the next few years.
§ Conservative Portfolio: This type of portfolio involves the collection of stocks after carefully observing the market returns, earnings growth and consistent dividend history.
KARISHMA SIROHI
