Portfolio Analysis

Unit – IV:

• Portfolio Analysis: Risk and Return Analysis, Markowitz Portfolio Theory, Mean-Variance Approach, Portfolio Selection, Efficient Portfolios, Single Index Model, Capital Asset Pricing Model, Arbitrage Pricing Theory.

​

What is Portfolio�

What is Portfolio

Portfolio is a group of financial assets such as shares, stocks, bonds, debt instruments, mutual funds, cash equivalents, etc. A portfolio is planned to stabilize the risk of non-performance of various pools of investment.

​

• Portfolio refers to invest in a group of securities rather to invest in a single security.

​

• “Don’t Put all your eggs in one basket”

​

• Portfolio help in reducing risk without sacrificing return.

�

What is Management

Management is the organization and coordination of the activities of an enterprise in accordance with well-defined policies and in achievement of its pre-defined objectives.

Portfolio Management

Portfolio Management is the process of creation and maintenance of investment portfolio.

​

Portfolio management is a complex process which tries to make investment activity more rewarding and less risky.

​

Risk and Return Analysis

• As a first step in portfolio analysis, an investor needs to specify the list of securities eligible for selection or inclusion in the portfolio. Next he has to generate the risk-return expectations for these securities. These are typically expressed as the expected rate of return (mean) and the variance or standard deviation of the return. The expected return of a portfolio of assets is simply the weighted average of the return of the individual securities held in the portfolio. The weight applied to each return is the fraction of the portfolio invested in that security.

Let us consider a portfolio of two equity shares P and Q with expected returns of 15 per cent and 20 per cent respectively. If 40 per cent of the total funds are invested in share P and the remaining 60 per cent, in share Q, then the expected portfolio return will be:

(0.40 x 15) + (0.60 x 20) = 18 per cent

The formula for the calculation of expected portfolio return may be expressed as shown below:

Return of Portfolio (Two Assets)

The expected return from a portfolio of two or more securities is equal to the weighted average

of the expected returns from the individual securities.

P (R ) = W_A(R_A) + W_B(R_B)

Where,

P (R ) = Expected return from a portfolio of two securities

W_A = Proportion of funds invested in Security A

W_B = Proportion of funds invested in Security B

R_A = Expected return of Security A

R_B = Expected return of Security B

W_A+ W_B = 1

Example: A Ltd.'s share gives a return of 20% and B Ltd.'s share gives 32% return. Mr.Gotha invested 25% in A Ltd.'s shares and 75% of B Ltd.'s shares. What would be the expected return of the portfolio?

Solution:

Portfolio Return = 0.25(20) + 0.75 (32) = 29%

Example: Mr. RKV's portfolio consists of six securities. The individual returns of each of the security in the portfolio are given below:

​

Calculate the weighted average of return of the securities consisting of the portfolio.

• Risk of Portfolio (Two Assets)
• The risk of a security is measured in terms of variance or standard deviation of its returns. The portfolio risk is not simply a measure of its weighted average risk. The securities that a portfolio contains are associated with each other. The portfolio risk also considers the covariance between the returns of the investment. Covariance of two securities is a measure of their co-movement; it expresses the degree to which the securities vary together. The standard deviation of a two-share portfolio is calculated by applying formula given below:

​

Risk and Return of Portfolio (Three Assets)

Formula for calculating risk of portfolio consisting three securities

​

Example: A portfolio consists of three securities P, Q and R with the following

parameters:

If the securities are equally weighted, how much is the risk and return of the portfolio of these three securities?

Phases of Portfolio Management

Portfolio management is a process of many activities that aimed to optimizing the investment. Five phases can be identified in the process:

​

1. Security Analysis.
2. Portfolio Analysis.
3. Portfolio Selection.
4. Portfolio revision.
5. Portfolio evaluation.

​

Each phase is essential and the success of each phase is depend on the efficiency in carrying out each phase.

​

Phases of Portfolio Management

Portfolio Management

Security

Analysis

Portfolio

Analysis

Portfolio

Selection

Portfolio

Revision

Portfolio

Evaluation

1. Fundamental Analysis
2. Technical Analysis
3. Efficient Market Hypothesis

Diversification

1. Markowitz Model
2. Sharpe’s Single index model
3. CAPM
4. APT

1. Formula Plans

2. Rupee cost Averaging

1. Sharpe’s index
2. Treynor’s measure
3. Jenson’s measure

Security Analysis

• Security analysis is the initial phase of the portfolio management process.

​

• The basic approach for investing in securities is to sell the overpriced securities and purchase under priced securities

​

• The security analysis comprises of Fundamental Analysis and technical Analysis.

​

Portfolio Analysis

• A large number of portfolios can be created by using the securities from desired set of securities obtained from initial phase of security analysis.

​

• . It involves the mathematically calculation of return and risk of each portfolio.

​

Portfolio Selection

• The portfolios that yield good returns at a level of risk are called as efficient portfolios.

​

• The set of efficient portfolios is formed and from this set of efficient portfolios, the optimal portfolio is chosen for investment.

Portfolio Revision

• Due to dynamic changes in the economy and financial markets, the attractive securities may cease to provide profitable returns.

​

​

Portfolio Evaluation

• This phase involves the regular analysis and assessment of portfolio performances in terms of risk and returns over a period of time.

Conclusion

• SECURITY ANALYSIS: Classification of securities( shares, debentures, bonds etc..), examining the risk-return characteristics of individual securities, fundamental and technical analysis.

​

• PORTFOLIO ANALYSIS: Identification of range of possible portfolio from a different set and ascertaining risk and return.

​

• PORTFOLIO SELECTION: Efficient portfolio is identified and optimal portfolio is selected.

​

• PORTFOLIO REVISION: Addition or deletion of securities due to change in availability of additional funds, change in risk, need for cash etc.

​

• PORTFOLIO EVALUATION : Comparison of objective norms with relative performance. Provides feedback mechanism for improving the entire portfolio management process.

​

​

​

​

Portfolio theory

Harry Markowitz Model�

• Harry Max Markowitz (born August 24, 1927) is an American economist.
• He is best known for his pioneering work in Modern Portfolio Theory.
• Harry Markowitz put forward this model in 1952.
• Studied the effects of asset risk, return, correlation and diversification on probable investment portfolio returns.

Harry Max Markowitz 

Markowitz Model

•  It assists in the selection of the most efficient by analyzing various possible portfolios of the given securities. By choosing securities that do not 'move' exactly together, the HM model shows investors how to reduce their risk.

​

• Also known as Mean-Variance Model.

​

• We all agree that holding two stocks is less risky as compared to one stock. But building the optimal portfolio is very difficult. Markowitz provides an answer to it with the help of risk and return relationship.

​

• Determination of a set of efficient portfolios.

​

• Selection of the best portfolio out of the efficient set.

​

Essence of Markowitz Model

1. Markowitz model assists in the selection of the most efficient by analysing various possible portfolios of the given securities.
2. By choosing securities that do not 'move' exactly together, the HM model shows investors how to reduce their risk.
3. The HM model is also called Mean-Variance Model due to the fact that it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios. 

Assumptions

• An investor has a certain amount of capital he wants to invest over a single time horizon. 
• He can choose between different investment instruments, like stocks, bonds, options, currency, or portfolio. 
• The investment decision depends on the future risk and return. 
• The decision also depends on if he or she wants to either maximize the yield or minimize the risk.
• The investor is only willing to accept a higher risk if he or she gets a higher expected return.

Tools for selection of portfolio- Markowitz Model

1. Expected return (Mean)

​

Mean and average to refer to the sum of all values divided by the total number of values.

The mean is the usual average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

​

​

Where:

ER = the expected return on Portfolio

E(R_i) = the estimated return in scenario i

W_i= weight of security i occurring in the port folio

R_p=R₁W₁+R₂W_{2………..n}

R_p = the expected return on Portfolio

R₁ = the estimated return in Security 1

R₂ = the estimated return in Security 1

W₁= Proportion of security 1 occurring in the port folio

W₂= Proportion of security 1 occurring in the port folio

​

Where:

1. Expected return (Mean)
2. Standard deviation (variance)
3. Co-efficient of Correlation

​

Tools for selection of portfolio- Markowitz Model

2. Variance & Co-variance

​

The variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean (expected value).

​

1. Covariance reflects the degree to which the returns of the two securities vary or change together.
2. A positive covariance means that the returns of the two securities move in the same direction.
3. A negative covariance implies that the returns of the two securities move in opposite direction.

​

Co-variance

Cov_AB=Covariance between security A and B

R_A=Return on security A

R_B=Return on Security B

=Expected Return on security A

=Expected Return on security B

Tools for selection of portfolio- Markowitz Model

3. Co-efficient of Correlation

​

Covariance & Correlation are conceptually analogous in the sense that of them reflect the degree of Variation between two variables.

1. The Correlation coefficient is simply covariance divided the product of standard deviations.
2. The correlation coefficient can vary between -1.0 and +1.0

Cov_AB=Covariance between security A and B

r_AB=Co-efficient correlation between security A and B

-1.0

0

1.0

Perfectly negative

Opposite direction

Perfectly Positive

Opposite direction

No

Correlation

Standard deviation of A and B security

Affect of Perfectly Negatively Correlated Returns�Elimination of Portfolio Risk

CHAPTER 8 – Risk, Return and Portfolio Theory

Example of Perfectly Positively Correlated Returns�No Diversification of Portfolio Risk

CHAPTER 8 – Risk, Return and Portfolio Theory

Time 0 1 2

If returns of A and B are perfectly positively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be risky. There would be no diversification (reduction of portfolio risk).

Returns

%

10%

5%

15%

20%

Grouping Individual Assets into Portfolios

​

• The riskiness of a portfolio that is made of different risky assets is a function of three different factors:
• the riskiness of the individual assets that make up the portfolio
• the relative weights of the assets in the portfolio
• the degree of variation of returns of the assets making up the portfolio
• The standard deviation of a two-asset portfolio may be measured using the Markowitz model:

Implications for Portfolio Formation

• Assets differ in terms of expected rates of return, standard deviations, and correlations with one another
• While portfolios give average returns, they give lower risk
• Diversification works!
• Even for assets that are positively correlated, the portfolio standard deviation tends to fall as assets are added to the portfolio

Implications for Portfolio Formation

• Combining assets together with low correlations reduces portfolio risk more
• The lower the correlation, the lower the portfolio standard deviation
• Negative correlation reduces portfolio risk greatly
• Combining two assets with perfect negative correlation reduces the portfolio standard deviation to nearly zero

Efficient frontier

Return on Portfolio

Risk

Any portfolio which gives more return for the same level of risk.

​

Or

​

Same return with Lower risk.

​

Is more preferable then any other portfolio.

Amongst all the portfolios which offers the highest return at a particular level of risk are called efficient portfolios.

Efficient frontier

Risk and Return

Portfolios

D

E

F

G

H

I

A

B

C

ABCD line is the efficient frontier along which attainable and efficient portfolios are available.

Which portfolio investor should choose?

Utility analysis with Indifference Curves

Utility of Investor

Risk Lover

Risk Averse

Risk Neutral

Utility

Return

A

B

C

Marginal utility of different class of investors.

I₁

I₂

I₃

I₄

I₁

I₂

I₃

I₄

I₁

I₂

I₃

I₄

I₁

I₂

I₃

I₄

Indifference curves of the risk Loving

Indifference curves of the risk Fearing

Indifference curves of the less risk Fearing

Indifference curves & Efficient frontier.

R_p

R_p

R_p

R_p

Risk

Risk

Risk

Risk

2

4

6

8

10

12

14

14

18

R

��SECURITY ANALYSIS & PORTFOLIO MGT.

​

​

Sharp Index Modal

Where,

σ_m² = Variance of the Market Index

σ_ei² = Variance of a stock’s movement that is not associated with the movement of Market Index i.e. stock’s unsystematic risk.

​

​

​

​

​

SOLUTION OF EXAMPLE- 1:

EXAMPLE- 1:

​

​

​

​

​

SOLUTION OF EXAMPLE- 2:

Portfolio Revision

Portfolio Revision

• The investor should have competence and skill in the revision of the portfolio.
• The portfolio management process needs frequent changes in the composition of stocks and bonds.
• Mechanical methods are adopted to earn better profit through proper timing.
• Such type of mechanical methods are Formula Plans and Swaps.

​

Passive Management

• Passive management refers to the investor’s attempt to construct a portfolio that resembles the overall market returns.
• The simplest form of passive management is holding the index fund that is designed to replicate a good and well defined index of the common stock such as BSE-Sensex or NSE-Nifty.

​

Active Management

• Active Management is holding securities based on the forecast about the future.
• The portfolio managers who pursue active strategy with respect to market components are called ‘market timers’.
• The managers may indulge in ‘group rotations’.
• Group rotation means changing the investment in different industries stocks depending on the assessed expectations regarding their future performance.

​

The Formula Plans

• The formula plans provide the basic rules and regulations for the purchase and sale of securities.
• The aggressive portfolio consists more of common stocks which yield high return with high risk.
• The conservative portfolio consists of more bonds that have fixed rate of returns.

​

Assumptions of the Formula Plan

• Certain percentage of the investor’s fund is allocated to fixed income securities and common stocks.
• The stocks are bought and sold whenever there is a significant change in the price.
• The investor should strictly follow the formula plan once he chooses it.
• The investors should select good stocks that move along with the market.

​

Advantages of the Formula Plan

• Basic rules and regulations for the purchase and sale of securities are provided.
• The rules and regulations are rigid and help to overcome human emotion.
• The investor can earn higher profits by adopting the plans.
• It controls the buying and selling of securities by the investor.
• It is useful for taking decisions on the timing of investments.

​

Disadvantages of the�Formula Plan

• The formula plan does not help the selection of the security.
• It is strict and not flexible with the inherent problem of adjustment.
• Should be applied for long periods, otherwise the transaction cost may be high.
• Investor needs forecasting.

​

Rupee Cost Averaging

• Stocks with good fundamentals and long term growth prospects should be selected.
• The investor should make a regular commitment of buying shares at regular intervals.
• Reduces the average cost per share and improves the possibility of gain over a long period.

​

Constant Rupee Plan

• A fixed amount of money is invested in selected stocks and bonds.
• When the price of the stocks increases, the investor sells sufficient amount of stocks to return to the original amount of the investment in stocks.
• The investor must choose action points or revaluation points.
• The action points are the times at which the investor has to readjust the values of the stocks in the portfolio.

​

Constant Ratio Plan

• Constant ratio between the aggressive and conservative portfolios is maintained.
• The ratio is fixed by the investor.
• The investor’s attitude towards risk and return plays a major role in fixing the ratio.

​

Variable Ratio Plan

• At varying levels of market price, the proportions of the stocks and bonds change.
• Whenever the price of the stock increases, the stocks are sold and new ratio is adopted by increasing the proportion of defensive or conservative portfolio.
• To adopt this plan, the investor is required to estimate a long term trend in the price of the stocks.

​