6 SEM TDC DSE COM (CBCS) 601 (GR-I)
2024 (May)
COMMERCE
(Discipline Specific Elective)
(For Honours and Non-Honours)
Paper: DSE-601 (GR-I)
(Security Analysis and Portfolio Management)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions
1. (a) Write whether the following statements are True or False:
(1×4 = 4)
(i) The government securities have maturity period between 3 and 20 years.
Answer: True
(ii) The basic principles of technical analysis originate from Dow theory.
Answer: True
(iii) APM is a single-factor model.
Answer: False
(iv) Formula plans do not help in deciding the timing of investment.
Answer: False
1. (b) Fill in the blanks with appropriate word(s):
(1×4 = 4)
(i) Capital index bonds are linked with Consumer Price Index. (BSE-100 / Consumer Price Index / BSE-Sensex)
Answer: Consumer Price Index
(ii) The peak price of the stock is called resistance area. (market price / low price / peak price)
Answer: Peak price
(iii) The stock above the security market line is underpriced security. (of high risk / overpriced / underpriced)
Answer: Underpriced
(iv) The beta coefficient is treated as a measure of systematic risk. (systematic risk / unsystematic risk / average return)
Answer: Systematic risk
2. Write short notes on : (4×4 = 16)
(a) Money Market Security
Money market securities are short-term debt instruments used by governments, financial institutions, and corporations to meet short-term funding requirements. These securities typically have maturities of one year or less, making them highly liquid and low-risk.
Common types of money market securities include:
Treasury Bills (T-Bills): Issued by the government and considered risk-free.
Commercial Papers: Unsecured promissory notes issued by corporations.
Certificates of Deposit (CDs): Issued by banks to depositors for a fixed term.
Repurchase Agreements (Repos): Short-term loans backed by government securities.
These instruments are ideal for investors looking for capital preservation and quick returns, and they play a vital role in maintaining liquidity in the financial system.
(b) Charting Analysis
Charting analysis, a key part of technical analysis, involves studying historical price data and trading volumes through visual tools like charts to predict future price movements. Traders and investors use different types of charts, such as:
Line Charts – Simplest form, showing closing prices.
Bar Charts – Show opening, high, low, and closing prices.
Candlestick Charts – Provide more detailed patterns and visual cues.
Chartists look for patterns such as head and shoulders, triangles, and double tops/bottoms to make investment decisions.
Technical indicators like Moving Averages, Relative Strength Index (RSI), and MACD are also used.
This method assumes that all market information is reflected in prices and that history tends to repeat itself.
(c) Portfolio Analysis
Portfolio analysis refers to the evaluation of investments held by an individual or institution to understand their performance, risk level, and diversification. The main goals are to maximize returns and minimize risk through a well-balanced mix of assets.
Key elements of portfolio analysis include:
Asset Allocation: Distribution of investments among various asset classes like equities, bonds, and cash.
Diversification: Reducing risk by investing in different securities and sectors.
Risk-Return Trade-off: Balancing the desire for higher returns with the investor’s risk tolerance.
Performance Measurement: Using ratios such as Sharpe Ratio, Treynor Ratio, and Alpha.
Tools like Modern Portfolio Theory (MPT) help in selecting an optimal portfolio that lies on the efficient frontier, representing the best possible risk-return combinations.
(d) Empirical Test of the CAPM
The Capital Asset Pricing Model (CAPM) suggests that the expected return of a security is determined by its sensitivity to market risk (beta), the risk-free rate, and the expected market return. The Security Market Line (SML) represents this relationship graphically.
Empirical testing of the CAPM involves checking whether:
Securities with higher betas earn higher returns.
Real-world data aligns with the theoretical predictions of the model.
However, empirical results have shown mixed outcomes:
Some studies support CAPM predictions, especially in large markets.
Other studies show that other factors (like size, value, and momentum) also affect returns, which led to the development of multi-factor models like the Fama-French 3-factor model.
Despite its limitations, CAPM is still widely used for asset pricing, portfolio evaluation, and estimating cost of equity.
(e) Components of Performance
Performance evaluation of a portfolio or investment involves analyzing several components to understand how well the investment has done. The key components are:
Return: The total income (interest, dividends, and capital gains) received from an investment. It can be expressed as an absolute amount or percentage.
Risk: The degree of uncertainty or variability in returns. It is typically measured using standard deviation, beta, or value at risk (VaR). Risk can be systematic (market-related) or unsystematic (firm-specific).
Risk-Adjusted Return: This measures the return earned per unit of risk. Popular metrics include:
Sharpe Ratio: (Return – Risk-free rate) / Standard deviation
Treynor Ratio: (Return – Risk-free rate) / Beta
Jensen’s Alpha: Measures the excess return above the CAPM-predicted return.
By evaluating all these components, investors can judge whether their portfolio is performing efficiently relative to the risk taken.
3.(a) Define security. What are the investor’s objectives in investing his funds in the stock market?[4 + 10 = 14]
Answer: Definition of Security (4 marks): A security is a financial instrument that holds monetary value and can be traded in financial markets. It represents an ownership position (in the case of stocks), a creditor relationship (in the case of bonds), or rights to ownership (as in derivatives).
Securities are broadly classified into three categories:
Equity securities (e.g., shares)
Debt securities (e.g., bonds, debentures)
Derivative securities (e.g., futures, options)
Securities are regulated under legal frameworks like the Securities Contracts (Regulation) Act, 1956 in India. They are bought and sold in stock markets and other financial exchanges.
Investor’s Objectives in Investing in the Stock Market (10 marks):
Investors put their funds into the stock market with various short-term and long-term objectives. The main objectives are:
Capital Appreciation: The primary goal of many investors is to see their invested capital grow over time as the value of their stocks increases.
Dividend Income: Investors often invest in stocks that offer regular dividend payments, which provide a steady source of income.
Portfolio Diversification:
Investing in a range of stocks allows investors to diversify their holdings, which helps reduce overall risk.Hedge Against Inflation: Equity investments typically offer returns that can outpace inflation, preserving the purchasing power of investors' money.
Liquidity: Stocks traded on the stock exchange offer high liquidity, meaning investors can buy or sell them quickly when needed.
Ownership in Companies: Purchasing shares makes investors part-owners of the company, giving them rights such as voting in shareholder meetings.
Speculative Gains: Some investors invest with the intent to profit from short-term price movements through trading.
Tax Benefits: Long-term capital gains from equity investments may attract lower tax rates, depending on the prevailing tax laws.
Retirement Planning: Many investors use the stock market as part of their long-term retirement plans, aiming for wealth creation over time.
Psychological Satisfaction and Status:
For some, being involved in the stock market brings a sense of participation in the economic system and offers social prestige.
In conclusion, investment in the stock market helps investors meet financial goals by offering opportunities for income, growth, and wealth creation, while also allowing risk management through diversification.
Or
(b) Explain in detail the Dow Theory and how it is used to determine the direction of the stock market.[14 marks]
Answer: Introduction: The Dow Theory is one of the oldest and most widely respected technical analysis tools used to understand and predict stock market trends. It was developed by Charles H. Dow, co-founder of Dow Jones & Company and the Wall Street Journal, and later expanded by William Hamilton and Robert Rhea.
Key Assumptions of Dow Theory:
The Market Discounts Everything:
All information, whether public or insider, is already reflected in stock prices.Market Moves in Trends:
The market moves in identifiable trends – upward, downward, or sideways.Three Types of Trends:
Primary Trend: Long-term movement lasting months or years (bull or bear market).
Secondary Trend: Intermediate corrections or rallies within the primary trend.
Minor Trend: Short-term daily fluctuations.
Three Phases of Primary Trends:
Accumulation Phase: Smart investors start buying/selling while the majority is inactive.
Public Participation Phase: Wider market recognizes the trend and joins in.
Distribution Phase: Smart investors begin to exit as the trend nears its end.
Volume Confirms the Trend:
Rising volumes during upward trends and falling volumes during downward trends confirm the strength of a movement.Indices Must Confirm Each Other:
The theory uses two key indices – the Dow Jones Industrial Average (DJIA) and the Dow Jones Transportation Average (DJTA). A trend is confirmed only when both indices show the same direction.Trends Continue Until Definite Signals of Reversal Appear:
A trend remains in effect until a clear reversal is indicated by price and volume actions.
How Dow Theory Determines Market Direction:
Bull Market Indication:
When both the DJIA and DJTA make higher highs and higher lows, it signals an ongoing upward trend or bull market.Bear Market Indication:
When both indices form lower highs and lower lows, it indicates a downward trend or bear market.Confirmation & Reversal:
If one index makes a new high but the other fails to do so, it’s a warning of a potential trend reversal.
Practical Application:
Investors use Dow Theory to determine entry and exit points in the market.
It serves as a broad market barometer to assess economic cycles.
Traders watch for index confirmations to avoid false signals.
Conclusion: Dow Theory provides a systematic and disciplined approach to understanding market behavior. Though developed over a century ago, it remains relevant and is considered the foundation for modern technical analysis. It helps investors make informed decisions based on observed market trends and patterns.
4. (a) Explain the nature of portfolio risk if two securities (i) are perfectly positively correlated, (ii) are perfectly negatively correlated and (iii) have zero correlation. Illustrate with diagrams. [14]
Portfolio risk refers to the overall variability in the return of a portfolio comprising two or more securities. This risk is influenced by the individual risks (standard deviations) of the securities and the correlation between their returns. Correlation is measured on a scale from -1 to +1. The nature of portfolio risk changes based on the correlation coefficient as follows:
(i) Perfectly Positively Correlated Securities (r = +1):
When two securities are perfectly positively correlated, it means they move together in the same direction and with the same intensity. In such a case, the diversification benefit is zero. The portfolio’s standard deviation becomes a simple weighted average of the individual standard deviations. This is because the positive movement of one security is not balanced by any negative movement in the other.
For example, if Security A and Security B both increase or decrease together by the same proportion, the portfolio’s overall volatility remains unchanged. Diversifying between them does not reduce the risk.
Diagram: The graph of risk vs return would be a straight line connecting the two assets. There is no "dip" in the curve since no risk is reduced.
(ii) Perfectly Negatively Correlated Securities (r = -1):
In this case, when one security’s return increases, the other decreases by the same proportion. This is the ideal case for diversification. With the right allocation (weights), an investor can construct a portfolio with zero standard deviation, i.e., completely eliminate risk.
This works because the losses from one security are completely offset by gains from the other. Thus, the combined effect leads to stabilized returns.
Diagram: In the risk-return space, the curve dips down and touches the x-axis (zero risk) at a certain combination of weights, showing that it is possible to eliminate all risk.
(iii) Zero Correlation (r = 0):
When two securities have zero correlation, it means their returns are unrelated — the movement of one security has no predictable effect on the other. In this case, diversification does reduce risk, but not as effectively as in the case of negative correlation.
The portfolio’s standard deviation will be less than the weighted average of the individual standard deviations but greater than zero.
Diagram: The graph of risk-return forms a curved line that bends inward between the two securities, showing moderate risk reduction through diversification.
Conclusion:
When correlation is +1, no risk is reduced.
When correlation is -1, all risk can be eliminated.
When correlation is 0, risk is reduced partially.
This concept forms the basis of Modern Portfolio Theory, which states that combining securities with less-than-perfect correlation reduces overall portfolio risk.
Or
(b) Discuss in detail Markowitz efficient frontier. Differentiate between efficient portfolio and feasible portfolio. [10+4=14]
Answer: Markowitz Efficient Frontier ): Harry Markowitz introduced the Modern Portfolio Theory (MPT), which emphasizes risk reduction through diversification. The efficient frontier is one of the key concepts in this theory. It represents the set of optimal portfolios that offer the highest return for a given level of risk or the lowest risk for a given level of return.
To understand this concept, imagine plotting all possible combinations of two or more assets in a risk-return graph:
The x-axis represents risk (standard deviation).
The y-axis represents expected return.
By combining assets with different returns and correlations, many portfolio combinations can be created. These combinations form a region called the feasible set or investment opportunity set.
Within this set, the efficient frontier is the upper edge or boundary. Portfolios on this boundary are called efficient portfolios because:
No other portfolio exists with higher return for the same level of risk.
No other portfolio has lower risk for the same level of return.
The efficient frontier is upward sloping and curved, due to the benefit of diversification. As we move along the curve from left to right:
Risk increases.
Expected return also increases.
An investor would prefer a portfolio on the efficient frontier rather than inside the feasible region because it is optimally balanced in terms of return and risk.
This concept helps investors make better decisions by choosing portfolios that lie on the frontier based on their risk tolerance. Risk-averse investors choose points toward the left (low risk, moderate return), while aggressive investors may choose portfolios on the right side of the frontier (high risk, high return).
Difference Between Efficient Portfolio and Feasible Portfolio (4 marks):
Efficient Portfolio:
A portfolio that lies on the efficient frontier.
Offers the best possible return for a given level of risk.
There are no other portfolios with better risk-return combinations.
Investors choose efficient portfolios to optimize performance.
Feasible Portfolio:
Any portfolio that lies within or on the feasible region (including inefficient ones).
May not provide the best return for the level of risk taken.
Includes both efficient and inefficient portfolios.
These portfolios are technically possible but not optimal.
Conclusion: The Markowitz efficient frontier is a foundational concept in modern finance. It encourages investors to consider both return and risk while constructing portfolios and guides them in selecting optimal portfolios based on their investment preferences and risk appetite.
Here is the detailed answer for both options of Question 5, written clearly for a 14-mark response without any horizontal lines:
5. (a) Discuss the basic Arbitrage Pricing Model of single and multiple factor. Mention the assumptions of Arbitrage Pricing Model. [10+4=14]
Answer: Arbitrage Pricing Theory (APT) – Basic Concept :
The Arbitrage Pricing Theory (APT), developed by Stephen Ross, is a multi-factor asset pricing model that describes the expected return on a security as a linear function of various macroeconomic factors or theoretical market indices. It is an alternative to the Capital Asset Pricing Model (CAPM).
APT states that the expected return of a security can be predicted using the relationship between that return and a set of common risk factors. These factors affect all securities but with different intensities.
(i) Single-Factor Model:
In its simplest form, APT can be expressed as a single-factor model, similar to CAPM. The formula is:
Ri = Rf + βi (RP)
Where:
Ri = Expected return of asset i
Rf = Risk-free rate
βi = Sensitivity of the asset to the single factor (similar to beta)
RP = Risk premium for the factor
In the single-factor model, it is assumed that the only factor influencing returns is the market portfolio, making it similar to CAPM. However, APT is more flexible in allowing other types of risk factors.
(ii) Multiple-Factor Model:
APT is more effective as a multi-factor model, where returns are influenced by multiple sources of risk. The formula becomes:
Ri = Rf + b1F1 + b2F2 + ... + bnFn + ei
Where:
Ri = Expected return of asset i
Rf = Risk-free rate
F1, F2, ..., Fn = Risk factors (e.g., inflation, GDP growth, interest rates)
b1, b2, ..., bn = Sensitivity of the asset to each factor
ei = Idiosyncratic (unsystematic) risk
Each factor has an associated risk premium, and each security reacts differently to these factors based on its sensitivity coefficients (factor loadings).
APT does not specify what the exact factors should be — researchers and analysts may use different factors depending on empirical studies or theoretical reasoning.
Assumptions of Arbitrage Pricing Theory (4 marks):
Investors are risk-averse and rational: Investors prefer higher returns for a given level of risk and act rationally to maximize wealth.
Capital markets are perfectly competitive: There are no transaction costs, taxes, or restrictions on short selling, and all investors have equal access to information.
Asset returns follow a linear relationship with risk factors: The return on any asset is a linear function of a limited number of common risk factors.
There are no arbitrage opportunities: In equilibrium, mispriced assets are corrected by arbitrage, ensuring that no risk-free profit can be earned without investment.
A large number of securities exist:
This enables diversification and reduces idiosyncratic risk to zero in well-diversified portfolios.
Conclusion: APT provides a more generalized and flexible approach than CAPM, allowing for multiple risk factors that can influence asset returns. It is widely used in practice for portfolio construction and risk management.
Or
5. (b) Discuss in detail the Capital Asset Pricing Model. Distinguish between CML and SML. [10+4=14]
Capital Asset Pricing Model (CAPM) – Explanation : The Capital Asset Pricing Model (CAPM) is a foundational theory in finance that describes the relationship between the expected return of an asset and its systematic risk as measured by beta. It was developed by William Sharpe, John Lintner, and others.
The formula for CAPM is:
Ri = Rf + βi (Rm - Rf)
Where:
Ri = Expected return of the asset
Rf = Risk-free rate
βi = Beta of the asset (sensitivity to market risk)
Rm = Expected return of the market
(Rm - Rf) = Market risk premium
Key Concepts of CAPM:
Risk-Free Rate (Rf):
The return on a riskless investment, typically government securities like Treasury bills.Market Return (Rm):
The expected return from a diversified market portfolio.Beta (β):
A measure of the asset’s sensitivity to movements in the market.If β = 1: Asset moves with the market.
If β > 1: Asset is more volatile than the market.
If β < 1: Asset is less volatile than the market.
Market Risk Premium (Rm - Rf):
The extra return expected by investors for taking on market risk.
CAPM assumes that investors are rational, markets are efficient, and all investors hold a diversified market portfolio. The model helps in evaluating whether a stock is overpriced or underpriced based on its expected return and risk.
Applications of CAPM:
Used in estimating the cost of equity in corporate finance.
Helps investors assess whether to buy, hold, or sell a security.
Assists in portfolio construction and asset pricing.
Difference between CML and SML (4 marks):
Capital Market Line (CML):
Represents the risk-return trade-off for efficient portfolios only.
X-axis shows total risk (standard deviation).
All combinations of the risk-free asset and the market portfolio lie on the CML.
Equation: E(Rp) = Rf + [(Rm - Rf)/σm] × σp
Security Market Line (SML):
Represents the risk-return trade-off for all assets, both individual securities and portfolios.
X-axis shows systematic risk (beta).
Helps in determining if an asset is fairly priced based on its beta.
Equation: E(Ri) = Rf + βi (Rm - Rf)
Summary of Differences:
Conclusion: While CAPM provides a clear framework for pricing securities based on their risk, CML and SML are essential tools in visualizing how expected returns relate to different types of risk. CAPM remains a widely used model in finance despite its limitations.
6. (a) (i) What do you understand by portfolio revision? What are its constraints? [3 + 4 = 7]
Portfolio Revision: Portfolio revision refers to the process of adjusting the composition of a portfolio over time to maximize returns or minimize risks, in response to changing market conditions, investor goals, or economic variables. It involves the buying and selling of securities to rebalance the portfolio to ensure it remains aligned with the investor’s objectives.
Investors revise portfolios to:
Adapt to changes in interest rates, inflation, or stock market trends
Incorporate better-performing securities
Remove underperforming or riskier assets
Maintain a desired asset allocation or risk level
Constraints of Portfolio Revision:
Transaction Costs: Buying and selling securities involve brokerage fees, taxes, and other costs. Frequent revision may reduce net returns.
Tax Implications: Capital gains from selling appreciated assets may attract taxes, especially in the short term.
Availability of Information: Investors may not always have timely or accurate data to make informed decisions.
Regulatory and Legal Restrictions: Certain institutional investors may face legal or policy restrictions that limit frequent trading or restrict investment in certain asset classes.
Time and Effort: Portfolio revision requires continuous monitoring and evaluation, which may not be feasible for every investor.
Risk of Over-Trading: Excessive revisions based on short-term market movements can increase risk instead of optimizing returns.
6. (a) (ii) Explain the Treynor’s Performance Index Model. [7]
Treynor’s Performance Index (Treynor Ratio): The Treynor Ratio is a performance evaluation tool developed by Jack Treynor. It measures the returns earned in excess of the risk-free rate per unit of systematic risk (beta). This model is particularly useful when comparing portfolios that are well-diversified, as it focuses only on systematic risk, which cannot be diversified away.
Formula:
Treynor Ratio (T) = (Rp – Rf) / βp
Where:
Rp = Return of the portfolio
Rf = Risk-free rate
βp = Beta of the portfolio
Interpretation:
A higher Treynor Ratio indicates better risk-adjusted performance.
It tells the investor how much excess return (over the risk-free rate) is earned for each unit of market risk.
It assumes that the investor’s portfolio is already well-diversified and only systematic risk is relevant.
Usefulness:
Useful for comparing the performance of different mutual funds or portfolio managers.
Helps assess how efficiently the portfolio manager has used market risk to generate returns.
Limitation: Not suitable for portfolios that are not well-diversified, since it ignores unsystematic risk.
6. (b) (i) Write a note on Sharpe’s Reward to Volatility Model. [7]
Sharpe’s Performance Index (Sharpe Ratio): The Sharpe Ratio, developed by William F. Sharpe, is a measure of the risk-adjusted return of a portfolio. It is also known as the Reward to Variability Ratio, as it considers the total risk (standard deviation) of the portfolio, not just the systematic risk.
Formula:
Sharpe Ratio (S) = (Rp – Rf) / σp
Where:
Rp = Return of the portfolio
Rf = Risk-free rate
σp = Standard deviation of the portfolio’s return (total risk)
Interpretation:
A higher Sharpe Ratio indicates better risk-adjusted performance.
It shows how much excess return (above the risk-free rate) is generated per unit of total risk.
It considers both systematic and unsystematic risk, making it more suitable when the portfolio is not fully diversified.
Significance:
Helps in comparing portfolios or mutual funds with similar returns but different risk levels.
Helps investors choose funds that give higher returns for lower volatility.
Limitations:
Assumes that returns are normally distributed.
Can be misleading if used for portfolios with non-linear risks, such as options.
Conclusion: While both Sharpe and Treynor ratios measure risk-adjusted performance, the Sharpe ratio is broader as it considers total risk, making it more suitable for non-diversified portfolios, whereas the Treynor ratio is better for well-diversified portfolios.
(ii) Astha firm gives the following information: r
The current risk-free rate of return is 9 percent.
Astha firm is trying to decide two out of the four investment funds. You are required to choose the best two alternatives through using Sharp index. [7]
Solution: To evaluate the performance of the funds using risk-adjusted returns, we use the Sharpe Index (Sharpe Ratio).
Formula:
Sharpe Index (S) = (Rp – Rf) / σp
Where,
Rp = Average return of the portfolio
Rf = Risk-free rate (given as 9%)
σp = Standard deviation of the portfolio
Now, calculating Sharpe Index for each fund:
1. Fund-A
S = (17 – 9) / 19
S = 8 / 19
S ≈ 0.421
2. Fund-B
S = (18 – 9) / 20
S = 9 / 20
S = 0.45
3. Fund-C
S = (16 – 9) / 13
S = 7 / 13
S ≈ 0.538
4. Fund-D
S = (14 – 9) / 12
S = 5 / 12
S ≈ 0.417
Sharpe Index Summary:
Conclusion: From the above calculations, we can see that Fund-C has the highest Sharpe Index (0.538), followed by Fund-B (0.45).
These two funds provide the highest risk-adjusted returns and are, therefore, the best two investment choices for the firm.
Answer: Fund-C and Fund-B should be selected.
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