Mutual funds

UNIT-V

Performance Evaluation of Mutual Fund: Mutual Funds, Types of Mutual Funds Schemes, Structure, Trends in Indian Mutual Funds, Net Asset Value, Risk and Return, Performance Evaluation Models: Sharpe Model, Treynor Model, Jensen Model, Fama’s Decomposition Financial calculations in excel Exchange traded funds momentum strategies.

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A mutual fund is an investment vehicle that pools money from multiple investors to purchase a diversified portfolio of stocks, bonds, or other securities. The fund is managed by professional fund managers who use the collective assets to achieve the investment objective of the fund. Investors in a mutual fund own units of the fund, each representing a share of the fund's holdings and earnings. The value of the units is determined by the net asset value of the underlying securities.

A Mutual Fund is a trust that pools the savings of a number of investors who share a common financial goal. The money thus collected is then invested in capital market instruments such as shares, debentures and other securities. The income earned through these investments and the capital appreciations realized are shared by its unit holders in proportion to the number of units owned by them.

When an investor subscribes for the units of a mutual fund, he becomes part owner of the assets of the fund in the same proportion as his contribution amount put up with the corpus (the total amount of the fund). Mutual Fund investor is also known as a mutual fund shareholder or a unit holder.

Any change in the value of the investments made into capital market instruments (such as shares, debentures etc) is reflected in the Net Asset Value (NAV) of the scheme. NAV is defined as the market value of the Mutual Fund scheme's assets net of its liabilities.

NAV of a scheme is calculated by dividing the market value of scheme's assets by the total number of units issued to the investors.

For example:

• If the market value of the assets of a fund is Rs. 100,000.
• The total number of units issued to the investors is equal to 10,000.
• Then the NAV of this scheme = (A)/ (B), i.e. 100,000/10,000 or 10.00.
• Now if an investor 'X' owns 5 units of this scheme.
• Then his total contribution to the fund is Rs. 50 (i.e. Number of units held multiplied by the NAV of the scheme).

The Evolution:

The formation of Unit Trust of India marked the evolution of the Indian mutual fund industry in the year 1963. The primary objective at that time was to attract the small investors and it was made possible through the collective efforts of the Government of India and the Reserve Bank of India. The history of mutual fund industry India can be better understood by divided into following:

Phase-1 : Establishment and Growth of Unit Trust of India-1964-87

Phase-II : Entry of Public Sector Funds - 1987-1993

Phase-III : Emergence of Private Sector Funds - 1993-96

Phase-IV : Growth and SEBI Regulation - 1996-2004

Phase V : Growth and Consolidation - 2004 Onwards

Phase-1 Establishment and Growth of Unit Trust of India - 1964-87:

Unit Trust of India enjoyed complete monopoly when it was established in the year 1963 by an act of Parliament. UTI was set up by the Reserve Bank of India and it continued to operate under the regulatory control of the RBI until the two were de-linked in 1978 and the entire control was transferred in the hands of Industrial Development Bank of India (IDBI). UTI launched its first scheme in 1964, named as Unit Scheme 1964 (US-64), which attracted the largest number of investors in any single investment scheme over the years.

UTI launched more innovative schemes in 1970s and 80s to suit the needs of different investors. It launched ULIP in 1971, six more schemes between 1981 & 84, Children's Gift Growth Fund and India Fund (India's first offshore fund) in 1986, Master share (India’s first equity diversified scheme) in 1987 and Monthly Income Schemes (offering assured returns) during 1990s. By the end of 1987, UTI's assets under management grew ten times to Rs 6700 crores.

Phase-II Entry of Public Sector Funds - 1987-1993:

The Indian mutual fund industry witnessed a number of public sector players entering the market in the year 1987. In November 1987, SBI Mutual Fund from the State Bank of India became the first non-UTI mutual fund in India. SBI Mutual Fund was later followed by canara bank Mutual Fund, LIC Mutual Fund, Indian Bank Mutual Fund, Bank of India Mutual Fund, GIC Mutual Fund and PNB Mutual Fund. By 1993, the assets under management of the industry increased seven times to Rs. 47,004 crores. However, UTI remained to be the leader with about 80% market share.

Phase-III Emergence of Private Sector Funds - 1993-96:

The permission given to private sector funds including foreign fund management companies (most of them entering through joint ventures with Indian promoters) to enter the mutual fund industry in 1993, provided a wide range of choice to investors and more competition in the industry. Private funds introduced innovative products, investment techniques and investor-servicing technology. By 1994-95, about 11 private sector funds had launched their schemes.

Phase-IV Growth and SEBI Regulation - 1996-2004:

The mutual fund industry witnessed robust growth and stricter regulation from the SEBI after the year 1996. The mobilization of funds and the number of players operating in the industry reached new heights as investors started showing more interest in mutual funds.

Investors' interests were safeguarded by SEBI and the Government offered tax benefits to the investors in order to encourage them. SEBI (Mutual Funds) Regulations, 1996 was introduced by SEBI that set uniform standards for all mutual funds in India. Various Investor Awareness Programmes were launched during this phase, both by SEBI and AMFI, with an objective to educate investors and make them informed about the mutual fund industry.

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Phase-V Growth and Consolidation - 2004 Onwards:

The industry has also witnessed several mergers and acquisitions recently, examples of which are acquisition of schemes of Alliance Mutual Fund by Birla Sun Life, Sun F&C Mutual Fund and PNB Mutual Fund by Principal Mutual Fund. Simultaneously, more international mutal fund players have entered India like Fidelity, Franklin Templeton Mutual Fund etc. There were 29 funds as at the end of March 2015. This is a continuing phase of growth of the industry through consolidation and entry of new international and private sector players.

The mutual fund industry in India is growing at an exponential pace. The Indian mutual fund industry recorded an Average Assets Under Management (AAUM) of Rs. 23.16 trillion as on February 28, 2019. The AUM of the industry stood Rs. 5.09 trillion on February 28, 2009, which means the Indian mutual fund industry has registered a more than 4 ½ fold increase in a period of 10 years.

There are as many as 44 AMFI (Association of Mutual Funds in India) registered fund houses in India which together offer more than 2,500 mutual fund schemes. The wide array of funds often make it a little difficult for investors to choose the best scheme for them. To ease this process, we list out the 10 most popular mutual fund houses in India along with the 10 most popular schemes across all mutual fund categories namely equity, debt and hybrid.

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Indian Mutual Fund Industry’s Average Assets Under Management (AAUM) stood at ₹ 

38.89 Lakh Crore (INR 38.89Trillion)

Average Assets Under Management (AAUM) of Indian Mutual Fund Industry for the month of January 2022 stood at ₹ 38,88,571 crore.

Assets Under Management (AUM) of Indian Mutual Fund Industry as on January 31, 2022 stood at ₹38,01,210 crore.

The AUM of the Indian MF Industry has grown from ₹ 6.59 trillion as on January 31, 2012 to ₹38.01 trillion as on January 31, 2022 more than 5½ fold increase in a span of 10 years.

The MF Industry’s AUM has grown from ₹ 17.37 trillion as on January 31, 2017 to ₹38.01 trillion as on January 31, 2022, more than 2 fold increase in a span of 5 years.

The Industry’s AUM had crossed the milestone of ₹10 Trillion (₹10 Lakh Crore) for the first time in May 2014 and in a short span of about three years, the AUM size had increased more than two folds and crossed ₹ 20 trillion (₹20 Lakh Crore) for the first time in August 2017. The AUM size crossed ₹ 30 trillion (₹30 Lakh Crore) for the first time in November 2020. The Industry AUM stood at ₹38.01 Trillion (₹ 38.01 Lakh Crore) as on January 31, 2022.

The mutual fund industry has crossed a milestone of 10 crore folios during the month of May 2021.�

The total number of accounts (or folios as per mutual fund parlance) as on January 31, 2022 stood at 12.31 crore (123.1 million), while the number of folios under Equity, Hybrid and Solution Oriented Schemes, wherein the maximum investment is from retail segment stood at about 9.95 crore (99.5 million). 

A.Bank Sponsored

1. Joint Ventures - Predominantly Indian

• - BOI AXA Investment Managers Private Limited
• - Canara Robeco Asset Management Company Limited
• - SBI Funds Management Limited
• - Union Asset Management Company Private Limited (formerly Union KBC Asset Management Co. Pvt. Ltd)

2. Others

• - Baroda Asset Management India Limited (formerly known as Baroda Pioneer Asset Management Co. Ltd.)
• - IDBI Asset Management Limited
• - UTI Asset Management Company Ltd

B.Institutions

1. Indian

• - IIFCL Asset Management Co. Ltd.
• - LIC Mutual Fund Asset Management Limited

C.Private Sector

1. Indian

• - DSP Investment Managers Private Limited
• - Edelweiss Asset Management Limited
• - IDFC Asset Management Company Limited
• - IIFL Asset Management Ltd. (Formerly known as India Infoline Asset Management Co. Ltd.)
• - IL&FS Infra Asset Management Limited (CIN U65191MH2013PLC239438)
• - Indiabulls Asset Management Company Ltd.
• - ITI Asset Management Limited
• - JM Financial Asset Management Limited
• - Kotak Mahindra Asset Management Company Limited(KMAMCL)
• - L&T Investment Management Limited
• - Motilal Oswal Asset Management Company Limited
• - Navi AMC Limited
• - NJ Asset Management Private Limited
• - PPFAS Asset Management Pvt. Ltd.
• - quant Money Managers Limited
• - Quantum Asset Management Company Private Limited
• - Samco Asset Management Private Limited
• - Shriram Asset Management Co. Ltd.
• - Sundaram Asset Management Company Limited
• - Tata Asset Management Private Limited
• - Taurus Asset Management Company Limited
• - Trust Asset Management Private Limited
• - WhiteOak Capital Asset Management Limited

2. Foreign

• - BNP Paribas Asset Management India Private Limited
• - Franklin Templeton Asset Management (India) Private Limited
• - HSBC Asset Management (India) Private Ltd.
• - Invesco Asset Management (India) Private Limited
• - Mirae Asset Investment Managers (India) Pvt. Ltd.
• - Nippon Life India Asset Management Limited
• - PGIM India Asset Management Private Limited

3. Joint Ventures - Predominantly Indian

• - Aditya Birla Sun Life AMC Limited
• - Axis Asset Management Company Ltd.
• - HDFC Asset Management Company Limited (Corporate Identification Number - L65991MH1999PLC123027)
• - ICICI Prudential Asset Management Company Limited
• - Mahindra Manulife Investment Management Pvt Ltd (Formerly Mahindra Asset Management Company Pvt Ltd)

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Mutual funds typically have one or more investment objectives, such as:

1. Growth: To achieve capital appreciation by investing in stocks or other equity securities.
2. Income: To generate regular income through investments in fixed-income securities such as bonds and debentures.
3. Preservation of Capital: To preserve the investor's capital by investing in low-risk securities such as government bonds.
4. Diversification: To spread risk by investing in a variety of assets and industries.
5. Balance: To provide a balance of growth and income by investing in both equities and fixed-income securities.
6. Market Indexing: To track the performance of a specific market index, such as the S&P 500, by investing in the same securities as the index.

The advantages of investing in mutual funds include:

Diversification: Mutual funds invest in a basket of stocks, bonds, or other securities, reducing risk compared to investing in a single security.

Professional Management: Fund managers with expertise and resources are responsible for making investment decisions, monitoring the portfolio, and executing trades.

Liquidity: Mutual fund shares can be easily bought and sold, providing investors with the flexibility to access their money as needed.

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Affordability: Mutual funds often have low minimum investment requirements, making them accessible to a wide range of investors.

Convenience: With one purchase, investors can gain exposure to a diverse portfolio of securities, simplifying the investment process.

Potential for higher returns: Mutual funds have the potential to provide higher returns compared to savings accounts or money market funds, although past performance is not a guarantee of future results.

Transparency: Mutual funds are required to disclose their holdings and other information on a regular basis, providing investors with a clear picture of their investments.

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Tax Shelter: Some mutual funds are permitted by Government of India that launch equity linked tax saving schemes. Those who invest in such schemes get the benefit of rebate in income tax.

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Disadvantage of Mutual funds

1. Fees: Mutual funds charge management fees and other expenses, which can impact the overall return of the investment.

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• Market Risk: Like any investment, mutual funds are subject to market fluctuations and the value of an investment can go down as well as up.

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• Underperformance: Some mutual funds may underperform compared to the broader market or their benchmark index.

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• Lack of Control: As an investor in a mutual fund, you have limited control over the specific securities in the portfolio and the investment decisions made by the fund manager.

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• Complexity: With the large number of mutual funds available, it can be difficult to compare and select the right fund for your investment goals.

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Disadvantages of mutual funds

• Professional Management- Some funds don’t perform in the market, as their management is not dynamic enough to explore the available opportunity in the market.

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• Costs – The biggest source of AMC income is generally from the entry & exit load which they charge from investors, at the time of purchase. The mutual fund industries are thus charging extra cost under layers of jargon.

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• Dilution - Because funds have small holdings across different companies, high returns from a few investments often don't make much difference on the overall return.

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• Taxes- when making decisions about your money, fund managers don't consider your personal tax situation. For example, when a fund manager sells a security, a capital-gain tax is triggered, which affects how profitable the individual is from the sale.

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No guarantee: Mutual funds are not guaranteed or insured by the FDIC or any other government agency - even if you buy through a bank and the fund carries the bank's name. You can lose money investing in mutual funds.

STRUCTURE OF MUTUAL FUND

Sponsor:

Sponsor is the person who acting alone or in combination with another body corporate establishes a mutual fund. Sponsor must contribute atleast 40% of the net worth of the investment managed and meet the eligibility criteria prescribed under the SEBI (Mutual Funds) Regulations, 1996. The Sponsor is not responsible or liable for any loss or shortfall resulting from the operations of the schemes beyond the initial contribution made by it towards setting up of the Mutual Fund.

Trust:

The Mutual Fund is constituted as a trust in accordance with the provisions of the Indian Trusts Act, 1882 by the Sponsor. The trust deed is registered under the Indian Registration Act, 1908.

 Trustee:

Trustee is usually a company (corporate body) or a board of trustees (body of individuals). The main responsibility of the trustee is to safeguard the interest of the unit holders and inter-alia ensure that the AMC functions in the interest of investors in accordance with the SEBI (Mutual Funds) Regulations, 1996, the provision of the Trust Deed and the Offer Documents of the respective Schemes.

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Asset Management Company:

The AMC is appointed by the Trustee as the Investment manager of the Mutual Fund. The AMC is required to be approved by the SEBI to act as an asset management company of the Mutual Fund. At least 50% of the directors of the AMC are independent directors who are not associated with the Sponsor in any manner. The AMC must have a net worth of atleast 10 crore at all times.

Registrar and Transfer Agent:

The AMC is so authorized by the Trust Deed appoints the Registrar and Transfer Agent to the Mutual Fund. The Registrar process the application form, redemption requests and dispatches account statements to the unit holders.

Custodian:

A Custodian handles the investment back office of a Mutual Fund. Its responsibilities include receipt and delivery of securities, collection of income, distribution of dividends, and segregation of assets between schemes. The Sponsor of a Mutual fund cannot act as a Custodian to the Fund.

 Depository: Indian capital markets are moving away from having physical certificates for securities, to ownership of these securities in ‘dematerialized’ form with a Depository.

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https://cafinalshortnotes.blogspot.com/2015/11/mutual-fund-ca-final-sfm.html

TYPES OF MUTUAL FUNDS

• No matter what type of investor you are, there is bound to be a mutual fund that fits your style. It's important to understand that each mutual fund has different risks and rewards. In general, the higher the potential return, the higher the risk of loss. Although some funds are less risky than others, all funds have some level of risk - it's never possible to diversify away all risk. This is a fact for all investments.

Each fund has a predetermined investment objective that tailors the fund's assets, regions of investments and investment strategies. At the fundamental level, mutual funds can be classified on three parameters:

• On the basis of structure.
• On the basis of investment objective.
• On the basis of special schemes.

TYPES OF MUTUAL FUNDS

Type of Mutual Fund Schemes

Structure

Investment Objective

Special Schemes

Open Ended Funds

Close Ended Funds

Growth Funds

Income Funds

Balanced Funds

Money Market Funds

Industry Specific Schemes

Index Schemes

Sectoral Schemes

ON THE BASIS OF STRUCTURE

• Open ended Schemes
• Closed ended Schemes.

OPEN ENDED SCHEMES

• Open ended Schemes are schemes which offers unit for sale without specifying any duration for redemption.
• They sell and repurchase schemes on a continuous basis.
• The main feature of such kind of scheme is liquidity

CLOSED ENDED SCHEMES

• These are the schemes in which redemption period is specified.
• Once the units are sold by mutual funds, then any transaction takes place in secondary market only i.e stock exchange.
• Price is determined by forces of market.

ON THE BASIS OF GROWTH OBJECTIVE

• Growth funds
• Income funds
• Balanced Funds
• Money Market funds

GROWTH FUND

• The aim of growth funds is to provide capital appreciation over the medium to long- term. Such schemes normally invest a major part of their corpus in equities. Such funds have comparatively high risks

INCOME FUNDS

• Funds that invest in medium to long-term debt instruments issued by private

companies, banks, financial

institutions, governments and other entities belonging to various sectors (like infrastructure companies etc.) are known as Debt / Income Funds

BALANCED FUND

• These funds provide both growth and regular income as these schemes invest in debt and equity.
• The NAV of these schemes is less volatile as compared pure equity funds.

MONEY MARKET FUNDS

• Money market / liquid funds invest in short-term (maturing within one year) interest bearing debt instruments. These securities are highly liquid and provide safety of investment, thus making money market / liquid funds the safest investment option when compared with other mutual fund types.

ON THE BASIS OF SPECIAL SCHEMES

• Industry Specific Schemes
• Index Schemes
• Sectoral Schemes.

INDUSTRY SPECIFIC SCHEMES

• Industry Specific Schemes invest only in the industries specified in the offer document. The investment of these funds is limited to specific industries like Infotech, FMCG, Pharmaceuticals etc

INDEX SCHEMES

• In this schemes, the funds collected by mutual funds are invested in shares forming the Stock Exchange Index.
• Example- Nifty Index Scheme of UTI Mutual Fund and Sensex Index Scheme of Tata Mutual Fund.

SECTORAL SCHEMES

Sectoral funds are those mutual funds which invest in a particular sector of the

market, e.g. banking, information technology etc. Sector funds are riskier than equity diversified funds since they invest in shares belonging to a particular sector which gives them fewer diversification opportunities

OTHER SCHEMES

• Gilt Security Schemes
• Funds of Funds
• Domestic Funds
• Tax Saving Schemes.

The trends in Indian mutual funds

The trends in Indian mutual funds are shaped by various factors, including market conditions, investor behaviour, government policies, and technological advancements. Here are some key trends in Indian mutual funds:

• 1. Growth of Mutual Fund Assets
• Increase in Assets Under Management (AUM): The Indian mutual fund industry has witnessed consistent growth in AUM over the past few years. Both equity and debt funds have contributed significantly to the growth of the industry.
• Systematic Investment Plans (SIPs): The popularity of SIPs continues to rise, as they offer a disciplined and low-risk way of investing in mutual funds. Many investors prefer SIPs for long-term wealth creation.

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Shift Towards Equity Funds

• Higher Risk Appetite: With the growing optimism in the stock market, a significant number of investors are moving from traditional fixed-income instruments to equity-oriented mutual funds, attracted by higher potential returns.
• Equity ETFs and Index Funds: Exchange-traded funds (ETFs) and index funds are gaining popularity due to their low costs and transparency.

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• Focus on Tax Efficiency
• ELSS (Equity Linked Savings Schemes): ELSS funds, which offer tax benefits under Section 80C, have been increasingly popular among investors looking to save on taxes while benefiting from equity market returns.
• Long-Term Capital Gains Tax: Changes in tax regulations around long-term capital gains (LTCG) and short-term capital gains (STCG) taxes have also impacted investor behaviour.

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4.Technological Integration

Robo-Advisors: Automated investment platforms or robo-advisors are becoming increasingly common. These platforms use algorithms to manage investments based on the investor’s risk profile and financial goals.

Online Platforms and Apps: With the rise of digital tools, investors can easily track their investments, invest in mutual funds, and analyze their portfolio performance via apps and online platforms.

5. Focus on ESG (Environmental, Social, and Governance) Funds

Sustainable Investing: ESG-focused mutual funds are gaining traction as investors look for sustainable, socially responsible, and ethical investment opportunities.

Green Bonds and Funds: There is an increasing emphasis on green and impact investing, and funds are integrating ESG criteria into their investment strategies.

6. Diversification in Mutual Fund Categories

• Thematic and Sectoral Funds: Investors are increasingly opting for thematic and sector-specific mutual funds, such as those focusing on the technology, pharma, or infrastructure sectors, to capitalize on specific market trends.
• Debt and Hybrid Funds: As an alternative to equity funds, hybrid funds (which invest in both equities and debt) and debt funds (which invest in fixed-income securities) have attracted conservative investors seeking stable returns.

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• 7. Regulatory Changes

SEBI’s Guidelines: The Securities and Exchange Board of India (SEBI) has introduced several regulations aimed at improving transparency and governance in the mutual fund industry. These include the introduction of Total Expense Ratio (TER) caps and guidelines for fund manager performance.

Disclosure Norms: Increased transparency in terms of fund disclosures, such as the performance and risk profile of funds, has improved investor confidence.

• 8. Retail Investor Participation

Increased Retail Investment: Mutual funds have seen more retail investor participation, particularly with the rise of financial literacy and awareness. Platforms like mutual fund distributors, banks, and online brokers have made it easier for small investors to access the mutual fund market.

Demographic Shift: The younger generation, especially millennials, is showing increasing interest in mutual funds, particularly SIPs, as a long-term investment vehicle.

9. Improved Risk Management

• Risk-Based Fund Allocation: Asset management companies (AMCs) are providing more customized risk-based portfolios, allowing investors to select funds based on their risk tolerance.
• Volatility Management: In a volatile market, many investors are shifting towards safer, less volatile investment options such as debt funds and balanced funds to mitigate risks.

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Performance measurement of mutual fund

• Sharpe’s performance index
• Treynor's performance index
• Jensen’s performance index
• Fama's Decomposition of Return

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• Sharpe’s Performance Index, also known as the Sharpe Ratio, is a measure used to evaluate the risk-adjusted return of an investment portfolio. It quantifies the excess return per unit of risk (volatility), allowing investors to assess how well an investment compensates for the risk taken. The higher the Sharpe ratio, the better the risk-adjusted return.

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Interpretation:

• A higher Sharpe ratio indicates that the portfolio is providing higher returns for the same amount of risk.
• A lower Sharpe ratio suggests that the portfolio’s returns are not compensating adequately for the risks.
• If the Sharpe ratio is negative, it indicates that the risk-free rate is higher than the portfolio return, suggesting the portfolio is not providing enough return relative to the risk.

• Sharpe ratios above 1.0 are generally considered “good," as this would suggest that the portfolio is offering excess returns relative to its volatility. Having said that, investors will often compare the Sharpe ratio of a portfolio relative to its peers. Therefore, a portfolio with a Sharpe ratio of 1.0 might be considered inadequate if the competitors in its peer group have an average Sharpe ratio above 1.0.

• To calculate the Sharpe ratio, investors first subtract the risk-free rate from the portfolio’s rate of return, often using U.S. Treasury bond yields as a proxy for the risk-free rate of return. Then, they divide the result by the standard deviation of the portfolio’s excess return. Note that, in using the standard deviation, this formula implicitly assumes that the portfolio’s returns are normally distributed, which may not in fact be the case.

Treynor ratio

• The Treynor ratio was developed by Jack Treynor, an American economist who was one of the inventors of the Capital Asset Pricing Model (CAPM).
• The Treynor ratio, also known as the reward-to-volatility ratio, is a performance metric for determining how much excess return was generated for each unit of risk taken on by a portfolio.
• he Treynor Ratio, also known as the Reward-to-Systematic-Risk Ratio, is a measure used to assess the performance of an investment or portfolio relative to the systematic risk (market risk) it takes on. It is similar to the Sharpe Ratio but focuses on the risk that cannot be diversified away (systematic risk), rather than the total risk (which includes both systematic and unsystematic risk).

• Excess return in this sense refers to the return earned above the return that could have been earned in a risk-free investment. Although there is no true risk-free investment, treasury bills are often used to represent the risk-free return in the Treynor ratio.
• Risk in the Treynor ratio refers to systematic risk as measured by a portfolio's beta. Beta measures the tendency of a portfolio's return to change in response to changes in return for the overall market.

• If a portfolio has a negative beta, however, the ratio result is not meaningful. A higher ratio result is more desirable and means that a given portfolio is likely a more suitable investment. Since the Treynor ratio is based on historical data, however, it's important to note this does not necessarily indicate future performance, and one ratio should not be the only factor relied upon for investing decisions.

The following three portfolios provide the particulars given below

Portfolio Average annual return Standard deviation Correlation co-efficient

A 18 27 0.8

B 14 18 0.6

C 15 8 0.9

MARKET 13 12 ----

Risk free rate of interest is 9

• Rank this portfolio’s using Sharpe’s and Trenyor’s methods.

• Case study:
• You are given the following historical performance information on the capital market and a mutual fund
• Calculate the following risk adjusted return measures for the mutual fund:
• Reward-to-variability ratio
• Reward –t0-volatility ratio
• Comment on the mutual fund’s performance.

Jensen’s Performance index

The absolute risk adjusted return measure was developed by Michael 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 predicative ability. Successful predication of security price would enable the manager to earn the higher returns that the ordinary investor expects to earn in a given level of risk .

The Jensen's Alpha (often referred to simply as Jensen's Ratio) is a measure used to evaluate the performance of an investment portfolio relative to a benchmark index, adjusting for systematic risk. It quantifies the excess return that a portfolio generates compared to the return predicted by the Capital Asset Pricing Model (CAPM), given the portfolio's beta (systematic risk).

Meaning of Jensen’s Alpha:

• Jensen’s Alpha represents the abnormal return or excess return of a portfolio over the expected return predicted by the CAPM.
• A positive Jensen’s Alpha indicates that the portfolio has outperformed the benchmark after adjusting for systematic risk, whereas a negative value suggests underperformance.

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Ranking purpose , Jensen measure should be properly adjusted .each assets alpha value should be divided by its beta co-efficient

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Fama's Decomposition of Return

Fama's Decomposition is a method used to break down the sources of a fund’s or an asset's returns. It was developed by Eugene Fama, a prominent figure in financial economics, particularly for his work on the Efficient Market Hypothesis (EMH) and asset pricing.

In essence, Fama’s decomposition helps to analyze the sources of risk and return in a portfolio or asset to better understand the factors that influence its performance.

Fama's Decomposition Model

Fama's Decomposition divides a portfolio's total return into components that come from various factors. These factors can help in understanding the performance of an investment strategy relative to the market.

Fama’s model breaks down the returns into the following main components:

1. Market Return: The overall market return, often represented by a broad market index (e.g., the S&P 500 in the U.S. or the Nifty 50 in India). The market return is considered the benchmark for measuring the performance of any portfolio.
2. Risk-Free Return: This is the return on an asset with zero risk, commonly represented by short-term government securities, such as Treasury bills. The risk-free rate serves as the baseline return for comparing other investments.
3. Beta (Systematic Risk): Beta measures the sensitivity of the asset's returns to the overall market return. It represents the systematic risk that cannot be diversified away. A beta of 1 means the asset's returns move in line with the market, while a beta greater than 1 indicates the asset is more volatile than the market, and a beta less than 1 indicates it is less volatile.
4. Alpha (Excess Return): Alpha represents the excess return that a portfolio generates above the expected return based on its beta and the market return. Positive alpha indicates that the asset is performing better than expected, given the market's movements, while negative alpha suggests underperformance.

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Let’s say you have the following information:

• Portfolio Return (R_p) = 15%
• Risk-Free Rate (R_f) = 3%
• Market Return (R_m) = 10%
• Beta (β) = 1.2

Using Fama’s Decomposition:

Problem 1: Basic Calculation of Alpha and Beta

A mutual fund has the following details:

• Portfolio Return (Rp​) = 12%
• Risk-Free Rate (Rf​) = 4%
• Market Return (Rm) = 10%
• Beta (β) = 1.5

Questions:

1. Calculate the market-adjusted return using Fama’s Decomposition.
2. Calculate the portfolio's alpha (excess return) using Fama's Decomposition.

Problem 2: Evaluating a Portfolio’s Performance

A portfolio has the following details:

• Portfolio Return (Rp​) = 18%
• Risk-Free Rate (Rf​) = 5%
• Market Return (Rm​) = 15%
• Beta (β) = 0.8

Questions:

1. Calculate the expected return based on the market.
2. Calculate the alpha (excess return) of the portfolio.
3. Does the portfolio perform better or worse than expected? Justify your answer.

Problem 3: Impact of High Beta on Portfolio Performance

Consider a mutual fund with the following details:

• Portfolio Return (Rp​) = 20%
• Risk-Free Rate (Rf​) = 3%
• Market Return (Rm) = 15%
• Beta (β) = 2.0

Questions:

1. Calculate the expected return of the portfolio based on the market.
2. Calculate the portfolio’s alpha.
3. Interpret the result based on the portfolio’s beta.

Problem 4: Market Outperformance with High Beta

Given the following details for a mutual fund:

• Portfolio Return (Rp​) = 25%
• Risk-Free Rate (Rf) = 4%
• Market Return (Rm​) = 18%
• Beta (β\betaβ) = 1.7

Questions:

1. Calculate the expected return based on the market.
2. Calculate the portfolio’s alpha.
3. Interpret the portfolio's performance.