THEORY BASE
INTRODUCTION TO PORTFOLIO MANAGEMENT
The art of selecting the right investment policy for the individuals in terms of minimum risk and maximum return is called as portfolio management.
Portfolio management refers to managing an individual’s investments in the form of bonds, shares, cash, mutual
funds etc. so that he earns the maximum profits within the stipulated time frame.
Portfolio management refers to managing money of an individual under the expert guidance of portfolio managers.
In a layman’s language, the art of managing an individual’s investment is called as portfolio management.
Portfolio management is 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 against performance. Portfolio management is all about determining strengths, weaknesses, opportunities and threats in the
choice of debt vs. equity, domestic vs. international, growth vs. safety, and many other trade-offs encountered in
the attempt to maximize return at a given appetite for risk
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The Key Elements of Portfolio Management
Asset allocation
“The key to effective portfolio management is the long-term mix of assets.”
Asset allocation is based on the understanding that different types of assets do not move in concert, and some
are more volatile than others. Asset allocation seeks to optimize the risk/return profile of an investor by investing in a mix of assets that have low correlation to each other. Investors with a more aggressive profile can
weight their portfolio toward more volatile investments. Investors with a more conservative profile can weight
their portfolio toward more stable investments.
Diversification
The only certainty in investing is it is impossible to consistently predict the winners and losers, so the prudent
approach is to create a basket of investments that provide broad exposure within an asset class. Diversification
is nothing but spreading of risk and reward within an asset class. Because it is difficult to know which particular
subset of an asset class or sector is likely to outperform another, diversification seeks to capture the returns of
all of the sectors over time but with less volatility at any one time. Effective diversification takes place across
different classes of securities, sectors of the economy and geographical regions.
Rebalancing
Rebalancing is a method used to return a portfolio to its original target allocation at annual intervals. It is important for retaining the asset mix that best reflects an investor’s risk/return profile. Otherwise, the movements
of the markets could expose the portfolio to greater risk or reduced return opportunities.
For example, a portfolio that starts out with a 70% equity and 30% fixed-income allocation could, through an
extended market rally, shift to an 80/20 allocation that exposes the portfolio to more risk than the investor can
tolerate. Rebalancing almost always entails the sale of high-priced/low-value securities and the redeployment of
the proceeds into low-priced/high-value or out-of-favor securities. The annual iteration of rebalancing enables
investors to capture gains and expand the opportunity for growth in high potential sectors while keeping the
portfolio aligned with the investor’s risk/return profile.
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Types of Portfolio Management
Portfolio Management is further of the following types:
◾Active Portfolio Management:
As the name suggests, in an active portfolio management service, the portfolio managers are actively involved
in buying and selling of securities to ensure maximum profits to individuals.
◾Passive Portfolio Management:
In a passive portfolio management, the portfolio manager deals with a fixed portfolio designed to match the current market scenario.
◾Discretionary Portfolio management services:
In Discretionary portfolio management services, an individual authorizes a portfolio manager to take care of his
financial needs on his behalf. The individual issues money to the portfolio manager who in turn takes care of all
his investment needs, paper work, documentation, filing and so on. In discretionary portfolio management, the
portfolio manager has full rights to take decisions on his client’s behalf.
◾Non-Discretionary Portfolio management services :
In non-discretionary portfolio management services, the portfolio manager can merely advise the client what is
good and bad for him but the client reserves full right to take his own decisions.
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Need for Portfolio Management
Portfolio management presents the best investment plan to the individuals as per their income, budget, age and
ability to undertake risks.
Portfolio management minimizes the risks involved in investing and also increases the chance of making profits.
Portfolio managers understand the client’s financial needs and suggest the best and unique investment policy for
them with minimum risks involved. Portfolio management enables the portfolio managers to provide customized investment solutions to clients as per their needs and requirements
PREREQUISITES OF A GOOD PORTFOLIO
Stable Current Return:
Once investment safety is guaranteed, the portfolio should yield a steady current income. The current returns
should at least match the opportunity cost of the funds of the investor. What we are referring to here current income by way of interest of dividends, not capital gains.
Marketability:
A good portfolio consists of investment, which can be marketed without difficulty. If there are too many unlisted or inactive shares in your portfolio, you will face problems in encasing them, and switching from one investment to another. It is desirable to invest in companies listed on major stock exchanges, which are actively
traded.
Tax Planning:
Since taxation is an important variable in total planning, a good portfolio should enable its owner to enjoy a favorable tax shelter. The portfolio should be developed considering not only income tax, but capital gains tax,
and gift tax, as well. What a good portfolio aims at is tax planning, not tax evasion or tax avoidance.
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Appreciation in the value of capital:
A good portfolio should appreciate in value in order to protect the investor from any erosion in purchasing
power due to inflation. In other words, a balanced portfolio must consist of certain investments, which tend to
appreciate in real value after adjusting for inflation.
Liquidity:
The portfolio should ensure that there are enough funds available at short notice to take care of the investor’s
liquidity requirements. It is desirable to keep a line of credit from a bank for use in case it becomes necessary to
participate in right issues, or for any other personal needs.
Safety of the investment:
The first important objective of a portfolio, no matter who owns it, is to ensure that the investment is absolutely
safe. Other considerations like income, growth, etc., only come into the picture after the safety of your investment is ensured.
Investment safety or minimization of risks is one of the important objectives of portfolio management. There
are many types of risks, which are associated with investment in equity stocks, including super stocks. Bear in
mind that there is no such thing as a zero risk investment. Moreover, relatively low risk investment gives correspondingly lower returns. You can try and minimize the overall risk or bring it to an acceptable level by developing a balanced and efficient portfolio. A good portfolio of growth stocks satisfies the entire objectives outline
above
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Portfolio Manager
An individual who understands the client’s financial needs and designs a suitable investment plan as per his income and risk taking abilities is called a portfolio manager. A portfolio manager is one who invests on behalf of
the client.
A portfolio manager counsels the clients and advises him the best possible investment plan which would guarantee maximum returns to the individual. A portfolio manager must understand the client’s financial goals and
objectives and offer a tailor made investment solution to him. No two clients can have the same financial needs.
A portfolio manager is one who helps an individual invest in the best available investment plans for guaranteed
returns in the future.
Roles and responsibilities of a Portfolio manager:
◾A portfolio manager plays a pivotal role in deciding the best investment plan for an individual as per his income, age as well as ability to undertake risks. Investment is essential for every earning individual. One must
keep aside some amount of his/her income for tough times. Unavoidable circumstances might arise anytime and
one needs to have sufficient funds to overcome the same.
◾A portfolio manager is responsible for making an individual aware of the various investment tools available in
the market and benefits associated with each plan. Make an individual realize why he actually needs to invest
and which plan would be the best for him
◾A portfolio manager is responsible for designing customized investment solutions for the clients. No two individuals can have the same financial needs. It is essential for the portfolio manager to first analyze the background of his client. Know an individual’s earnings and his capacity to invest. Sit with your client and understand his financial needs and requirement.
◾A portfolio manager must keep himself abreast with the latest changes in the financial market. Suggest the
best plan for your client with minimum risks involved and maximum returns. Make him understand the invest6
ment plans and the risks involved with each plan in a jargon free language. A portfolio manager must be transparent with individuals. Read out the terms and conditions and never hide anything from any of your clients. Be
honest to your client for a long term relationship.
◾A portfolio manager ought to be unbiased and a thorough professional. Don’t always look for your commissions or money. It is your responsibility to guide your client and help him choose the best investment plan. A
portfolio manager must design tailor made investment solutions for individuals who guarantee maximum returns and benefits within a stipulated time frame. It is the portfolio manager’s duty to suggest the individual
where to invest and where not to invest? Keep a check on the market fluctuations and guide the individual accordingly.
◾A portfolio manager needs to be a good decision maker. He should be prompt enough to finalize the best financial plan for an individual and invest on his behalf.
◾Communicate with your client on a regular basis. A portfolio manager plays a major role in setting financial
goal of an individual. Be accessible to your clients. Never ignore them. Remember you have the responsibility
of putting their hard earned money into something which would benefit them in the long run.
◾Be patient with your clients. You might need to meet them twice or even thrice to explain them all the investment plans, benefits, maturity period, terms and conditions, risks involved and so on. Don’t ever get hyper
with them
◾Never sign any important document on your client’s behalf. Never pressurize your client for any plan. It is his
money and he has all the rights to select the best plan for himself
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SEBI COMPLIANCE
1. Portfolio Managers are registered and regulated under the SEBI (Portfolio Managers) Regulations, 1993.
SEBI vide notification dated August 11, 2008 deleted the word ‘Scheme’ from PMS Regulations. However, it is
seen that in some cases, portfolio managers still group portfolios in separate investment categories and term
them as ‘schemes’.
2. In order to bring about greater uniformity, clarity and transparency with regard to above issues, portfolio
managers are advised to ensure the following:
a) To ensure compliance with regulation 15(1A) of SEBI (Portfolio Managers) Regulations, 1993, it is clarified
that the first single lump sum investment amount received as funds or securities from clients should not be less
than ` 5 lakh.
b) To ensure compliance with regulation 14(2)(b)(iv) of SEBI (Portfolio Managers) Regulations, 1993, Portfolio
Managers shall disclose the performance of portfolios grouped by investment category for the past three years
as per the enclosed prescribed tabular format. Portfolio Managers shall also ensure that the disclosure document
is given to all clients along with the account opening form at least two days in advance of signing of the agreement. In order to ensure that the clients have access to updated information about the portfolio manager, portfolio managers shall place the latest disclosure document on their website, wherever possible.
c) Portfolio Managers shall not organize investment portfolios as ‘Schemes’ akin to Mutual Fund Schemes
while marketing their services to clients.
3. This circular is issued in exercise of powers conferred under section 11(1) of the Securities and Exchange
Board of India Act, 1992 read with the provisions of Regulation 39 of the SEBI (Portfolio Managers) Regulations, 1993, to protect the interests of investors in securities and to promote the development of, and to regulate
the securities market.
4. This circular is available on SEBI website at www.sebi.gov.in under the category “Legal Framework” and
under the drop down “Portfolio Managers
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CHAPTER 2
THEORITICAL BAGROUND
PORTFOLIO AND PORTFOLIO CONSTRUCTION
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can
also consist of non-publicly tradable securities, like real estate, art, and private investments. Portfolio manager
should construct an investment portfolio in accordance with the risk tolerance and their investing objectives of
the Investors. Investors can also have multiple portfolios for various purposes. It all depends on one's objectives
as an investor.
Factors to be considered when choosing investments to fill out a portfolio are
RISK TOLERANCE
A conservative investor should be given a portfolio with large-cap value stocks, broad-based market index
funds, investment-grade bonds, and a position in liquid, high-grade cash equivalents In contrast, a risk-tolerant
investor should add some small-cap growth stocks to an aggressive growth, large-cap growth stock position,
assume some high-yield bond exposure, and look to real estate, international and alternative investment opportunities for his or her portfolio. In general, an investor should be advised to minimize exposure to securities or
asset classes whose volatility makes them uncomfortable
TIME HORIZON
Similar to risk tolerance, investors should consider how long they have to invest when building a portfolio. Investors should generally be moving to a more conservative asset allocation as the goal date approaches, to protect the portfolio's principal that has been built up to that point.
For example, an investor saving for retirement may be planning to leave the workforce in five years. Despite the
investor's comfort level investing in stocks and other risky securities, the investor may want to invest a larger
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portion of the portfolio's balance in more conservative assets such as bonds and cash, to help protect what has
already been saved. Conversely, an individual just entering the workforce may want to invest their entire portfolio in stocks, since they may have decades to invest, and the ability to ride out some of the market's short-term
volatility
DIVERSIFICATION AND RISK MITIGATION
Diversification is a technique that reduces risk by allocating investments among various financial instruments,
industries, and other categories. It aims to maximize return by investing in different areas that would each react
differently to the same event; diversification is the most important component of reaching long-range financial
goals while minimizing risk
There are 2 types of Risk which can be classified on the basis of diversification they are

Undiversifiable
Also known as "systematic" or "market risk," undiversifiable risk is associated with every company.
Common causes are things like inflation rates, exchange rates, political instability, war, and interest
rates. This type of risk is not specific to a particular company or industry, and it cannot be eliminated or
reduced through diversification; it is just a risk that investors must accept.

Diversifiable
This risk is also known as "unsystematic risk" and it is specific to a company, industry, market, economy, or country; it can be reduced through diversification. The most common sources of unsystematic
risk are business risk and financial risk. Thus, the aim is to invest in various assets so that they will not
all be affected the same way by market events.
ASSET ALLOCATION
Asset allocation is an investment strategy that aims to balance risk and reward by apportioning a portfolio's assets according to an individual's goals, risk tolerance and investment horizon. The three main asset classes - equities, fixed-income, and cash and equivalents - have different levels of risk and return, so
each will behave differently over time.
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In general, stocks are recommended for holding periods of five years or longer. Cash and money market
accounts are appropriate for objectives less than a year away. Bonds fall somewhere in between. In the
past, financial advisors have recommended subtracting an investor's age from 100 to determine how
much should be invested in stocks.
For example, a 40-year old would be 60% invested in stocks. Variations of the rule recommend subtracting age from 110 or 120 given that the average life expectancy continues to grow. As individuals approach retirement age, portfolios should generally move to a more conservative asset allocation so as to
help protect assets that have already been accumulated
ALTERNATIVE INVESTMENT
An alternative investment is an asset that is not one of the conventional investment types, such as
stocks,bonds and cash. Most alternative investment assets are held by institutional investors or accredited,
high-net- worth individuals because of the complex nature and limited regulations of the investments. Alternative investments include private equity, hedge funds, and managed futures, real estate, commodities
& derivatives contracts.
SUSTAINABLE INVESTMENT
Sustainable, responsible and impact investing (SRI) is an investment discipline that considers environmental, social and corporate governance (ESG) criteria to generate long-term competitive financial returns and positive societal impact
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BEST INVESTMENT STRATEGIES
The best investing strategies are not always the ones that have the greatest historical returns. The best strategies
are those that work best for the individual investor's objectives and risk tolerance..
Best Investing Strategies: Fundamental Analysis
We begin with fundamental analysis because it is one of the oldest and most basic forms of investing styles.
Primarily used for researching and analyzing equities (individual stocks, rather than mutual fund selection),
fundamental analysis is a form of an active investing strategy that involves analyzing financial statements for
the purpose of selecting quality stocks.
Data from the financial statements is used to compare with past and present data of the particular business or
with other businesses within the industry. By analyzing the data, the portfolio manager may arrive at a reasonable valuation (price) of the particular company's stock and determine if the stock is a good purchase or not.
Best Investing Strategies: Technical Analysis
Technical analysis can be considered the opposite of fundamental analysis. Portfolio manager using technical
analysis (technical traders) often use charts to recognize recent price patterns and current market trends for the
purpose of predicting future patterns and trends. In different words, there are particular patterns and trends that
can provide the technical trader certain cues or signals, called indicators, about future market movements..
Best Investing Strategies: Value Investing
Mutual fund and ETF investors can employ the fundamental investment strategy or style by using value stock
mutual funds In simple terms, the value investor is looking for stocks selling at a "discount;" they want to find
a bargain. Rather than spending the time to search for value stocks and analyze company financial statements, a
mutual fund investor can buy index funds, Exchange Traded Funds (ETFs) or actively-managed funds that hold
value stocks.
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Best Investing Strategies: Growth Investing
As the name implies, growth stocks typically perform best in the mature stages of a market cycle when the
economy is growing at a healthy rate. The growth strategy reflects what corporations, consumers, and investors
are all doing simultaneously in healthy economies--gaining increasingly higher expectations of future growth
and spending more money to do it. Again, technology companies are good examples here. They are typically
valued high but can continue to grow beyond those valuations when the environment is right.
A nuanced version of growth investing can be found in the momentum investing strategy, which is a strategy of
capitalizing on current price trends with the expectation that momentum will continue to build in the same direction. Most commonly, and especially with mutual funds designed to capture the momentum investing strategy, the idea is to "buy high and sell higher." For example, a mutual fund manager may seek growth stocks that
have shown trends for consistent appreciation in price with the expectation that the rising price trends will continue.
Best Investing Strategies: Buy and Hold
Buy and hold investors believe "time in the market" is a more prudent investment style than "timing the market." The strategy is applied by buying investment securities and holding them for long periods of time because
the investor believes that long-term returns can be reasonable despite the volatility characteristic of short-term
periods. This strategy is in opposition to absolute market timing, which typically has an investor buying and
selling over shorter periods with the intention of buying at low prices and selling at high prices.
The buy-and-hold investor will argue that holding for longer periods requires less frequent trading than other
strategies. Therefore trading costs are minimized, which will increase the overall net return of the investment
portfolio.
Portfolios employing the buy and hold strategy have been called lazy portfolios because of their lowmaintenance, passive nature.
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PROCESS/METHODOLOGY
Constructing an investment portfolio requires a deliberate and precise portfolio-planning process that follows
five essential steps.
Step 1: Assess Current Financial Situation and Goals
Planning for the future requires having a clear understanding of an investor’s current situation in relation to
where they want to be. That requires a thorough assessment of current assets, liabilities, cash flow and investments in light of the investor's most important goals. Goals need to be clearly defined and quantified so that the
assessment can identify any gaps between the current investment strategy and the stated goals. This step needs
to include a frank discussion about the investor’s values, beliefs and priorities, all of which set the course for
developing an investment strategy.
Step 2: Establish Investment Objectives
Establishing investment objectives centers on identifying the investor’s risk-return profile. Determining how
much risk that an investor is willing and able to assume, and how much volatility that the investor can withstand, is key to formulating a portfolio strategy that can deliver the required returns with an acceptable level of
risk. Once an acceptable risk-return profile is developed, benchmarks can be established for tracking the portfolio’s performance. Tracking the portfolio’s performance against benchmarks allows smaller adjustments to be
made along the way.
Step 3: Determine Asset Allocation
Using the risk-return profile, an investor can develop an asset allocation strategy. Selecting from various asset
classes and investment options, the investor can allocate assets in a way that achieves optimum diversification
while targeting the expected returns. The investor can also assign percentages to various asset classes, including
stocks, bonds, cash and alternative investments, based on an acceptable range of volatility for the portfolio. The
asset allocation strategy is based on a snapshot of the investor’s current situation and goals, and is usually adjusted as life changes occur. For example, the closer an investor gets to his or her retirement target date, the
more the allocation may change to reflect less tolerance for volatility and risk.
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Step 4: Select Investment Options
Individual investments are selected based on the parameters of the asset allocation strategy. The specific investment type selected depends in large part on the investor’s preference for active or passive management. An
actively managed portfolio might include individual stocks and bonds if there are sufficient assets to achieve
optimum diversification, which is typically over $1 million in assets. Smaller portfolios can achieve the proper
diversification through professionally managed funds, such as mutual funds or with exchange-traded funds. An
investor might construct a passively managed portfolio with index funds selected from the various asset classes
and economic sectors.
Step 5: Monitor, Measure and Rebalance
After implementing a portfolio plan, the management process begins. This includes monitoring the investments
and measuring the portfolio’s performance relative to the benchmarks. It is necessary to report investment performance at regular intervals, typically quarterly, and to review the portfolio plan annually. Once a year, the investor’s situation and goals get a review to determine if there have been any significant changes. The portfolio
review then determines if the allocation is still on target to track the investor’s risk-reward profile. If it is not,
then the portfolio can be rebalanced, selling investments that have reached their targets, and buying investments
that offer greater upside potential.
When investing for lifelong goals, the portfolio planning process never stops. As investors move through their
life stages, changes may occur, such as job changes, births, divorce, deaths or shrinking time horizons, which
may require adjustments to their goals, risk-reward profiles or asset allocations. As changes occur, or as market
or economic conditions dictate, the portfolio planning process begins anew, following each of the five steps to
ensure that the right investment strategy is in place.
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For analyzing the risk capacity of the clients these ratios are used
1.Savings ratio:
The more you are able to save; you have more capacity to take risks. Usually 60%+ saving ratio is considered
to be very good.
2. Expense Coverage ratio:
High Net-worth compared to your Annual expenses is a healthy sign. Higher the ratio, higher the risk capacity.
3. Income Multiplier:
Higher net worth compared to annual income is sign of the investment career cycle. Better the multiplier, higher
the risk capacity.
4. Leverage ratio:
As mentioned previously, the lesser liabilities we have the better it is, Though sometimes it make more sense to
take loans specially in case of appreciating assets like education/home etc. Liabilities/ Assets are lower the better for risk capacity.
5. Liquidity ratio:
If you have high allocation to real assets, which are less liquid in nature. it makes it difficult to meet your financial needs in case of emergency. This should be captured in two forms. Financial Assets/ Total Assets & Financial Assets/ Liabilities, higher the ratios better it is for risk capacity.
6. EMI Coverage ratio:
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Total EMIs/ Take home Income should be measured to calculate the pressure of EMIs on financial health. The
lower the value better it is for risk capacity.
7. Income Stability:
This depends on how many households are earning members, if 2 people in family of 4 are earning it is better vs
1 person. There might be cases when all 4 are earning members especially in case of people in their 50s when
their kids also start earning. Their risk appetite increases as a household vs common philosophy that with age
risk capacity reduces.
C) ANALYSING PORFOLIO RETURNS
Portfolio returns come in the form of current income and capital gains. Current income includes dividends on
stocks and interest payments on bonds. A capital gain or capital loss results when a security is sold, and is equal
to the amount of the sale price minus the purchase price. The return of the portfolio is equal to the net of the
capital gains or losses plus the current income for the holding period. Unrealized capital gains or losses on securities still held are also added to the return to evaluate the holding period return of the portfolio. The portfolio
return is adjusted for the addition of funds and the withdrawal of funds to the portfolio, and is time-weighted
according to the number of months that the funds were in the portfolio. Below is the formula for calculating the
portfolio return for 1 year:
Time Weighted Adjustment of the Portfolio = (Added Funds × Number of Months in Portfolio / 12) - (Withdrawn Funds × Number of Months Withdrawn from Portfolio / 12)
Portfolio Return Formula
Portfolio Return = Dividends + Interest + Realized Gains or Losses + Unrealized Gains or Losses
Initial Investment + Time Weighted Adjustment of the Portfolio Return
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Realized gains (or losses) are gains or losses actualized by the selling of the securities, whereas unrealized gains
or losses are securities that are still owned but are marked to market to determine the portfolio's return.
A) Comparing Portfolio Returns
There are several ways of comparing portfolio returns with each other and with the market in general. A simple
comparison is to simply compare their returns. However, returns by themselves do not account for the risk taken. If 2 portfolios have the same return, but one has lower risk, then that would be the preferable, more efficient
portfolio.
There are 3 common ratios that measure a portfolio's risk-return tradeoff: Sharpe's ratio, Treynor's ratio, and
Jensen's Alpha.
Sharpe ratio
The Sharpe ratio (aka Sharpe's measure), developed by William F. Sharpe, is the ratio of a portfolio's total return minus the risk-free rate divided by the standard deviation of the portfolio, which is a measure of its risk.
The Sharpe ratio is simply the risk premium per unit of risk, which is quantified by the standard deviation of the
portfolio.
Risk Premium = Total Portfolio Return – Risk-free Rate
Sharpe Ratio = Risk Premium / Standard Deviation of Portfolio Return
The risk-free rate is subtracted from the portfolio return because a risk-free asset, often exemplified by the Tbill, has no risk premium since the return of a risk-free asset is certain.
Therefore, if a portfolio's return is equal to or less than the risk-free rate, then it makes no sense to invest in the
risky assets.
Hence, the Sharpe ratio measures the performance of the portfolio compared to the risk taken—the higher the
Sharpe ratio, the better the performance and the greater the profits for taking on additional risk.
Examples
Example—Calculating the Sharpe Ratio If a fund has a return of 12% and a standard deviation of 15%, and if
the risk-free rate is 2%, then what is its Sharpe ratio?
Solution:
Sharpe Ratio = (12% – 2%) / 15% = 10% / 15% = 66.7% (rounded)
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Treynor Ratio
While the Sharpe ratio measures the risk premium of the portfolio over the portfolio risk, or its standard deviation, Treynor's ratio, popularized by Jack L. Treynor, compares the portfolio risk premium to the systematic risk
of the portfolio as measured by its beta.
Treynor Ratio Formula
Treynor Ratio = Total Portfolio Return – Risk-Free Rate
Portfolio Beta
Note that since the beta of the general market is defined to be 1, the Treynor Ratio of the market equals its return minus the risk-free rate. The Treynor ratio measures the return per unit risk: it is higher with either higher
portfolio returns or lower portfolio betas.
Examples
Example—Calculating the Treynor Ratio
Case 1: If a portfolio has a return of 12% and a beta of 1.4, and if the risk-free rate is 2%, then what is its Treynor ratio?
Treynor Ratio = (12 – 2) / 1.4 = 10 / 1.4 = 7.14 (rounded)
Case 2: Same as Case 1, except that the portfolio Beta equals the market beta of 1:
Treynor Ratio = (12 – 2) / 1.0 = 10 / 1.0 = 10 (rounded)
Note that here we used whole numbers instead of percentages for the return and risk-free rate because it simplifies the math and because it makes no difference when comparing portfolios if the same method is used consistently. Also note that, in Case 2, the same return was achieved with lower risk, so that, therefore, would be a
more desirable portfolio.
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Jensen's Alpha (aka Jensen Index)
Alpha is a coefficient that is proportional to the excess return of a portfolio over its required return, or its expected return, for its expected risk as measured by its beta. Hence, alpha is determined by the fundamental values of the companies in the portfolio in contrast to beta, which measures the portfolio's return due to its volatility. Jensen's alpha (aka Jensen index), developed by Michael C. Jensen, uses the capital asset pricing model
(CAPM) to determine the amount of the return that is firm-specific over that which is due to market volatility as
measured by the firm's beta in relation to the market beta.
Jensen's Alpha = Total Portfolio Return – Risk-Free Rate – [Portfolio Beta × (Market Return – Risk-Free Rate)]
Jensen's alpha can be positive, negative, or zero. Note that, by definition, Jensen's alpha of the market is zero. If
the alpha is negative, then the portfolio is underperforming the market; thus, higher alphas are more desirable.
Examples
Example—Calculating Jensen's Alpha
Case 1:
•portfolio return = 12%
•market return rate = 8%
•beta = 1.4
•risk-free rate = 2%
Jensen's alpha = 12 – 2 – 1.4 × (8 – 2) = 10 – 1.4 × 6 = 10 – 8.4 = 1.6
Case 2:
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•beta = 1.0
Jensen's alpha = 12 – 2 – 1.0 × (8 – 2) = 10 – 1.0 × 6 = 10 – 6 = 4
Case 3:
•beta = 0.Jensen's alpha = 12 – 2 – 0.8 × (8 – 2) = 10 – 0.8 × 6 = 10 – 4.8 = 5.2
The 3 portfolios have the same return, but Case 3 achieves the return with the lowest volatility, and, therefore,
with lowest market risk among the 3 portfolios. Note also that in Case 2, a portfolio return that is 4% higher
than the market return was achieved with no more volatility due to systematic risk than the general market
BIBLIOGRAPHY
www.investopedia.com
www.wikipedia.com
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