INVESTMENT ANALYSIS AND PORTFOLIO MANAGEMENT (1) 111 (1).pptx

EXPECTATIONS FROM THE COURSE
 At the end of the course students will understand:-
 What are securities
 Investment markets and their functions.
 Investment media
 Investment companies,
 How to analyze risk and return
 How to analyze an investment
 How to make the valuation of shares and bonds.
 How to manage a portfolio of securities,
 Etc

COURSE PRE-REQUISITES
For a student to follow this course, one
must have done:
Accounting,
Financial Management,
Management of Financial Institutions and
Markets,
Statistics,
Mathematics,

REFERENCES
BOOK TITLE AUTHOR
Investments Mayo H.(2014)
Investment Analysis and Portfolio
Management
Cohen J., Zinbarg
E. (2011)
Investment Analysis and Portfolio Mgt Mittra, S. Gassen
(2010)

REFERENCES
BOOK TITLE AUTHOR
Security Analysis and Portfolio Management Dr. V.AAvandhani(2000)
Security Analysis, Principles and Techniques Benjamin Graham and David
L. Dodd
Investment Analysis and Portfolio Management Prasanna Chandra
Investments William F. Sharpe, Gordon J.
Alexander, Jeffery V. Bailey.
Essentials of investments (6th edition) Zvi Bodie, Alex Kane, Alan J.
Marcus (2007)
Capital markets –institutions and instruments Frank J. Fabozzi,Franco
Modigliani
Online references:
www.investopedia.com, nasdaq.com
www.TeachmeFinance.com

1. INTRODUCTION TO INVESTMENT PROCESS AND
FINANCIAL CONCEPTS
2. SECURITIES MARKETS
3. FINANCIAL PLANNING AND TAX
CONSIDERATIONS
4. RISK, RETURN & PORTFOLIO MANAGEMENT
5. INTRODUCTION TO CAPITALASSETS PRICING
MODEL
6. BOND AND STOCK VALUATION (Present value)
7. FUNDAMENTALAND TECHNICALANALYSIS
EFFICIENT MARKET HYPOTHESIS
8. INVESTMENT RETURNS AND AGGREGATE
MEASURES OF STOCK MARKETS
9. DERIVATIVES MARKET ANALYSIS
Course Topics

TOPIC ONE: INVESTMENT
PROCESS AND FINANCIAL
CONCEPTS

Introduction
Definition of investment concepts
Bonds ,
Stocks and
(Investment in the Bull and Bear
Markets)
Mutual funds.

1.1 INTRODUCTION TO SECURITIES
 DEFINITIONS
A SECURITY Is a financial instrument representing
financial value.
 Securities are tradable interests representing financial value.
 A financial instrument is a document that has monetary
value or represents a legally enforceable (binding)
agreement between two or more parties regarding a right
to payment of money.

A security
Traditionally, a security was a physical
document, such as a stock certificate or bond
certificate, that represented your investment in
that stock or bond, the term sometimes also
refers to derivatives such as futures and
options.
Recently, paper certificates are increasingly
being replaced by electronic documentation.

Examples of securities include stocks,
preferred shares, bonds, debentures, treasury
bills, options, futures, swap, right, warrant, a
note, or any other financial asset.
Securities are broadly categorized into:
1) Debt securities such as banknotes, bonds
and debentures.
2) Equity securities, such as common stocks;
3) Hybrid securities , such as preference
shares.
4) Derivative contracts,
such as forwards, futures, options and swaps.

Securities
 Debt securities- Debt securities include government
bonds, corporate bonds, CDs, municipal bonds , etc.
The interest rate on a debt security is to a large extent
determined by the perceived repayment ability of the
borrower; higher risks of payment default almost always
lead to higher interest rates.
 Equity securities- The holder of an equity is a
shareholder, owning a share, or fractional part of the issuer.
Unlike debt securities, which typically require regular
payments (interest) to the holder, equity securities are not
entitled to any payment.

Securities
 Hybrid securities -Combine some of the characteristics
of both debt and equity securities.
Examples of hybrid securities include-Preference shares,
convertibles, equity warrants, etc.
 Derivative instruments- are financial instruments
which derive their value from the value and characteristics
of one or more underlying entities such as an asset, or
interest rate. e.g Forwards, Futures , Swaps and
options.
A derivative is an instrument whose value depends on
the value of some underlying asset.

DEFINITIONS
 INVESTMENT- It involves the commitment of funds to
one or more assets to be held for some period in expectation
of some return in the future.
 Definition: The process of sacrificing something now for the
purpose of gaining something later.
 For example, when one buys shares on the stock market they
expect a return in the future of dividends.
 Funds invested arise from deferred (postponed/delayed)
consumption, that is invested, in anticipation of future
returns. (funds from savings and or borrowed funds).

Investment
Investment involves the movement of
funds from the surplus sector to deficit
sector for profitable purpose.
Investments could be made in financial
assets, like stocks, bonds, and similar
instruments or into real assets, like houses,
land, or commodities.

Risk
 Risk in finance is the uncertainty associated with any
investment.
 Risk is the possibility that the actual return on an
investment will be different from its expected return.
 Risk-In simple terms, is the probability that something
bad can happen.
 A vitally important concept in finance is the idea that
an investment that carries a higher risk has the
potential of a higher return.
Risk assessment is a highly quantitative process that
requires calculating the expected returns and total risk
involved.

INVESTMENT ANALYSIS
INVESTMENT ANALYSIS
Is the entire process of estimating risk
and return for a given investment.
Returns are profits or capital gain from
an investment.
Risks may include capital risk,
business risk, inflation risk, etc.

SECURITY ANALYSIS
 SECURITY ANALYSIS
is the entire process of estimating risk and return
for individual securities.
 Securities that have return and risk characteristics
of their own, in combination, make up a
portfolio.
 Security analysis is generally divided into -
fundamental analysis and technical analysis.

relies upon the
examination of fundamental business factors such
as,
 1.Economic analysis-studies Inflation,
government policies , etc
 2. Industry analysis –studies competition
markets, etc.
 3. Company analysis- considers the financial
statements, management of the firm, financial
ratios, etc, while

, focuses on price trends and
momentum.
 Technical analysis involves making decisions to
trade in securities by studying the trends / records
of past stock prices and the volume of trade.
 Technical analysts are sometimes called chartists.
 Quantitative analysis may use indicators from
both areas.

Investment process
The investment process describes how an
investor should go about making decisions
with regard to;
 what marketable securities to invest in,
 how extensive the investment should be, and
 when the investments should be made.

Investment decision steps
A five step procedure for making these
investment decisions forms the basis of
the investment process:
1) Set investment policy
2) Perform security or Investment analysis
3) Construct a portfolio
4) Revise the portfolio
5) Evaluate the performance of the portfolio

Investment process
1)Setting of investment policy this includes setting
of investment objectives. The investment policy
should have the specific objectives regarding the
investment return requirement and risk tolerance of
the investor.
2)Investment Analysis /Security analysis This step
involves examining investments and/or securities.
Most often two forms of analysis are used: technical
analysis and fundamental analysis.
 Technical analysis
 Fundamental analysis .

 Technical analysis is a trading discipline
employed to evaluate investments and identify
trading opportunities by analyzing statistical
trends gathered from trading activity, such as
price movement and volume.
 Fundamental analysis (FA) is a method of
measuring a security's intrinsic value by
examining related economic and financial
factors. ... The end goal is to arrive at a number
that an investor can compare with a security's
current price in order to see whether the
security is undervalued or overvalued

Investment process
3.) Portfolio construction
The third step in the investment process
is portfolio construction, which involves
identifying those specific assets in
which to invest, as well as determining
the proportions of the investor’s wealth
to put into each one. Here the issues of
selectivity, timing, and diversification
need to be addressed by the investor.

Investment process
 4. Portfolio revision. This step concerns the periodic
revision of the three previous stages.
 This is necessary, because over time investor with long-
term investment horizon may change his / her
investment objectives and this, in turn means that
currently held investor’s portfolio may no longer be
optimal and even contradict with the new settled
investment objectives.
 5. Measurement and evaluation of portfolio
performance. This the last step in investment
management process involves determining periodically
how the portfolio performed, in terms of not only the
return earned, but also the risk of the portfolio. It is
continuing process influenced by changes in
investment environment and changes in investor’s
attitudes as well.

CRITERIA FOR EVALUATION OF
INVESTMENTS
1. Rate Of Return
2. Risk
3. Duration
4. Cost Of Instrument / Security
5. Credibility
6. Marketability
7. Tax Shelter
8. Convenience
9. Liquidity

Return
 RETURN is the money generated by an
investment.
 Or RETURN is the profit or loss you have on
your investments, including incomes and
changes in value.
 Return can be expressed as a percentage and is
calculated by adding the income and the
change in value of the asset /instrument and
then dividing by the initial investment amount.

Rate of Return calculated cont...d
 Calculating the rate of return on an investment
= End of period wealth - beginning of period wealth
Beginning of period wealth
(multiply by 100 to get % return)
 Example
 Assume that ABC Corporation’s common stock was
selling for 180Frw per share at the beginning of the
year and for 200Frw at the end of the year and paid
dividends of 30frw per share during the year. Then the
rate of return on a ABC share for the year would be ?

Return cont……..d
ABC rate of return on investment
= (200+30) - 180 x 100%= 27.77778
%
180
So the rate of return on an investment in
shares of ABC Company is 28% .

Risk –systematic & unsystematic risk
In Finance risk is composed of systematic
& unsystematic risk.
Total risk= systematic risk +
unsystematic risk.
Systematic risk
Refers to that portion of total variability/
uncertainty in return caused by factors
affecting the prices of all securities.

Systematic risk
Economic, political, and social changes are sources
of systematic risk.
Systematic Risk is further subdivided into
Market Risk, (variation in returns caused by the
volatility of stock market)
Interest Rate Risk (, variation in costs of debt
and debt investments caused by interest rate
changes. Variation in bond prices due to change
in interest rate)
Purchasing Power Risk (Inflation results in
lowering of the purchasing power of money.

Unsystematic risk.
Unsystematic risk- is the portion/part of
total risks that is unique or specific to a
firm or an industry.
Factors such as firm management capability,
consumer preferences, raw material scarcity
and labour strikes cause unsystematic
variability of returns in a firm.

Unsystematic risk
Unsystematic risk factors are largely
independent of factors affecting
securities markets in general.
Business Risk
(Variability in Income caused by firm’s
Operating Conditions)
Financial Risk
(Variability in earnings due to the
presence of debt in Capital Structure)

Liquidity
 Liquidity is the term used to describe how easy it is to
convert assets to cash.
 In the case of securities it refers to how easy it is to
convert the security to cash.
 The market for a stock is said to be liquid if the shares
can be rapidly sold and the act of selling has little
impact on the stock's price.
 Generally, this translates to where the shares are
traded and the level of interest that investors have in
the company.
 Company stocks traded on the major exchanges can
usually be considered liquid.

Liquidity
Company stocks traded on the major
exchanges can usually be considered liquid.
One last aspect of liquidity is especially
important for investors: is the liquidity of
companies that one may wish to invest in.

In finance, a portfolio is a collection of
investments held by an institution or a
private individual.
The assets in the portfolio could include
stocks, bonds, options, warrants, gold
certificates, real estate, futures contracts,
production facilities, or any other item that is
expected to retain its value.
PORTFOLIO

Warrants are a derivative that give the
right, but not the obligation, to buy or
sell a security—most
commonly an equity—at a certain price
before expiration.
The price at which the underlying
security can be bought or sold is
referred to as the exercise price or
strike price.

An American Warrant can be
exercised at any time on or before
the expiration date, while European
warrants can only be exercised on
the expiration date.
Warrants that give the right to buy a
security are known as call warrants;
those that give the right to sell a
security are known as put warrants.

Warrants are in many ways similar to
options, but a few key differences
distinguish them.
Warrants are generally issued by the
company itself, not a third party, and
they are traded over-the-counter more
often than on an exchange. Investors
cannot write warrants like they can
options.

Unlike options, warrants are dilutive.
When an investor exercises
their warrant, they receive newly
issued stock, rather than already-
outstanding stock.
Warrants tend to have much longer
periods between issue and expiration
than options, of years rather than
months.

Warrants do not pay dividends or
come with voting rights. Investors are
attracted to warrants as a means of
leveraging their positions in a security,
hedging against downside (for
example, by combining a put warrant
with a long position in the underlying
stock), or exploiting arbitrage
opportunities.

 Covered warrants are issued by financial
institutions rather than companies, so no new
stock is issued when covered warrants are
exercised.
 Rather, the warrants are "covered" in that the
issuing institution already owns the underlying
shares or can somehow acquire them. The
underlying securities are not limited to equity, as
with other types of warrants, but may be
currencies, commodities, or any number of other
financial instruments.

Portfolio
When you own more than one security, you
have an investment portfolio. You build the
portfolio by buying additional stocks, bonds,
mutual funds, or other investments.
Your goal is to increase the portfolio's value
by selecting investments that you believe
will go up in price.

Portfolio management
 The art and science of making decisions about the
investment mix and policy. It attempts to
maximize return at a given appetite for risk.
 It can also be the process of managing the assets
of a mutual fund, including choosing and
monitoring appropriate investments and allocating
funds accordingly.
 Portfolio management – is the dynamic function
of evaluating and revising the portfolio in terms of
stated investor objectives.

• Portfolio management is the management of
various financial assets, which comprise the
portfolio. Owning a portfolio involves making
choices -- that is, deciding what additional
stocks, bonds, or other financial instruments to
buy; when to buy; what and when to sell; and
so forth. Making such decisions is a form of
management.
• The management of a portfolio is goal-driven.
For an investment portfolio, the specific goal is
to maximize portfolio return and at the same
time minimizing the portfolio risk by
diversification.

Identification of Objectives
Selection of Asset Mix
Formulation of Portfolio
Strategy
Selection of Securities
Portfolio Execution
Portfolio Revision
Performance Evaluation
Steps in Portfolio
Management
These steps are universal
and are applied in all
countries

Steps in Portfolio Management
i. Identification of portfolio objectives- It
involves consideration of the objectives of the
investor such as safety of investment. The
objectives are subject to constraints such as
liquidity , time, funds ,etc.
ii. Selection of portfolio asset mix- It is concerned
with the proportions of securities/assets in the
portfolio i.e shares , bonds, -stock-bond mix ,etc.
iii. Formulation of portfolio strategy- that is decide
on an active portfolio strategy or a passive
portfolio strategy.

Steps in Portfolio Management
iv. Selection of Securities: This is where the actual
choosing of which securities / assets will make
up the portfolio is made.
v. Portfolio execution: This involves implementing
the portfolio plan by buying and/ or selling
specified securities in given amounts.
vi. Portfolio revision: Prices of bonds and stocks or
other assets may change – resulting in a need to
change the proportions of the portfolio.
vii. Performance Evaluation : The performance of
a portfolio should be evaluated periodically.

Portfolio and diversification
According to Modern portfolio theory, you
can reduce your investment risk by
creating a diversified portfolio.
A diversified portfolio is one that includes
different types, or classes, of securities so
that at least some of them may produce
strong returns in any economic climate /
environment.

Bonds
A Bond, is a debt security. The authorized
issuer owes the holders a debt and, depending
on the terms of the bond, is obliged to pay
interest (the coupon) to use and/or to repay
the principal at a later date, termed as
maturity.
Interest is paid at fixed intervals (semi
annual, annual, sometimes monthly).

Each Bond instrument has three main features:
Maturity, coupon and principal.
 Maturity: Maturity of a bond refers to the date, on
which the bond matures, which is the date on which
the borrower has agreed to repay the principal.
Term-to-Maturity refers to the number of years
remaining for the bond to mature. The Term-to-
Maturity changes everyday, from date of issue of the
bond until its maturity. The term to maturity of a
bond can be calculated on any date, as the distance
between such a date and the date of maturity. It is
also called the term or the tenure of the bond.

Exercise
1. Each Bond instrument has three
main features. Describe those features
on both sides: investor and buyer.
2. Analyze the following statement:
“Therefore, in general, the longer the
time to maturity, the higher the
interest rate”.

Three main features of a bond
 Coupon: Coupon refers to the periodic interest
payments that are made by the borrower (who is
also the issuer of the bond) to the lender (the
subscriber of the bond). Coupon rate is the rate at
which interest is paid, and is usually represented
as a percentage of the par value of a bond.
 Principal: Principal is the amount that has been
borrowed, and is also called the par value or face
value of the bond. The coupon is the product of
the principal and the coupon rate.

Face Value/Par Value
The face value (also known as the par value or
principal) is the amount of money a holder will get
back once a bond matures.
 A newly issued bond usually sells at the par value.
Government bonds normally have a much greater
par value than Corporate bonds .
 When a bond trades at a price above the face
value, it is said to be selling at a premium. When a
bond sells below face value, it is said to be selling
at a discount.

Other bond features
The coupon is expressed as a percentage
of the par value.
 If a bond pays a coupon of 10% and its
par value is Rwf 1,000,000 then it'll pay
Rwf 100,000 of interest per year.
A rate that stays as a fixed percentage of
the par value like this is a fixed-rate
bond.

Other bond features
Another possibility is an fluctuating interest
payment, known as a floating-rate bond. In
this case the interest rate can be tied to
market rates through an index, such as the
rate on Treasury bills ,the LIBOR (London
Interbank offer Rate),etc.
A bond that matures in one year is much
more predictable and thus less risky than
a bond that matures in 20 years.

Other bond features
Therefore, in general, the longer the time
to maturity, the higher the interest rate.
Also, all things being equal, a longer term
bond will fluctuate more than a shorter
term bond.
Issuer The issuer of a bond is a crucial
factor to consider, as the issuer's stability is
your main assurance of getting paid back.
For example, a government bond is far
more secure than any corporation.

Other bond features
Government default risk (i.e chance of the debt
not being paid back) is extremely small - so
small that government securities are known as
risk-free assets.
The reason is that a government will always be
able to bring in future revenue through
taxation.
However ,the debt of many developing
countries, does carry substantial risk. Some,
countries / governments can default on their
payments.

Other bond features
A company, on the other hand, must make
profits revenue, which is not guaranteed.
The added risk for investors in companies
means corporate bonds must offer a higher
yield in order to attract investors.
In addition to the credit quality of the
issuer, the priority of the bond is a
determiner of the probability that the
issuer will pay you back your money.

Other bond features
The priority indicates your place in line
should the company default on payments.
If you hold an unsubordinated (senior)
bond if the company defaults, you will be
first in line to receive payment from the
liquidation of its assets.
On the other hand, if you own a
subordinated (junior) debt security,
you will get paid out only after the senior
debt holders have received their share.

Different types of bonds
Bonds are issued by public authorities,
credit institutions, and companies in the
primary markets.
Bonds can be classified based on the
issuer as follows:
Government bond/Treasury bond –
these are issued by the Government.

Corporate bond- these are issued by
companies. The corporate bonds have a
higher interest rate than the government
bonds.
Municipal bonds -Issued by municipalities.
Municipal bonds can be issued by states,
provinces, cities, and other political sub-
divisions (e.g., districts, etc).

Bonds issued in the local market and
denominated in local currency are
domestic bonds.
International bonds -these types of
bonds are issued within a market that is
foreign to the issuer's home market.
1. Foreign bonds
2. Euro bonds
3. Global bonds

1)Foreign bond –It refers to bond issued and
denominated in the currency of a country
where it is issued but issued by a foreign (
gov’t or company).
In issuing foreign bonds, the issuer must abide
by the rules and regulations imposed by the
government of the country in which the
bonds are issued. Compliance may be
relatively easy or difficult, depending on the
country involved.

A foreign bond is underwritten by a syndicate
composed of members from a single country,
sold principally within that country, and
denominated in the currency of that country.
One of the main advantages of purchasing
foreign bonds is the opportunity to obtain
international diversification of the default
risk of a bond portfolio without having to be
concerned about foreign exchange
fluctuations.

Example: An example of such a bond is
the samurai bond, which is a yen-
denominated bond issued in Japan by an
American company.
Other foreign bonds include, Bulldog
bonds which are bonds denominated in
British pounds and issued in Britain by
non British companies or government.

Yankee bonds are foreign bonds
denominated in U.S dollars issued in the U.S
by non US company or government.
2)Eurobonds: A Eurobond refers to any
bond that is denominated in a currency
other than that of the country in which it
is issued.
Bonds in the Eurobond market are
categorized according to the currency in
which they are denominated.

The definition of the Eurobond market
can be confusing because of its name.
Although the euro is the currency used
by countries participating in European
Union countries, Eurobonds refer neither
to the European currency nor to a
European bond market.
As an example, a Eurobond denominated
in Japanese yen but issued in the U.S.
would be classified as a euro yen bond.

Another example, a bond issued by a U.S
corporation that is denominated in Japanese
yen (or even in U.S dollars) and sold in
Europe would also be referred to as a
Eurobond. Because it is not denominated in
the currency of the country it is issued in.
A Eurobond is a bond that is issued in a
foreign market and denominated in currency
different from where it is issued.

Convertible bonds is another variation
of corporate bonds, which enable the
holder to convert the bond into stock at
redemption.
Callable bonds which allow the issuing
company/government the right (but not
obligation) to (buy back) redeem a bond
before its maturity.

Puttable Bonds These allow the holder of a
puttable bond the right (but not an obligation)
to seek redemption (sell) from the issuer at
any time before the maturity date.
N.B. All the above are related to the
redemption of bonds.
Zero-Coupon Bonds
This is a type of bond that makes no coupon
payments but instead is issued at a
considerable discount to par value.

For example, if you take a zero-coupon bond
with a 10,000,000Rwf par value and 10
years to maturity which is trading at
6,000,000Rwf; you'd be paying
6,000,000Rwf today for a bond that will be
worth 10,000,000 in 10 years.
Floating Rate Bonds In some bonds, fixed
coupon rate to be provided to the holders is
not specified.

Instead, the coupon rate keeps fluctuating
from time to time, with reference to a
benchmark rate.
Such types of bonds are referred to as
Floating Rate Bonds.
Bond rating: The bond rating system helps
investors determine a company's credit risk.
A bond rating is like the report card for a
company's credit rating.

Bond rating
Blue-chip firms, which are safer
investments, have a high rating, while
risky companies have a low rating.
The different bond rating scales from
the major rating agencies in the U.S.
include Moody's, Standard and Poor's
(S&P )and Fitch Ratings.

Bond rating
Bond Rating by
Grade Risk
Moody's S&P/ Fitch
Aaa AAA Investment Highest Quality
Aa AA Investment High Quality
A A Investment Strong
Baa BBB Investment Medium Grade
Ba, B BB, B Junk Speculative
Caa/Ca/C CCC/CC/C Junk
Highly
Speculative
C D Junk In Default

Different types of stocks
 Common stocks: This represents a commitment
on the part of a corporation to pay periodically
whatever its board of directors deems appropriate
as a cash dividend.
 Although the amount of cash dividends to be paid
during the next year is subject to some
uncertainty, it is generally relatively easy to
accurately predict.
 However, the amount for which a stock can be
bought or sold varies considerably, making the
annual return difficult to accurately predict.

• Common shares represent ownership in a
company and a claim (dividends) on a
portion of profits.
• Common stock investors get to vote the
board members, who oversee the major
decisions made by management.
• Preferred stock- is like perpetual bond. A
given fixed amount(Dividend) is to be paid
each year by the issuer to the investor.

This amount may be stated as a percent of the
stock’s par value (for example, 8% of
200Frw), meaning 16Frw per year) or
directly as a figure (for example, 20 Frw per
year).
Because the security is a stock, such
payments are called dividends instead of
interest and hence do not qualify as a tax-
deductible expense for the issuing
corporation.

• Preferred shareholders always receive
their dividends first before common
stock holders.
• In the event of liquidation, preferred
shareholders are paid off before the
common shareholder (but still after
debt holders).
•

Participating preferred stock: This
entitles the holder to receive extra
dividends when earnings permit. (In
addition to the fixed dividends entitled).
Convertible preferred stock: these may,
at the option of the holder, be converted
into another security (usually the firm’s
common stock) on stated terms.

Cumulative preference stock: A
cumulative preferred requires that if a
company fails to pay any dividend or any
amount below the stated rate, it must make
up for it at a later time.
Dividends accumulate with each passed
dividend period, which can be quarterly,
semi-annually, or annually.

Non cumulative preference stock:
The Dividend for this type of preferred
stock will not accumulate if it is unpaid.
For noncumulative or straight preferred
stock any dividends passed are lost
forever if not declared.

Bull and Bear markets
The terms bull market and bear market
describe upward and downward market
trends, respectively, and can be used to
describe either the market as a whole or
specific sectors and financial securities.
Bull Market: A bull market is associated
with increasing investor confidence, and
increased investing in anticipation of future
price increases (capital gains).

 If an investor is optimistic and believes that
stocks will go up, he or she is called a "bull" and
is said to have a "bullish outlook“.
 A bullish trend in the stock market often begins
before the general economy shows clear signs of
recovery.
 Bear market: is a general decline in the stock
market over a period of time. It is a transition
from high investor optimism to widespread
investor fear and pessimism.

This is a market condition in which the
prices of securities are falling, and there is
widespread pessimism causes the negative
sentiment to be self-sustaining. The
investors anticipate losses in a bear market.
If an investor is not optimistic and believes
that stocks will go down, he or she is said to
have a “bearish outlook”.

88
Someone who is bullish believes prices
are going to rise.
Someone who is bearish believes
prices are going to fall.
We can tailor our risk exposure to any
points we wish along a bullish/bearish
continuum.

89
FALLING PRICES FLAT MARKET RISING PRICES
EXPECTED EXPECTED EXPECTED
BEARISH NEUTRAL BULLISH
Increasing bearishness Increasing bullishness

Mutual Funds- Definition
A Mutual fund is made up of a pool of funds
collected from many investors for the
purpose of investing in securities such as
stocks, bonds, money market instruments
and similar assets.
OR A mutual fund is a professionally
managed type of collective investment that
pools money from many investors to buy
stocks, bonds, short-term money market
instruments, and/or other securities.

Mutual Fund- Features
A mutual fund's portfolio is structured and
maintained to match the investment
objectives stated in its list.
In the United States, a mutual fund is
registered with the Securities and Exchange
Commission (SEC) and is over seen by a
board of directors (if organized as a
corporation) or board of trustees (if organized
as a trust).

Mutual fund features
The board of a mutual fund is charged with
ensuring that the fund is managed in the best
interests of the fund's investors and with
hiring the fund manager and other service
providers to the fund.
The fund manager, also known as the fund
sponsor or fund management company,
trades (buys and sells) the fund's
investments in accordance with the fund's
investment objective.

Mutual fund features
A fund manager must be a registered
investment advisor.
To invest in a mutual fund, you have to buy
shares to become a shareholder of the fund.
Mutual funds invest their owners' money in
securities.
Each investor owns shares, which represent
a portion of the holdings of the fund.

Mutual fund- features
 A Mutual fund is also referred to as an open –
end investment company.
 Because it is characterized by the continual
selling to its members and the public and
redeeming of its shares.
Open-end investment company: The more
formal name for a mutual fund, which derives
from the fact that it continuously offers new
shares to investors and redeems them (buys
them back) on demand.

In other words, the mutual fund does not
have a fixed capitalization. It sells its
shares to the investing public whenever it
can at their net asset value per share, and
it stands ready to repurchase these shares
directly from the investment public for
their net asset value per share.
Mutual funds sell their shares to the
investing public and their members at the
Net Asset Value (NAV).

NAV=Market value of portfolio-Liabilities
Number of shares outstanding
For example a mutual fund with 10M shares
outstanding and has a portfolio value of
215M and liabilities of 15M.
NAV= $215,000,000 -$15,000,000 = $20
10,000,000
Therefore the mutual fund shares will be
sold at $20 each.

Investors can choose different funds based
on their risk-taking profile:
Stock funds invest more heavily in stocks
and have ups and downs over time;
Bond funds offer stable current income;
and
Money market funds (investing in short-
term debt) ensure that the invested principal
does not decline in value in the short term.

 A fund pays out nearly all of the income it
receives over the year to fund owners in the form
of a distribution.
 You can make money from a mutual fund in 3
ways:
1) Income is earned from the return on securities
–like dividends on stocks and interest on bonds.
2) If the fund sells securities that have increased in
price, the fund has a capital gain. Most funds also
pass on these gains to investors in a distribution.

3) If the mutual fund holdings (shares)
increase in price .If the fund's shares
increase in price you can then sell your
mutual fund shares for a profit.
Funds will also usually give you a choice
either to receive a cheque for distributions
or to reinvest the earnings and get more
shares.

Mutual Funds features
Mutual funds state specific investment
objectives in their prospectuses.
For example, the main types of objectives are
 Growth,
 balanced,
 income , and
 industry-specialized funds.
In general the above show the types of
mutual funds based on investment objective.

Types of mutual funds
1.)Growth mutual fund- these funds
typically possess diversified portfolios of
common stocks in the hope of achieving
large capital gains for their shareholders.
Most growth funds offer higher potential of
capital appreciation but usually at above-
average risk and little or no dividend payout
expected soon since such companies are in
an expansion phase.

2.) Balanced Mutual fund – these generally
holds a portfolio of diversified common stocks,
preferred stocks, and bonds with the hope of
achieving capital gains and dividend and
interest income, while at the same time
conserving the principal.
 A balanced fund is geared toward investors who
are looking for a mixture of safety, income and
modest capital appreciation. The amounts that
such a mutual fund invests into each asset class
usually must remain within a set minimum and
maximum.

3.)The industry-specialized mutual funds –
These specialize in investing in portfolios of
selected industries;
 such a fund appeals to investors who are
extremely optimistic about the prospects for
these few industries and are willing to assume
the risks associated with such a concentration of
their investment money.
 Examples of industry specialized mutual funds-
could be in finance, technology, health, etc.

4.) Income funds concentrate heavily on high
interest and high dividend yielding securities.
It is common for income funds to also be
referred to as bond funds or fixed income
funds.
Bond funds vary also in the average duration of
their holdings.
Portfolios with low durations are significantly
less sensitive to changes in interest rates than
those with high durations.

Types of Stock / equity Funds
A.) Large Cap equity funds: Primarily invests in "Blue-chip"
companies - large, well-known industrials, utilities,
technology, and financial services companies with large
market capitalization.
 Large cap stocks are perceived to be less risky than the
smaller capitalized companies.
B.) Mid Cap: Primarily invests in companies whose market
capitalization is smaller than large caps but larger than small
caps.
 Mid caps are generally considered more risky than large cap
stocks but have a higher return expectation.

Types of Stock Funds
C.) Small Cap stock funds: Primarily invests
in emerging companies, thought to have
potential for future growth and profit.
Small caps are generally considered the
riskiest stocks compared to larger
capitalized firms but carry the expectation
of higher returns.
Small cap funds are subject to greater
volatility than those in other asset
categories.

Advantages of mutual funds
1.) Professional investment management
Often investors lack the education,
background, time, foresight, resources, and
temperament to carry out the proper handling
of a portfolio.
Mutual funds are managed by professional
portfolio managers who devote their full time
to the carrying out of the fund’s investment
objectives as specified in its prospectus.

2.) Diversification -large amounts of
money entrusted to the fund enable it to
be diversified in investments across
industry and security types (that is,
common stocks with various prospects,
preferred stocks, and bonds) to an extent
not possibly achieved by the average
investor. When investing in a mutual
fund, an investor is actually investing
in numerous securities.

3.)Liquidity-that is, shares can be readily
converted into cash, because the company
stands ready to redeem its outstanding
shares.
4.) Lower brokerage commissions - than an
individual small investor.
5.) Ability to participate in investments that
may be available only to larger investors.

(large Numbers of investors and amounts
readily available to invest e.g in bonds).
6.) Service and convenience- the investors
can leave much of the inconvenience of
managing their investments to the mutual
fund.
7.)Small and unsophisticated investors can
also invest in securities through mutual
funds .

Disadvantages of mutual funds
1) Less predictable income-the income for
members of the mutual fund is dependent
on how the mutual fund is managed.
2) No opportunity to customize- An
individual in a mutual fund is not able to
choose their investments individually, e.g
to buy which stocks or bonds.

MUTUAL FUND IN RWANDA
 An example of a mutual fund in Rwanda is the
Rwandan Diaspora Mutual Fund (RDMF).
 The former Governor of the Central Bank (BNR),
Mr.Francois Kanimba, officially approved the
Rwanda Diaspora Mutual Fund and licensed it to
operate in December 2009.
RDMF VISION
1.)To act as a pool of investments from Rwandans
in Diaspora together for collective investments in
Rwanda.

Mutual Fund in Rwanda
RDMF MISSION
1.)To promote the financial well being of the
Rwandan Diaspora while participating in the
socio-economic growth of the motherland;
2.)To create attractive investment strategies
and diversify portfolios
3.)To ensure effective participation to the
fund of the Rwandan Diaspora communities
around the world.

RDMF OBJECTIVES
Mobilize funds to invest in Rwanda;
Mobilize funds from foreign investors;
Tap the various opportunities available
in Rwanda;
Diversify investments and minimize
the risk;
Involve Rwandan Diaspora in the socio-
economic growth of their Country.

RDMF INVESTMENT OBJECTIVES
The Fund has three primary objectives are:
1. Stability (preservation of the principal);
2. Growth (increased value of principal over
time); and
3. Income (generating a stream of payments).

PROFILE OF TYPICAL INVESTORS
IN RDMF
-Families of all levels, children,
students, low and mid-income levels as
well as high income people planning
for the future;
-Physical and moral persons seeking for
domestic investment opportunities
through collective investment schemes.

Monthly income groups (civil
servants, private sector, workers at
home and abroad, business people,
students at all levels, minors,..).
Explain Hedge funds REITs ,ETFs
as used in investment Finance.
(Homework)

sit: www.LearningPresentation.com 3
vi
Step 1: Determine Where You Are Financially
Step 2: Set Goals
Step 3: Develop A Plan
Step 4: Monitor Your Progress
Financial planning steps

•
•
Calculating Your Net Worth
Analyzing Your Cash Flow
4
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Step 1: Determine Where
You Are Financially

5
Calculating Your
Net Worth
Net worth = what’s left
after you subtract your
liabilities from your assets

6
Analyzing Your
Cash Flow
• Assessing your cash flow will:
• Indicate your ability to save
• Let you size up your standard of living
• Indicate if you're living within or beyond
your means
• Highlight problem areas

Set Goals
7
Step 2:
• Questions to be addressed before
setting goals
• How long will you continue to work?
• What will happen with your income -
will it remain the same, rise, or fall?
• What will happen with tax rates?

Set Goals
8
Step 2:
What investment rates can you
reasonably expect?
• What about the rate of inflation?
How much involvement do you wish to
have in managing your investments?

Short-Term
Goals
9
• Pay off credit card and consumer debt
• Start savings plan
• Set aside cash for a contingency fund
equaling 3 months' expenses
• Acquire additional term life insurance
• Acquire individual disability insurance

Medium-
Term Goals
10
• Start college savings plan
• Diversify investment portfolio
• Convert term life insurance policy to
cash-value policy
• Contribute maximum to 401 (k) plan and
IRA

Long-Term
Goals
11
• Purchase retirement property
• Retire at age 62
• Maintain pre-retirement standard
of living during retirement

•
•
•
Flexibility
Liquidity
Minimization of Taxes
12
Step 3:
Develop Your Plan

You need a plan that's flexible
enough to change with your
circumstances throughout the
major and minor
experience.
life events you
13
Flexibility

Most financial advisors
recommend that you have funds
available that are equivalent to 3
to 6 months of your expenses.
Appropriate locations for these
funds are checking, savings, and
money market accounts.
14
Liquidity

Minimizing taxes must serve as
a means to meet your objectives;
it isn't an end in itself.
An effective plan will minimize
both income
taxes.
taxes and estate
15
Minimization
of Taxes

16
Step 4:
Monitor Your Progress
Here are the general questions to
ask:
• Have your financial goals stayed the
same?
• Are you meeting your budget?
Are you earning the investment rates
of return you anticipated?

17
Step 4:
Monitor Your Progress
• To what degree is inflation affecting
your finances?
• Has your tax situation changed?

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Source :
Ernst & Young’s Personal Financial
Planning Guide

TOPIC 4: RISK, RETURN AND
PORTFOLIO MANAGEMENT

 One of the major advances in the investment
field during the past few decades has been the
recognition that the creation of an optimum
investment portfolio is not simply a matter of
combining numerous unique individual
securities that have desirable risk-return
characteristics.
 Specifically, it has been shown that an investor
must consider the relationship among the
investments to build an optimum portfolio
that will meet investment objectives.

 The combination of securities which will give
maximum return with minimum risk (optimum
portfolio) is what we call “Portfolio management”.
 The object of the portfolio management is to
provide maximum return on the investments by
taking only optimum risk. To achieve these
objectives, the portfolio manager should invest
in diversified securities and see that the
coefficient of correlation between these
securities is as less as possible (only then the
portfolio will be able to reduce the risk). This is the
foundation of portfolio management.

The portfolio manager should follow the
following principles to further strengthen his
targets of higher returns and optimum risk:
The first principle suggests that investment
should be made only in those securities
which are fundamentally strong: The
strength of a security depends upon three
strengths:
1. The strength of the company;
2. The strength of the industry, and
3. The fundamentals of the economy.

Strength of the Company
The strength of the company depends
upon various factors or fundamentals like:
1. Intelligent, dedicated and motivated
human resources;
2. Management having positive values
and vision;
3. Policy regarding encouraging R&D;
4. Integrity of promoters, and Long range
planning for profits.

Strength of the Industry
The strength of the industry depend upon
the following fundamentals:
1. The product’s consumer surplus that the
product provides to its users,
2. Various possible alternative uses of the
product, and
3. Availability (rather we should say non-
availability of the substitutes).
The portfolio manager should see that
most of the fundamentals are favorably
placed.

Strength of the Economy
 Economy, here, means national economy. By
fundamentals of the economy we mean
1. Recession/boom; Tax policy; Monetary policy;
Budgetary policies;
2. Stability of government;
3. Possibility of war and its impact on economy;
4. Closed/open economy and finally;
5. The government’s attitude towards business
houses.

 The second principle suggests that the portfolio
should be reviewed continuously and if need be, revised
immediately. The Fundamentals of the company,
industry and economy keep on changing. Accordingly,
the portfolio should be revised according to emerging
situations.
 For example, in case of monsoon failure, investments
should move from fertilizer companies to irrigation
companies, in case some sick-minded person takes
over as CEO of the company, perhaps desired step will
be to disinvest the securities of the company, in case
cheaper substitutes have emerged for any industry’s
product, better move to some other industry, etc.

Two points regarding the second
principle
1. Sometimes, after making the investment in some
securities, portfolio manager realizes that his
decision of investing in that security is wrong, he
should not wait for happening of some event which
will make his decision as a right one (if there is some
loss on that investment, he should not even wait for
breakeven).
Rather he should move immediately liquidate his
position in that security. Actually no portfolio
manager has ever made 100 % correct decisions.

2. Do not bother much about
transaction cost related to
reorganization of the portfolio.
Consideration of such small costs
generally result in heavy losses or
foregone opportunities of earning
profit.

 Before presenting portfolio theory, we need to
clarify some general assumptions of the theory.
This includes not only what we mean by an
optimum portfolio but also what we mean by
the terms risk aversion and risk.
 One basic assumption of portfolio theory is
that as an investor you want to maximize the
returns from your total set of investments for a
given level of risk. To adequately deal with
such an assumption, your portfolio should:

Include all of your assets and
liabilities without any exception;
The full spectrum of investments
must be considered because the
returns from all these investments
interact, and this relationship among
the returns for assets in the portfolio
is important.

4.2.1 Risk
 Although there is a difference in the specific
definitions of risk and uncertainty, for our
purposes and in most financial literature the two
terms are used interchangeably. For most
investors, risk means the uncertainty of future
outcomes.
 An alternative definition might be the probability
of an adverse outcome. Risk refers to the
uncertainty that the actual return the investor
realizes will differ from the expected return.

4.2.2 Risk aversion
 Portfolio theory assumes that investors are basically
risk averse, meaning that, given a choice between two
assets with equal rates of return, they will select the
assets with lower level of risk.
 Evidence that most investors are risk averse is that they
purchase various types of insurance, including life
insurance, car insurance, and health insurance. This
does not imply that everybody is risk averse, or that
investors are completely risk averse regarding all
financial commitments. People exhibit different degree
of risk aversion. Some of them tolerate more risk than
others.

 To the extreme it is said that most investors are risk
averse, whereas others are either risk indifferent or
risk seeking. The combination of risk preference and
risk aversion can be explained by an attitude toward
risk that depends on the amount of money involved.
 Our basic assumption is that most investors
committing large sums of money to developing an
investment portfolio are risk averse. Therefore, most
studies find a positive relationship between the rates
of return on various assets and their measures of risk.
That is for a high expected return the expected risk is
also high.

 In the earlier 1960s, the investment community talked
about risk, but there was no specific measure for the
term. To build a portfolio model, however, investors
had to quantify their risk variable. The basic portfolio
model was developed by Harry Markowitz (1952,
1959), who derived the expected rate of return for a
portfolio of assets and an expected risk measure.
 Markowitz showed that the variance of the rate of
return was a meaningful of portfolio risk under a
reasonable set of assumptions, and he derived the
formula for computing the variance of a portfolio.

 This portfolio variance formula not only indicated the
importance of diversifying investments to reduce the
total risk of a portfolio but also showed how to
effectively diversify. The Markowitz model is based on
several assumptions regarding investor behavior:
1. Investors consider each investment alternative as
being represented by a probability distribution of
expected returns over some holding period;
2. Investors estimate the risk of a portfolio on the
basis of the variability of expected returns;
3. For a given risk level, investors prefer higher
returns to lower returns. Similarly, for a given
expected return, investors prefer less risk to more
risk.

4.3.1 The Concept of Return
People have many motives for investing.
Some people invest in order to gain sense of
power or prestige. Often the control of
corporate empires is a driving motive.
For most investors, their interest in
investments is to earn a return on their
money. However, selecting stocks
exclusively on the basis of maximization of
return is not enough.

 These decisions are normally made in two steps.
First, estimates of return and risk associated
with available securities over a forward holding
period are prepared. This is known as security
analysis.
 Second, return-risk estimates must be
compared in order to decide how to allocate
available funds among these securities on a
continuing basis. This step comprises portfolio
analysis, selection, and management. In
effect, security analysis provides the necessary
inputs for analysing and selecting portfolios.

Security analysis is built around the idea
that investors are concerned with two
principal properties inherent in securities:
The return that can be expected from
holding a security, and the risk that the
return that is achieved will be less than
the return that was expected.
Investors want to maximize expected
returns subject to their tolerance for
risk.

Return is the motivating force and the
principal reward in the investment process and
it is the key method available to investors in
comparing alternative investments.
Measuring historical returns allows
investors to assess how well they have done,
and it plays a part in the estimation of future
unknown returns.

 Return on a typical investment consists of two
components. The basic component is the
periodic cash receipts (or income) on the
investment, either in the form of interest or
dividends.
 The second component is the change in the
price of the asset commonly called the capital
gain or loss. This element of return is the
difference between the purchase price and the
price at which the asset can be or is sold;
therefore, it can be a gain or loss.

The income from an investment consists of
one or more cash payments paid at
specified intervals of time. Interest
payments on most bonds are paid semi
annually, whereas dividends on
common stocks are usually paid
quarterly.
The distinguishing feature of these
payments is that they are paid in cash by
the issuer to the holder of the asset.

The term yield is often used in connection
with income component of return. Yield refers
to the income component in relation to some
price for a security. For our purposes, the price
that is relevant is the purchase price of the
security.
Example
The yield on a common stock paying $2 in dividends
per year and purchased for $50 per share is
($2/$50) *100 = 4%

One must remember that yield is not, for
most purposes, the proper measure of return
from a security.
The capital gain or loss must be
considered.
Total Return = Income + Price Change
(+/-)
The important point is that a security’s total
return consists of the sum of two
components, income and price change.

Investments are made to earn a return, but to
earn a return , the investor must accept the
possibility of loss. Portfolio theory is
concerned with risk and return. Its purpose is
to determine the combination of risk and
return that allows the investor to achieve the
highest return for a given level of risk.
The word return is often modified by an
adjective, including the expected return, the
required return, and the realized return.

 1. Expected return: the sum of the anticipated
dividend yield and capital gains. In other words, it is
the anticipated flow of income and/or price
appreciation. An investment may offer return from
either two sources: The first source is the flow of
income that may be generated by the investment. A
saving account generates interest income.
 The second source is capital appreciation. If an
investor buys stock and its price subsequently
increases, the investor receives a capital gain. All
investments offer the investor potential income
and/or capital appreciation.

 Example: If an investor buys a stock for $10 and
expects to earn a dividend of $0.60 and sells the
stock for $12 so there is a capital gain of 20
percent [($12-$10)/$10], the expected return is
E(r) = $0.60/$10 + 0.2= 0.26=26%
 The investor expects to earn a return of 26%
during the time period. It is important to realize
that this return is anticipated. The yield that is
achieved on the investment is not known until
after the investment is sold and converted into
cash.

It is important to differentiate between the
expected return, the required return, and the
realized return.
The expected return is the incentive for
accepting the risk, it must be compared with
the investor’s required return, which is the
return necessary to induce the investor to
bear the risk associated with a particular
investment.

2. Required return: the return necessary to
induce the investor to purchase an asset.
The required return includes:
1. What the investor may earn on alternative
investments, such as the risk-free return
available on Treasury bills, and
2. A premium for bearing risk that includes
compensation for the expected rate of
inflation and for fluctuations in security
prices.

 N.B: Since the required return includes a measurement
of risk, the discussion of the required return must be
postponed until measurement of risk is covered.
 3. Realized return: is the return actually earned on an
investment and is essentially the sum of the flow of
income generated by the asset and the capital gain. In
other words, realized return is the sum of income and
capital gains earned on investment.
 The realized return is summarized by the following
equation: r= D/P +g (this is essentially the same as the
equation for expected return with the expected value,
E, removed.)

Example
 Consider the following information of an equity
stock:
 Price at the beginning of the year is $60, dividend
paid at the end of the year is $2.40, and the price at
the end of the year is $69.
 Therefore, the total return on this stock is
calculated as follows:
 2.40+(69-60) *100= 0.19 = 19%
60

Questions
What are the sources of return on an
investment?
What are the differences among the
expected return, the required return, and
the realized return?
You are considering the following three
stocks (the stock price of each is $10) with
the following expected dividend yields and
capital gains, what is the expected return
on each stock?

Ex Ante Returns
Return calculations may be done ‘for
future returns,’ in which case,
assumptions must be made about the
future.
Ex Post Returns
Return calculations done ‘after-they
are made,’ in order to analyze what
rate of return was earned.

4.3.2 Measuring Average Returns:
Ex-post return
Measurement of historical rates of return that
have been earned on a security or a class of
securities allows to identify trends or tendencies
that may be useful in predicting the future.
There are two different types of ex post mean or
average returns used:
1.) Arithmetic average returns
2.) Geometric mean returns.

Arithmetic average
Where:
ri = the individual returns
n = the total number of observations
 The most commonly used value in statistics. It is
the sum of all returns divided by the total number of
observations.

Example
If a company’s stock has had the
following returns for the last five
years respectively: 98%, 10%, 20%,
30% and -90%, the arithmetic
average returns would be 13.6%.
This would be calculated as: (0.98 +
0.1 + 0.2 + 0.3 + -0.9) / 5 = 0.136

Ex-Ante Returns
While past-ante returns might be
interesting, if investors are most concerned
with their future returns. Sometimes,
historical average returns will not be
realized in the future.
Developing an independent estimate of ex
ante returns usually involves use of
forecasting discrete scenarios with
outcomes and probabilities of occurrence.

4.3.2 Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns
Where,
ER = the expected return on an investment
Ri = the estimated return in scenario i
Probi = the probability of state i occurring

Example:
This is type of forecast data that are required
to make an ex ante estimate of expected
return.

Sum the products of the probabilities and
possible returns in each state of the economy.

OR
Sum the products of the probabilities and possible
returns in each state of the economy.

4.3.2 Alternative Measures of Risk
 One of the most-known measures of risk is the
variance or the standard deviation of expected returns.
It is a statistical measure of dispersion of returns
around the expected value whereby a larger variance or
standard variation indicates greater dispersion.
 The idea is that the more disperse the expected returns,
the greater the uncertainty of future returns. Another
measure of risk is the range of returns. It is assumed
that a larger range of expected returns, from the lowest
to the highest expected return, means greater
uncertainty and risk regarding future expected returns.

Range
The Range measures the difference between
the maximum and minimum values (Returns).
The wider the range the more risky an investment
is. For instance over a given period of time the
range of returns on government securities such as
T. bills is smaller than most other securities.
 This indicates that (Treasury bills) they have
lower variation of returns than other securities
hence the lower risk.

 Range measures risk based on only two observations
(i.e minimum and maximum value of returns)
 The Standard deviation uses all observations.
 Standard deviation can be calculated on forecast or
possible returns as well as historical or ex post
returns. Standard deviation, as applied to
investment returns, is a quantitative statistical
measure of the variation of specific returns to the
average of those returns.
 Standard deviation, as applied to investment returns,
is a quantitative statistical measure of the variation
of specific returns to the expected or average
of those returns.

Therefore, although there are numerous
potential measures of risk, we will use
the variance or standard deviation of
returns because:
1. This measure is somewhat
intuitive;
2. It is correct and widely recognized
risk measure;
3. It has been used in most of the
theoretical asset pricing models.

4.3.1.1 Expected Rates of Return
 The expected return may be computed for an
individual investment and for a portfolio.
Expected return for a single Investment
 We compute the expected rate of return for a
single investment using the following formula:

Where,
E(Ri)= Expected return on the single
investment;
Pi= The probability to get Ri from an
individual investment at situation (i)
Ri= possible rate of return in situation
i

Example: Computation of the Expected
Return for an Individual Asset

 The expected return for an individual risky
asset with the set of potential returns and an
assumption of the different probabilities used
in this example would be 10.30%.
 The expected rate of return for a portfolio is
computed using the following formula:

Where,
Wi= the weight of an individual
asset in the portfolio, or the percent
of the portfolio in Asset i;
Ri= The expected rate of return for
the Asset i.

Example: Computation of the Expected
Return for a Portfolio of Risky assets

The expected return for this portfolio of
investments would be 11.50%.
The effect of adding or dropping any
investment from the portfolio would be
easy to determine; we would use the new
weights based on value and the expected
returns for each of the investments.

4.3.1.2 Variance (Standard Deviation) of
Returns for an Individual Investment
 As previously stated, we will be using the variance or the
standard deviation of returns as the measure of risk.
Therefore, at this point we demonstrate how to compute
the standard deviation of returns for an individual
Investment.
 The variance and the standard deviation are calculated as
follows:

 Where,
Pi= probability of the possible rate of return
Ri
Ri= Rate of return for the individual
investment, in the i state of the economy
E(Ri)= Expected rate of return for the
individual investment.
The Standard deviation formula is the
following:

Example: Computation of the Variance for
an Individual Risky asset
σ2= 0.000451 and σ= 0.021237= 2.12%

4.3.1.3 Variance (Standard Deviation) of
Returns for a Portfolio
The risk of a portfolio, which may be, itself,
considered as a single asset held in
isolation, is measured by the standard
deviation of its returns. The equation used
to calculate the portfolio standard deviation
is the following:

Where,
σport= the portfolio’s standard deviation;
Rpi= the rate of return for the portfolio in
the i state of the economy;
E(Rpi)= the expected rate of return on the
portfolio;
Pi= the probability of occurrence of the ith
state of the economy; and there are n
economic states.

4.3.1.4 Covariance and Correlation
Coefficient of returns
Two key concepts in portfolio analysis are
Covariance and the Correlation
coefficient. The mathematical
descriptions of covariance and
correlation are very similar.
Both describe the degree of similarity
between two random variables or sets of
random variables.

Covariance of returns
Covariance is a measure of the degree to
which two variables move together relative to
their individual mean values over time. In
portfolio analysis, we usually are concerned
with the covariance of rates of return rather
than prices or some variables.
A positive covariance means that the rates of
return for two investments tend to move in
the same directions relative to their means
during the same period.

 In contrast, a negative covariance indicates that
the rates of return for two investments tend to
move in different directions relative to their
means during the specified time intervals over
time. A zero covariance indicates that there is
no relationship between rates of return for two
investments over time.
 The magnitude of the covariance depends on
the variances of the individual return series, as
well as on the relationship between the series.

Example: Computation of Monthly Rates of
Return for U.S. Stocks and Bonds

 Although the rates of return for the two assets
moved together during some months, in other
months they moved in opposite directions.
The covariance statistic provides an absolute
measure of how they moved together over
time.
 For the two assets, i and j, we define the
covariance of rates as follows:

 The formula can also be written as follows:
 When we apply this formula to actual sample
data, we use the sample mean E(Ri) as an
estimate of the expected return and divide the
values by N-1 rather than by N to avoid
statistical bias, that is,

Interpretation of a number such as 0.637
is difficult; is it high or low for
covariance? We know the relationship
between the two assets is generally
positive, but it is not possible to be more
specific.
However, we can conclude that when the
covariance is a small positive value, the
relationship between the two assets is not
strong.

Correlation Coefficient
 Covariance is affected by the variability of the two
individual return indexes. Therefore, a number such
as the 0.637 in our example might indicate a weak
positive relationship if the two individual indexes were
volatile, but would reflect a strong positive
relationship if the two indexes were stable.
 Obviously, we want to standardize this covariance
measure. We do so by taking into consideration the
variability of the two individual return indexes, as
follows:

 The correlation coefficient is generally used to
measure the degree of comovement between two
variables; in portfolio management it indicates
the comovement of two individual investments
or two portfolios.
 The sign of the correlation coefficient is the same
as the sign of the covariance, so a positive sign
means that the variables move together, a
negative sign indicates that they move in
opposite directions, and if the correlation
coefficient is close to zero, they move
independently one from another.

 The standardization process confines the
correlation coefficient to values between -1
and 1. A value of 1 indicates a perfect positive
linear relationship between Ri and Rj, meaning
that the returns for the two assets or portfolios
move together in a completely lineal manner.
 A value of -1 indicates a perfect negative
relationship between the two assets or
portfolio returns, so that an asset (portfolio)’s
rate of return will be bellow its mean by a
comparable amount.

 Where,
 This formula indicates that the standard deviation
for a portfolio of assets is a function of the weighted
average of the individual variance (where the
weights are squared), plus the weighted covariance
between all the assets in the portfolio.
 The very important point is that the standard
deviation for a portfolio of assets encompasses not
only the variances of the individual assets, but also
includes the covariance between all the pairs of
individual assets in the portfolio.

Actually, in a portfolio with a large number of
securities, this formula reduces to the sum of the
weighted covariance.
Impact of a new security in a portfolio
Although in most discussions we will consider
portfolios with only two assets (because it is easier to
show the effect in two dimensions) time will come
when we will also demonstrate the computations for a
three –asset portfolio.
Still, it is important at this point to consider what
happens in a large portfolio with many assets.
Specifically it is important to know what happens to the
portfolio’s standard deviation when we add a new
security to such a portfolio.

As shown by the formula, we see two
effects:
 Effect on the asset’s own variance of
returns, and
 Effect on the covariance between the
returns of this new assets and the
returns of every other asset that is
already in the portfolio;

 The relative weight of these numerous
covariances is subsequently greater than the
asst’s unique variance; the more assets in the
portfolio, the more this is true.
 This means that the important factor to
consider when adding an investment to a
portfolio that contains a number of other
investments is not the new security’s own
variance but its average covariance with all the
other investments in the portfolio.

4.3.1.5 Portfolio Standard Deviation
Calculation
 Because of the assumption used in developing
the Markowitz portfolio model, any asset or
portfolio of assets can be described by two
characteristics:
The expected rate of return, and
The expected standard deviation of returns.
 Therefore, the following demonstrations can
be applied to two individual assets, two
portfolios of assets, or two assets classes with
the indicated return-standard deviation
characteristics and correlation coefficients.

Equal Risk and Return-Changing
Correlation
 Consider first the case in which both assets have
the same expected return and expected standard
deviation of return. As an example, let’s assume
E (R1) = 0.20; E (σ) = 0.10
E (R1) = 0.20; E (σ) = 0.10
 To show the effect of different covariance, assume
different levels of correlation between the two
assets. Also assume the two assets have equal
weights in the portfolio (W1=50% and W2= 50%).
Therefore the only value that changes in each
example is the correlation between the returns for
the two assets.

In this case where the returns for the two
assets are perfectly positively correlated,
the standard deviation for the portfolio is,
in fact, the weighted average of the
individual standard deviations.
The important point is that we get no real
benefit from combining assets that are
perfectly correlated; they are like one
asset already because their returns move
together.

 Here, the negative covariance term exactly offsets
the individual variance terms, leaving an overall
standard deviation of the portfolio of zero. This
would be a risk free portfolio.
 Perfect negative correlation gives a mean combined
return for the two securities over time equal to the
mean for each of them, so the returns for the
portfolio show no variability. Any returns above
and below the mean for each of the assets are
completely offset by the return for the other asset,
so there is no variability in total returns, that is, no
risk for the portfolio.

 Thus, a pair for completely negatively correlated
assets provides the maximum of benefits of
diversification by completely eliminating risk. As
noted, the only effect of the change in correlation
is the change in the standard deviation of this two-
asset portfolio.
 Combining assets that are not perfectly correlated
does not affect the expected return of the
portfolio, but it does reduce the risk of the
portfolio (as measured by its standard deviation).
When we eventually reach the ultimate
combination of perfect negative correlation, risk is
eliminated.

Combining Stocks with Different Returns
and Risk
 We have seen what happens when only the
correlation coefficient (covariance) differs
between the assets. We now consider two
assets (or portfolios) with different expected
rates of return and individual standard
deviations.
 We will show what happens when we vary the
correlations between them. Assume two assets
with the following characteristics:

After required calculations, the results are shown in the table below:

 Because we are assuming the same weights in
all cases (50% to 50%), the expected return in
every instance will be:

 Again, with perfect positive correlation, the
portfolio standard deviation is the weighted
average of the standard deviations of the
individual assets:
 (0.5) (0.07) + (0.5) (0.10) = 0.085
 As you might envision, changing the weights
with perfect positive correlation causes the
portfolio standard deviation to change in a
linear fashion. This will be an important point
to remember when we discuss the capital asset
pricing model (CAPM) in the next chapter. For
Cases b, c, d, and e, the portfolio standard
deviations are as follows:

 Note that, in this example, with perfect negative
correlation the portfolio standard deviation is not
zero. This is because the examples have equal
weights, but the asset standard deviations are not
equal.
Constant Correlation with Changing Weights
 If we changed the weights of the two assets while
holding the correlation coefficient constant, we
would derive a set of combinations that trace an
ellipse starting at Asset 2, going through the 0.50-
0.50 point, and ending at Asset 1.

 We can demonstrate this with Case c, in which the
Correlation Coefficient of zero eases the computations.
We begin with 100% in Asset 2 (Case f) and change the
weights as follows, ending with 100% in Asset 1 (Case l).

 A notable result of these combinations is that
with low or negative correlations, it is possible
to derive portfolios that have lower risk than
either single asset.
 In our set of examples, where
this occurs in Cases h, i, j, and k. This
ability to reduce risk is the essence of
diversification.

4.3.1 Estimation issues
 It is important to keep in mind that the results of this
portfolio asset allocation depend on the accuracy of the
statistical inputs. In the current instance, this means
that for every asset (or asset class) being considered for
inclusion in the portfolio, we must estimate its
expected returns and standard deviation.
 We must also estimate the correlation coefficient
among the entire set of assets. The number of
correlation estimates can be significant. , for example,
for a portfolio of 100 securities, the number is 4,950
(that is, 99 + 98 + 97 +…). The potential source of error
that arises from the approximations is referred to as
estimation risk.

 We can reduce the number of correlation coefficients that must
be estimated by assuming that stock returns can be described
by the relationship of each stock to a market index, that is, a
single market model as follows:

This reduces the number of estimates
from 4,950 to 100, that is, once we have
derived a slope estimate for
each security, we can compute the
correlation estimates.
Keep in mind that this assumes that
the single index market model
provides a good estimate of security
returns.

6
4.4 Portfolio and Risk diversification
 As we just saw, the expected return on a portfolio is
simply the weighted average of the expected returns
on the individual assets in the portfolio. However,
unlike returns, the risk of a portfolio, σp, is generally
not the weighted average of the standard deviations
of the individual assets in the portfolio.
 Indeed, the portfolio’s standard deviation will
(almost always) be smaller than the assets’ weighted
standard deviations, and it is theoretically possible
to combine stocks that are individually quite risky as
measured by their standard deviations and form a
portfolio that is completely riskless, with σp = 0.

 In statistical terms, we say that this happens
when the returns are perfectly negatively
correlated, with ρ = −1.0.
 Conversely, returns on two perfectly positively
correlated stocks move up and down together,
and a portfolio consisting of two such stocks
would be exactly as risky as each individual
stock. Thus, diversification does nothing to
reduce risk if the portfolio consists of stocks
that are perfectly positively correlated.

 Thus, when stocks are perfectly negatively
correlated (ρ = −1.0), all risk can be diversified
away, but when stocks are perfectly positively
correlated (ρ = +1.0), diversification does no
good whatsoever. In reality, virtually all stocks
are positively correlated, but not perfectly so.
 Past studies have estimated that, on average, the
correlation coefficient for the monthly returns
on two randomly selected stocks is in the range
of 0.28 to 0.35. Under this condition, combining
stocks into portfolios reduces but does not
completely eliminate risk.

 What would happen if we included more than two
stocks in the portfolio? As a rule, the risk of a
portfolio declines as the number of stocks in the
portfolio increases. If we added enough partially
correlated stocks, could we completely eliminate
risk?
 The answer is “no,” but adding stocks to a portfolio
reduces its risk to an extent that depends on the
degree of correlation among the stocks: The smaller
the stocks’ correlation coefficients, the lower the
portfolio’s risk. If we could find stocks with
correlations of −1.0, all risk could be eliminated.

 However, in the real world the correlations among
the individual stocks are generally positive but less
than +1.0, so some (but not all) risk can be
eliminated.
 In general, there are higher correlations between
the returns on two companies in the same industry
than for two companies in different industries.
There are also higher correlations among similar
“style” companies, such as large versus small and
growth versus value. Thus, to minimize risk,
portfolios should be diversified across industries
and styles.

4.5 Diversifiable Risk versus Market Risk
 As already mentioned, it’s difficult if not impossible
to find stocks whose expected returns are negatively
correlated—most stocks tend to do well when the
national economy is strong and badly when it is
weak.
 Thus, even very large portfolios end up with a
substantial amount of risk, but not as much risk as
if all the money were invested in only one stock. The
risk of a portfolio consisting of large-company
stocks tends to decline and to approach some limit
as the size of the portfolio increases.

 Thus, almost half of the risk inherent in an
average individual stock can be eliminated if the
stock is held in a reasonably well-diversified
portfolio, which is one containing forty or more
stocks in a number of different industries.
 Some risk always remains—terrorists can attack,
recessions can get out of hand, meteors can
strike, and so forth—so it is impossible to
diversify away the effects of broad stock market
movements that affect virtually all stocks.

The part of a stock’s risk that can be
eliminated is called diversifiable risk,
while the part that cannot be eliminated
is called market risk.
The fact that a large part of the risk of any
individual stock can be eliminated is
vitally important, because rational
investors will eliminate it and thus render
it irrelevant.

Diversifiable risk is caused by such
random events as lawsuit, strikes,
successful and unsuccessful marketing
programs, winning or losing a major
contract, and other events that are unique
to a particular firm.
Because these events are random, their
effects on a portfolio can be eliminated by
diversification—bad events in one firm
will be offset by good events in another.

Market risk, on the other hand, stems
from factors that systematically affect
most firms: war, inflation, recessions,
and high interest rates.
Because most stocks are negatively
affected by these factors, market risk
cannot be eliminated by
diversification.

4.5.1 Systematic Risk
 Systematic risk refers to those factors that
affect the returns on all comparable investments.
i.e. it is risk associated with fluctuation in
security prices and other investments; e.g.,
market risk.
 Example: when a market as whole rises, the
prices of most individual securities and other
investments also rise. There is a systematic
relationship between the return on a specified
asset and the return on all other assets in its
class (i.e.; all other comparable assets).

Because this systematic relationship exists,
diversifying the portfolio by acquiring
comparable assets does not reduce this
source of risk; thus, systematic risk is often
referred to as non diversifiable risk.
 While constructing a diversified portfolio
has little impact on systematic risk, one
should not conclude that this non
diversifiable risk can not be managed.

An individual company cannot control
systematic risk. Systematic risk can be
partially mitigated by asset allocation.
Owning different asset classes with low
correlation can smooth portfolio
volatility because asset classes react
differently to macroeconomic factors.

 Systematic Risk does not have a specific definition
but is intrinsic risk existing in the stock market. These
risks are applicable to all the sectors but can be
controlled. If there is an announcement or event which
impacts the entire stock market, a consistent reaction
will flow in which is a systematic risk.
 For e.g. if Government Bonds are offering a yield of
5% in comparison to the stock market which offers a
minimum return of 10%. Suddenly, the government
announces an additional tax burden of 1% on stock
market transactions, this will be a systematic risk
impacting all the stocks and may make the
Government bonds more attractive.

Systematic risk can be partially mitigated
by asset allocation. Owning different asset
classes with low correlation can smooth
portfolio volatility because asset classes
react differently to macroeconomic
factors.
When some asset categories (i.e. domestic
equities, international stocks, bonds, cash,
etc.) are increasing others may be falling
and vice versa.

To further reduce risk, asset allocation
investment decisions should be based on
valuation. I want to adjust my asset allocation
target according to valuations.
I want to overweight those asset classes that are
bargains and own less or avoid investments
which are overpriced. When mitigating
systematic risk within a diversified portfolio,
cash may be the most important and under
appreciated asset category.

Types of Systematic Risk
1. Market Risk refers to the tendency of security
prices/ assets to move together. i.e. the risk
associated with the tendency of a stock’s price to
fluctuate within the market.
 While it may be frustrating to invest in a firm that
appears to be undervalued and then watch the
Security prices drop due to fluctuations, and the
investor must either accept the risk associated with
those fluctuations or not participate in the market.

 While market risk is generally applied to stocks,
the concept also applies to other assets, such as
precious metals and real estates. The prices of
these assets fluctuate. If the value of houses were
to rise in general, then the value of a particular
house would also tend to increase.
 But the converse is also true because the prices of
houses could decline, causing the value of a
specific house to fall. Market risk can not be
avoided if one acquires an asset whose prices may
fluctuate.

2. Interest ate risk
 Interest rate risk refers to the tendency of security
prices, especially fixed-income securities, to move
inversely with changes in the rate of interests. i.e. the
uncertainty associated with changes in interest rates;
the possibility of loss resulting from increases in
interest rates. The prices of bonds and preferred stock
depend in part on current purchasers required
competitive yield.
 The investor who acquires these securities must face
the uncertainty of fluctuating interest rates that, in turn,
cause the price of these fixed-income securities to
fluctuate.

3. Reinvestment rate risk
 Reinvestment rate risk refers to the risk associated
with reinvesting funds generated by an investment .i.e.
the risk associated with reinvesting earnings or
principal at a lower rate than was initially earned.
 If an individual receives interest or dividends, these
funds could be spent on goods and services. For
example; many individuals who live on pension
consume a substantial portion, and perhaps all, of the
income generated by their assets. Other investors,
however, reinvest their investment earnings in order to
accumulate wealth.

Example
 Consider an individual who wants to accumulate a sum
of money and purchases a $1,000 bond that pays $100
a year and matures after ten years. The anticipated
annual return based on the annual interest and the
amount invested is 10% ($100/$1000).
 The investor wants to reinvest the annual interest, and
the question then becomes what rate will be earned on
these reinvested funds: will the return be more or less
that the 10% initially earned? The essence of
reinvestment risk is the uncertainty that the investor
will earn less than the anticipated return when
payments are received.

4. Purchasing power risk
Purchasing power risk is the risk that inflation
will erode the buying power of the investor’s
assets and income. i.e. the uncertainty that
future inflation will erode the purchasing power
of assets and income.
The investor must also bear the risk associated
with inflation. Inflation is the loss of purchasing
power through the rise in prices. If prices of
goods and services increase, the real purchasing
power of the investor’s assets and the income
generated by them is reduced.

 The opposite of inflation is deflation, which is a
general decline in prices. During the period of
deflation, the real purchasing power of the
investor’s assets and income is increased.
 Investors will naturally seek to protect
themselves from the loss of purchasing power by
constructing a portfolio of assets with an
anticipated return that is higher than the
anticipated rate of inflation. It is important to
note the anticipated, because it influences the
selection of particular assets.

 If inflation is expected to be 4%, a saving account
offering 6% will produce a gain and thereby
“beat” inflation. However, if the inflation rate
were to increase unexpectedly to 7%, the savings
account would result in a loss of purchasing
power.
 The real rate of return would be negative. If the
higher rate of inflation had been expected, the
investor would not have chosen the savings
account but would have purchased some other
asset with a higher expected return.

5 Exchange rate risk
Exchange rate risk is the uncertainty associated
with the changes in the value of foreign currencies.
i.e. it refers to the currency risk associated with
foreign investments.
Exchange rate risk is the uncertainty of the future
value of a currency; since the foreign investment
must be converted back to the domestic currency.
Of course, this source of risk applies only if the
investor acquires foreign investments denominated
in another currency, such as the stock of a Brazilian
company.

The individual, however, may not be able to
avoid exchange rate risk by eliminating
purchases of stock in domestic companies.
 Firms such as Coca-Cola (KO) or
Tupperware (TUP) generate more than half
their sales and earnings from foreign
operations, so U.S. investors indirectly bear
exchange rate risk when they buy stock in
Coca-Cola and Tupperware.

4.5.2 Unsystematic Risk
 The risk associated with individual events that
affect a particular security. Unsystematic risk which
is also referred to as diversifiable risk, depends on
factors that are unique to the specific asset.
 For example, a firm’s earnings may decline
because of a strike. Other firms in the industry may
not experience the same labor problem, and thus
their earnings may not be hurt or may even rise as
customers divert purchases from the firm whose
operations are temporarily halted.

In either case, the change in the firm’s
earnings is independent of factors that affect
the industry, the market, or the economy in
general. Because this source of risk applies
only to the specific firm, it may be reduced
through the construction of a diversified
portfolio.
The sources of unsystematic risk may be
subdivided into two general classifications:
business risk and financial risk.

 Business risk is the risk associated with the nature
of the business or the nature of the enterprise itself.
Not all the businesses are equally risk.
 Example: Drilling for new oil deposits is more
risky than running a commercial bank. The chances
of finding oil may be slim, and only one of many
new wells may actually produce oil and earn a
positive return. Commercial banks, however, can
make loans that are secured by particular assets,
such as residences or inventories.
1. Business Risk

While these loans are not risk-free, they
may be relatively safe because even if the
debtor defaults, the creditor(the bank) can
seize the asset to meet its claims.
Some businesses are by their very nature
riskier than others, and, therefore,
investing in them is inherently riskier. All
assets must be financed. Either creditors or
owners or both provide the funds to start
and to sustain the business.

Financial Risk is the risk associated with a firm’s
sources of financing. Borrowing funds to finance a
business may increase financial risk, because creditors
require that the borrower meet certain terms to obtain
the funds. The most common of these requirements is
the paying of interest and the repayment of the
principal.
The creditor can (and usually does) demand additional
terms, such as collateral or restrictions on dividend
payments, that the borrower must meet. These
restrictions mean that the firm that uses debt financing
bears more risk because it must meet these obligations
in addition to its other obligations.
2. Financial Risk

When sales and earnings are rising, these
constraints may not be burdensome, but
during periods of financial stress the
failure of the firm to meet these terms
may result in financial ruin and
bankruptcy.
A firm that does not use borrowed funds
to acquire its assets does not have these
additional responsibilities and does not
have the element of financial risk.

Diversification does, however, reduce unsystematic
risk, which applies to the specific firm and
encompasses the nature of the firm’s operation and its
financing. Because unsystematic risk applies only to
the individual asset, there is no systematic relationship
between the source of risk and the market as a whole.
A portfolio composed of 10 to 15 unrelated assets- for
eg., stocks in companies in different industries or
different types of assets, such as common stock,
bonds, mutual funds, and real estate, virtually
eradicates the impact of unsystematic risk on the
portfolio as a whole.

INVESTMENT ANALYSIS AND PORTFOLIO MANAGEMENT (1) 111 (1).pptx

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