unit i fm
TRANSCRIPT
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FINANCIAL MANAGEMENT :INTRODUCTION
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An Introduction to the
Ten Basic Principles
CORPORATE FINANCE
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Foundation of Finance
Finance fundamentals spring from 10simple principles that dont requireknowledge of finance to understand.
However, while it is not necessary tounderstand finance in order to understandthese principles, it is necessary tounderstand these principles in order tounderstand finance.
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PRINCIPLE 1
The Risk-Return Trade-Off
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PRINCIPLE 2
The Time Value ofMoney
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PRINCIPLE 3
Cash Not Profit isKing.
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PRINCIPLE 4
Incremental Cash Flows
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PRINCIPLE 5
The Curse of CompetitiveMarkets
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PRINCIPLE 6
Efficient Capital Markets
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PRINCIPLE 7
The Agency Problem
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PRINCIPLE 8
Taxes Bias BusinessDecisions.
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PRINCIPLE 9
All Risk is Not Equal
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PRINCIPLE 10
Ethical behaviour isdoing the right thing,and ethical dilemmas areeverywhere in finance.
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FINANCIAL MANAGEMENT
Financial Management is concerned with the acquisition,
financing and management of assets with some overall goal in
mind
-J.C.VANHORNE
"Financial Management is an area of financialdecision making, harmonizing individual motives
and enterprises goals
-Weston and Brigham
Financial Management is that managerial activity
which is concerned with the planning and controlling
of the firms financial resources.
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Financial Management: Defined
This is the business management function that is
concerned with managing abusiness finances
It refers to the application of financial management
tools and techniques to coordinate all the financial
functions in the business
Management of funds is a critical aspect offinancial management. Management of funds actas the foremost concern whether it is in a businessundertaking or in an educational institution.Financial management, which is simply meant
dealing with management of money matters.
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1-16Management
By Financial Management we mean efficient use of
economic resources namely capital funds. Financial
management is concerned with the managerial
decisions that result in the acquisition and financing of
short term and long term credits for the firm.
Here it deals with the situations that require selection
of specific assets, or a combination of assets and the
selection of specific problem of size and growth of anenterprise.
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1-17Management
Sound financial management is essential in all types of
organizations whether it be profit or non-profit. Financialmanagement is essential in a planned Economy as well as in a
capitalist set-up as it involves efficient use of the resources.
From time to time it is observed that many firms have been
liquidated not because their technology was obsolete or because
their products were not in demand or their labour was not skilled
and motivated, but that there was a mismanagement of financial
affairs. Even in a boom period, when a company make high
profits there is also a fear of liquidation because of bad financial
management.
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Contd..
Financial management optimizes the output from the given input of
funds. In a country like India where resources are scarce and thedemand for funds are many, the need of proper financial
management is required. In case of newly started companies with a
high growth rate it is more important to have sound financial
management since finance alone guarantees their survival.
Financial management is very important in case of non-profit
organizations, which do not pay adequate attentions to financial
management.
How ever a sound system of financial management has to be
cultivated among bureaucrats, administrators, engineers,
educationalists and public at a large.
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1-19Management
Profit Maximization:
The objective of financial management is the same as the objective of a
company which is to earn profit. But profit maximization alone cannot be
the sole objective of a company. It is a limited objective. If profits are
given undue importance then problems may arise, so profit maximization
objective is justified on the following grounds:
Rationality
Maximization of Social Benefit
Efficient allocation and uses of resources
Measurement of success of decisions
Sources of incentive
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Profit Maximization contd.
Profit Maximization objective is considered to be a very limited objective,
because it has a number of drawbacks, which render this objective as anineffective decisional criterion. These drawbacks (limitations) are as under:
Ambiguity / Loose expression of the term profit: The term profit is vague and
it involves much more contradictions.
Profit Maximization objective ignores timing of benefit (time-value-money):
Profit Maximization fails to take into account the time pattern of returns. Profitmaximization does not take into account the social considerations
Profit Maximization objective fails to recognize quality of benefits (risk
factor): Profit maximization must be attempted with a realization of risks
involved. A positive relationship exists between risk and profits. So both risk
and profit objectives should be balanced.
1-21Obj ti f Fi i l M t
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1-21Objectives of Financial Managementcontd..
Wealth Maximization:
The value of a firm is represented by the market price of the company's
stock (equity share). by Van Horne.
The market price of a firm's stock represents the assessment of all market
participants as to what the value of the particular firm is.
It takes in to account present and prospective future earnings per share,
the timing and risk of these earning, the dividend policy of the firm and
many other factors that bear upon the market price of the stock. Market
price acts as the performance index or report card of the firm's progress
and potential.
It is based on the concept of cash flows. It also signifies the net worth of the enterprise measured in terms of net
present value (NPV) i.e., the difference between Gross Present Value and
the Cost of Capital Investments required for achieving the benefits.
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1 22
Wealth Maximization contd.
Wealth maximization as a decision criterion isused in the context of three important areas of
financial management:
In case of investment decision, the value of firm is
maximized when projects with higher NPV areaccepted
In case of financing decision, it may be stated that
when the return is maximized with the minimum risk,
market value per share will be maximized. In case of dividend decision, the optimum dividend
policy is one that maximizes the market value for share.
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Functions of a Financial Manager
Financial Forecasting: It requires the applications of various statistical,
mathematical & accounting techniques.
Financial Planning: It is done under three distinct sub-activities Formulation of financial objectives Framing the financial policies Developing financial procedures
Financial Decisions: It involves the determination of financial sources,comparative study of their cost of capital, examining the impact on shareholdersequity, etc.
Financial Negotiations
Investment Decisions: It is function of financial management to determine the
volume of investments in fixed and current assets.
Management of Cash Flows
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1 24Functions of a Financial Managercontd
Management of Income: It comprises correct measurement of
income, distribution of income in correct proportion andfollowing the appropriate dividend policy.
Appraisal of Financial Performance: This function analyze andevaluate the financial performance of the business concern aftera definite interval and to communicate the results to top
management.
Understanding Capital Market: Financial Manager should knowhow risk is measured and how to cope with it in investment andfinancing decisions.
To make efforts for Increasing the Productivity of the Capital: Itis done by discovering the new opportunities of investments.
To Advise the top Management: Financial Manager advise inrespect of proper diagnosis of the problem, alternative solutions
to the problem and selection of the best solutions.
1-25Importance of Proper Financial
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1 25Importance of Proper FinancialManagement
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6
Importance of FM Contd
Maximize use of financial resources
FM allows you to identify and plan for the useof your financial resources.
It provides information for financial decisionmaking.
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Importance of FM Contd
Evaluate new business opportunities
FM provides the key information and answerquestions of whether to exploit such
opportunities or not.
That is, entrepreneurs can effectively analyze abusiness opportunity and determine whether it
is worthwhile or not.
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Importance of FM Contd
Measuring business performance
FM helps the investor to monitor the
progress of their business towards
achieving business goals and to take
corrective action where necessary.
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Importance of FM Contd
Making sound business decisions The financial information systems provides
a wide range of information that can beused to make better decisions.
This is done using financial ratios, breakeven analysis etc.
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MAJOR FINANCIAL MANAGEMNET
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MAJOR FINANCIAL MANAGEMNETDECISIONS
Investment decision
Working capital decision
Financing decision
Earnings management decision
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1. Investment decision
This is also known as the Capital budgeting, and it
refers to the decision to invest in long term assets.
The assets are expected to be used over a long
period of time e.g. when a firm acquires plant and
equipment or replaces an old equipment or when
you invest in research and development.
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Importance of Capital Budgeting
It determines the asset mix and hencethe business risk.
It involves heavy initial outlays of the
business resources.
Benefits accrue in future which future is
associated with risk and uncertainty.
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2. Working capital decision
This is the decision concerned with the short termassets/resources an organization uses to meet its day
to day obligations.
Such assets include:
Cash reserves of the organisation
Funds collected from debtors of the organization.
Inventories
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3. Financing decision This is the decision concerned with the sourcing of funds that are
utilized under the investment decision.
Much management time and effort is devoted to trying to ensurethe adequacy of the company's profit flow.
However, it is just as important that a company has an adequateflow of funds if it is to remain in business and very much less
management time and effort is devoted to this need. As companies expand, they require growing amounts of cash to
finance acquisitions of fixed assets. They also require growingamounts of cash to finance their growing working capitalrequirements.
Some of this funding requirement will come from INTERNALsources, whilst some will need to come from EXTERNALsources.
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4. Earnings Management Decision
The Financial Manager has to decide on what to
do with the earnings once they have been
realised. There are three options,
To declare and pay all dividends to shareholders
To retain all the earnings and hence declare and
pay no dividends
To decide on what proportion to be paid and what
to be retained.
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DECISIONS RETURN RISK
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DECISIONS, RETURN, RISK,
AND MARKET VALUE
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TIME VALUE OF MONEY
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The Time Value of Money
Would you prefer to have Rs. 1million now or Rs. 1 million 10years from now?
Of course,Of course, we would allwe would all
prefer the money now!prefer the money now!
This illustrates that thereThis illustrates that thereis an inherent monetaryis an inherent monetary
value attached to time.value attached to time.
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Money?
A rupee received today is worth more thana rupee received tomorrow This is because a rupee received today can be
invested to earn interest
The amount of interest earned depends on therate of return that can be earned on theinvestment
Time value of money quantifies the valueof a rupee through time
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Uses of Time Value of Money
Time Value of Money, or TVM, is a concept that is
used in all aspects of finance including:
Bond valuation
Stock valuation
Accept/reject decisions for project management
Financial analysis of firms
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Types of TVM Calculations
There are many types of TVMcalculations
The basic types will be covered areinclude: Present & Future value of an investment Future value with compounding Future value with continuous compounding
Present value ofperpetuity Present value ofgrowingperpetuity Present & Future value ofannuities
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Present Value of an Investment
Present value calculations determine what the valueof a cash flow received in the future would be worth
today (time 0)
The process of finding a present value is called
discounting (hint: it gets smaller)
The interest rate used to discount cash flows isgenerally called the discount rate
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Investment
General Present ValuePresent Value Formula:
PV = CFt/ (1+r)t
or PV = FVt/ (1+r)t
or PVPV = FVFVtt (PVIFPVIFr,t) -- See Table ISee Table I
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PVIFPVIFr,t is found on Table I at the end of the book.
Period 6% 7% 8%
1 .943 .935 .926
2 .890 .873 .857
3 .840 .816 .794
4 .792 .763 .735
5 .747 .713 .681
Valuation using Table I
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Example of PV of an Investment
How much would Rs. 10,000 received five years from now be
worth today if the current interest rate is 10%?
1. Draw a timeline
The arrow represents the flow of money and the numbers underthe timeline represent the time period.
Note that time period zero is today.
0 1 2 3 4 5
Rs. 10,000?r = 10%
PVPV
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Calculation based on general formula: PVPV = FVFVtt / (1+r)
t PVPV = 10,00010,000 / (1+
0.10)5 = Rs. 6,209.21Rs. 6,209.21
Calculation based on Table I:
PVPVtt = 10,00010,000 (PVIFPVIF10% , 5) = 10,00010,000(.621) =
Rs. 6,210.00Rs. 6,210.00 [Due to Rounding]
Example of PV of an Investment
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Future Value of an Investment
You can think of future value as theopposite of present value
Future value determines the amount that a
sum of money invested today will grow toin a given period of time
The process of finding a future value iscalled compounding (hint: it gets larger)
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FVIFFVIFr,t is found on Table II at the end of the book.
Valuation using Table II
Period 6% 7% 8%
1 1.060 1.070 1.080
2 1.124 1.145 1.166
3 1.191 1.225 1.260
4 1.262 1.311 1.360
5 1.338 1.403 1.469
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Example of FV of an Investment
How much money will you have in 5 years if you invest Rs.
10,000 today at a 10% rate of return?
1. Draw a timeline
00 11 22 33
Rs. 10,000Rs. 10,000 ??r = 10%r = 10%
44 55 FVFV
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Example of FV of an Investment
Calculation based on general formula:
FVFVnn = CFt * (1+r)t
FVFV55 = 10,000 (1+ 0.10)5
= Rs. 16,105.106,105.10
Calculation based on Table I:
FVFV55 = 10,000(FVIFFVIF10%, 5)
= 10,000(1.611)
= Rs. 16,110Rs. 16,110 [Due to Rounding]
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Some Things to Note
In both of the examples, note that if you were to
perform the opposite operation on the answers(i.e., find the future value of Rs. 6210 or the
present value of Rs. 16105) you will end up withyour original investment of Rs. 10,000.
This illustrates how present value and future valueconcepts are intertwined. In fact, they are thesame equation . . .
Take PV = FVt/ (1+r)t and solve for FV
t. You will get
FVt= PV * (1+r)t.
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Compounding Periods
Compounding an investment m times a year forTyears provides for future value of wealth:
Tm
m
r
CFV
+= 10For example, if you invest Rs. 50 for 3years at 12% compounded semi-
annually, your investment will grow to
93.70.)06.1(502
12.150 6
32
RsFV ==
+=
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(Ad d)
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(Advanced)
The general formula for the future value of an investment compoundedcontinuously over many periods can be written as:
FV= C0erT
WhereC0 is cash flow at date 0,
ris the stated annual interest rate,
T is the number of periods over which the cash is
invested, and
e is a transcendental number approximately equal to
2.718. ex is a key on your calculator.
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Perpetuity
A constant stream of cash flows that lasts forever.
0
1
C
2
C
3
C
The formula for the Present Value of a perpetuityis:
++
++
++
=32
)1()1()1( r
C
r
C
r
CPV
r
CPV =
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Perpetuity Example
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Perpetuity: Example
Q.What is the value of a British consol that promises to pay 15each year, every year until the sun turns into a red giant and
burns the planet to a crisp?
The interest rate is 10-percent.
0
1
15
2
15
3
15
15010.
15==PV
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Growing Perpetuity
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Growing Perpetuity
A growing stream of cash flows that lasts forever.
0
1
C
2
C(1+g)
3
C (1+g)2
The formula for the Present Value of a growing perpetuity is:
++
++
+
++
+=
3
2
2 )1(
)1(
)1(
)1(
)1( r
gC
r
gC
r
CPV
gr
CPV
=
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Growing Perpetuity: Example
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Growing Perpetuity: Example
Q. The expected dividend next year is $1.30 and dividends areexpected to grow at 5% forever.
If the discount rate is 10%, what is the value of this promiseddividend stream?
0
1
$1.30
2
$1.30(1.05)
3
$1.30 (1.05)2
00.26$05.10.
30.1$=
=PV
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A iti
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Annuities
An annuity is a cash flow stream in which
the cash flows are all equal and occur at
regular intervals.
Note that annuities can be a fixed amount,
an amount that grows at a constant rate
over time, or an amount that grows at
various rates of growth over time. Wewill focus on fixed amounts.
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T f A iti
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Types of Annuities
An Annuity An Annuity represents a series of equal payments (or receipts) occurring over aspecified number of equidistant periods.
Ordinary AnnuityOrdinary Annuity: Payments orreceipts occur at the end of each period.Annuity DueAnnuity Due: Payments or receipts
occur at thebeginning of each period.
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Examples of Annuities
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Examples of Annuities
Student Loan Payments Car Loan Payments
Insurance Premiums
Mortgage Payments
Retirement Savings
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PV f A it
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PV of an AnnuityA constant stream of cash flows with a fixed maturity.
The formula for the Present Value of an annuity is:
++
++
++
+= Tr
CrC
rC
rCPV
)1()1()1()1( 32
),(*
)1(
11
trPVIFACPV
or
rr
CPV
T
=
+=
0 1
C
2
C
3
C
T
C
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E l f PV f A it
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Example of PV of an Annuity
Q. Assume that Mr. X owns an investment that will pay her
Rs. 100 each year for 20 years. The current interest rateis 15%. What is the PV of this annuity?
1. Draw a timeline
00 11 22 33 .. 1919 2020
100100 100100 100100 100100 100100
??
r = 15%r = 15%
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E ample of PV of an Annuit
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Example of PV of an Annuity
2. Write out the formula using symbols:
PVA = C * {[1-(1+r)-t]/r}
3. Substitute appropriate numbers:
PVA = 100 * {[1-(1+.15)-20 ]/.15}
4.
Solve for the PVPVA = 100 * 6.2593
PVA = Rs. 625.93
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FV of an Annuity
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FV of an AnnuityA constant stream of cash flows with a fixed maturity.
The formula for the Future Value of an annuity is:
),(*
1)1(
trFVIFACFV
or
rr
rCFV
T
=
+=
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Example of FV of an Annuity
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Example of FV of an Annuity
Q. Assume that Mr. X owns an investment that will pay her
Rs. 100 each year for 20 years. The current interest rateis 15%. What is the FV of this annuity?
1. Draw a timeline
00 11 22 33 .. 1919 2020
100100 100100 100100 100100 100100
r = 15%r = 15%
??
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Example of FV of an Annuity
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Example of FV of an Annuity
2. Write out the formula using symbols:
FVAt = C* {[(1+r)t 1]/r}
3. Substitute the appropriate numbers:
FVA20 = 100 * {[(1+.15)20 1]/.15
4. Solve for the FV:
FVA20 = 100 * 102.4436
FVA20 = Rs. 10,244.36
1-68Formula for Ordinary Annuity & AnnuityD
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Due
ForForPresent ValuePresent Value CalculationCalculation
Formula for Ordinary AnnuityFormula for Ordinary Annuity
PVAPVAtt = CFt *(PVIFAr% ,t)
Formula for Annuity DueFormula for Annuity Due
PVADPVADtt = CFt *(PVIFAr% ,t)(1+r)
ForForFuture ValueFuture Value CalculationCalculation Formula for Ordinary AnnuityFormula for Ordinary Annuity
FVAFVAtt
= CFt
*(FVIFAr% ,t
)
Formula for Annuity DueFormula for Annuity Due
FVADFVADtt = CFt *(FVIFAr% ,t)(1+r)
Where CFt= Cash Flow
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RISK AND RETURNANALYSIS
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Risk Defined
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Risk Defined
There is no universally agreed-upon definition of risk.
In the context of business and finance, risk is defined as
the chance of suffering a financial loss.
Assets (real or financial) which have a greater chance ofloss are considered more risky than those with a lower
chance of loss.
Risk may be used interchangeably with the term
uncertainty to refer to the variability of returns associated
with a given asset.
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Return Defined
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Return Defined
Total Returnrepresents the total gain or loss on an
investment over a given period of time
Total return can be expressed either in rupee terms
or inpercentage terms.
Componentsof the total
return
Income stream from theinvestment
Capital gain or loss due tochanges in asset prices
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Rupee Returns
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Rupee Returns
The sum of the cash received and the change in
value of the asset, in rupees.
Time 0 1
Initialinvestment
Ending market
value
Dividends
Rupee Return = Dividend + Change in Market Value
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Percentage Return
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Percentage Return
The sum of the cash received and the change in
value of the asset divided by the original
investment.
Initial investment
Rupee ReturnPercentage Return =
Initial investment
Dividend + Change in Market ValuePercentage Return =
Capital gain yieldDividend Yield +=
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Returns: Example
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Returns: Example
Suppose you bought 100 shares of Infosys one year agotoday at Rs. 25. Over the last year, you received Rs. 20
in dividends (= 1 rupee per share 100 shares). At the
end of the year, the stock sells for Rs. 30. How did you
do? Quite well. You invested 25 100 = Rs. 2,500. At the
end of the year, you have stock worth Rs. 3,000 and cash
dividends of Rs. 100. Your rupee gain was Rs.600 = 100+ (3,000 2,500).
Your percentage gain for the year is = 24.0 %
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Average Rate of Return
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Average Rate of Return
The average rate of return is the sum of the
various one-period rate of return divided by
the number of periods.
Average rate of return,
T
RRR T
)( 1 ++=
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Holding Period Returns
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Holding-Period Returns
The holding period return is the return that
an investor would get when holding an
investment over a period of n years, when
the return during yeari is given as ri:
1)1()1()1(
returnperiodholding
21+++=
=
nrrr
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Holding Period Return: Example
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Holding Period Return: Example
Suppose your investment provides thefollowing returns over a four-year period:
Year Return
1 10%
2 -5%
3 20%
4 15% %21.444421.
1)15.1()20.1()95(.)10.1(
1)1()1()1()1(
returnperiodholdingYour
4321
==
=++++=
=rrrr
1-78
Holding Period Return: Example
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So, our investor made 9.58% on his money for fouryears, realizing a holding period return of 44.21%So, our investor made 9.58% on his money for fouryears, realizing a holding period return of 44.21%
An investor who held this investment would haveactually realized an annual return of 9.58%:
Year Return
1 10%2 -5%
3 20%
4 15%%58.9095844.
1)15.1()20.1()95(.)10.1(
)1()1()1()1()1(
returnaverageGeometric
4
43214
==
=
++++=+
=
g
g
r
rrrrr
4)095844.1(4421.1 =
Holding Period Return: Example
1-79
The Variability of Stock Returns
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Variance (2
) a measure of volatility in units of percentsquared
Standard deviation ( ) a measure of volatility in percentage
terms
1
)(
Variance 1
2
2
==
=N
RRN
t
t
The Variability of Stock Returns
VariancedeviationStandard =
1-80Individual Securities or Single FinancialAssets
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Assets
The characteristics of individualsecurities that are of interest are the:
Expected Return Variance and Standard Deviation
Covariance and Correlation
1-81Single Financial Assets:: Expected Return &Risk
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Risk
Investors and analysts often look at historical returns as
a starting point for predicting the future.
However, they are much more interested in what the
returns on their investments will be in the future.
For this reason, we need a method for estimating future
returns.
One way of doing this is to assign probabilities for
future states of nature and the returns that would be
realized if a particular state of nature would occur.
1-82Return Measurement for a SingleAsset E pected Return
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Asset: Expected Return
The most common statistical indicator of an assets risk is thestandard deviation,
k, which measures the dispersion
around the expected value.
The expected value of a return, k-bar, is the most likely
return of an asset.
1-83
Example : Expected Return,Variance & Standard Deviation
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Consider the following two risky asset world.
There is a 1/3 chance of each state of the
economy and the only assets are a stock fund anda bond fund.
Rate of ReturnScenario Probability Stock fund Bond fund
Recession 33.3% -7% 17%
Normal 33.3% 12% 7%
Boom 33.3% 28% -3%
Variance & Standard Deviation
1-84
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
Variance & Standard Deviation
1-85
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
%11)(
%)28(3
1%)12(3
1%)7(3
1)(
=
++=
S
S
rE
rE
Variance & Standard Deviation
1-86
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
%7)(
%)3(3
1%)7(3
1%)17(3
1)(
=
++=
B
B
rE
rE
Variance & Standard Deviation
1-87
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
%24.3%)7%11(2 =
Variance & Standard Deviation
1-88
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
%01.%)12%11(2 =
Variance & Standard Deviation
1-89
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
%89.2%)28%11(2 =
Variance & Standard Deviation
1-90
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
%)89.2%01.0%24.3(3
1%05.2 ++=
Variance & Standard Deviation
1-91
Example : Expected Return,Variance & Standard Deviation
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
0205.0%3.14 =
Variance & Standard Deviation
1-92
Portfolio Risk and Return
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Portfolio Risk and Return
An investment portfolio is any collection or combination of
financial assets.
If we assume all investors are rational and therefore risk averse,that investor will ALWAYS choose to invest in portfolios ratherthan in single assets.
Investors will hold portfolios because he or she will diversifyaway a portion of the risk that is inherent in putting all your eggsin one basket.
If an investor holds a single asset, he or she will fully suffer the
consequences of poor performance.
This is not the case for an investor who owns a diversifiedportfolio of assets.
1-93
Risk of a Portfolio
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Risk of a Portfolio
Diversification is enhanced depending upon the extent to
which the returns on assets move together. This movement is typically measured by a statistic known
as correlation as shown in the figure below.
1-94
Risk of a Portfolio (cont.)
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s o a o o o (co )
Even if two assets are not perfectly negatively
correlated, an investor can still realize diversificationbenefits from combining them in a portfolio as shown in
the figure below.
1-95
Portfolios
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Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 3.24% 17% 1.00%
Normal 12% 0.01% 7% 0.00%
Boom 28% 2.89% -3% 1.00%
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
Note that stocks have a higher expected return than bonds andhigher risk. Let us turn now to the risk-return tradeoff of a portfolio
that is 50% invested in bonds and 50% invested in stocks.
1-96
Portfolios
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Rate of Return
Scenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.160%
Normal 12% 7% 9.5% 0.003%
Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%
Variance 0.0205 0.0067 0.0010
Standard Deviation 14.31% 8.16% 3.08%
The rate of return on the portfolio is a weighted average of the
returns on the stocks and bonds in the portfolio:
SSBBP rwrwr +=
%)17(%50%)7(%50%5 +=
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Portfolios
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Rate of Return
Scenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.160%
Normal 12% 7% 9.5% 0.003%
Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%
Variance 0.0205 0.0067 0.0010
Standard Deviation 14.31% 8.16% 3.08%
The rate of return on the portfolio is a weighted average of the
returns on the stocks and bonds in the portfolio:
%)7(%50%)12(%50%5.9 +=
SSBBP rwrwr +=
1-98
Portfolios
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Rate of Return
Scenario Stock fund Bond fund Portfolio squared deviation
Recession -7% 17% 5.0% 0.160%
Normal 12% 7% 9.5% 0.003%
Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%Variance 0.0205 0.0067 0.0010
Standard Deviation 14.31% 8.16% 3.08%
The rate of return on the portfolio is a weighted average of the
returns on the stocks and bonds in the portfolio:
%)3(%50%)28(%50%5.12 +=
SSBBP rwrwr +=
1-99
Portfolios
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Rate of Return
Scenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.160%
Normal 12% 7% 9.5% 0.003%
Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%
Variance 0.0205 0.0067 0.0010
Standard Deviation 14.31% 8.16% 3.08%
The expectedrate of return on the portfolio is a weighted average
of the expectedreturns on the securities in the portfolio.
%)7(%50%)11(%50%9 +=
)()()( SSBBP rEwrEwrE +=
1-100
Portfolios
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Rate of Return
Scenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.160%
Normal 12% 7% 9.5% 0.003%
Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%
Variance 0.0205 0.0067 0.0010
Standard Deviation 14.31% 8.16% 3.08%
The variance of the rate of return on the two risky assets portfolio is
BSSSBB2
SS2
BB2
P ))(w2(w)(w)(w ++=
where BS is the correlation coefficient between the returns on the
stock and bond funds.
1-101
Portfolios
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Rate of ReturnScenario Stock fund Bond fund Portfolio squared deviation
Recession -7% 17% 5.0% 0.160%
Normal 12% 7% 9.5% 0.003%
Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%
Variance 0.0205 0.0067 0.0010
Standard Deviation 14.31% 8.16% 3.08%
Observe the decrease in risk that diversification offers.
An equally weighted portfolio (50% in stocks and 50% in bonds)
has less risk than stocks or bonds held in isolation.
1-102
Portfolio Risk and Return
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A measure of the degree to which two variables move together
relative to their individual mean values over time
The Covariance between the returns on two stocks can becalculated as follows:
N
Cov(RA,RB) = A,B = pi(RAi - E[RA])(RBi - E[RB]) i=1
Where: , = the covariance between the returns on stocks A and B
N = the number of states
pi = the probability of state i R
Ai= the return on stock A in state i
E[RA] = the expected return on stock A
RBi
= the return on stock B in state i
E[RB] = the expected return on stock B
1-103
Portfolio Risk and Return
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The correlation coefficient is obtained by standardizing (dividing) the
covariance by the product of the individual standard deviations
The Correlation Coefficient between the returns on two stocks can be
calculated as follows:
A,B Cov(RA,RB)
Corr(RA,RB) = A,B = A B = SD(RA)SD(RB)
Where:
A,B
=the correlation coefficient between the returns on stocks A and B
A,B
=the covariance between the returns on stocks A and B,
A=the standard deviation on stock A, and
B=the standard deviation on stock B
1-104Two-Security Portfolios with VariousCorrelations
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100%
bonds
re
turn
100%
stocks
= 0.2
= 1.0
= -1.0
Relationship depends on correlation coefficient
-1.0 < < +1.0
If = +1.0, no risk reduction is possible
If = 1.0, complete risk reduction is possible
1-105Portfolio Risk as a Function of the Numberof Stocks in the Portfolio
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Nondiversifiable risk;
Systematic Risk;Market Risk
Diversifiable Risk;
Nonsystematic Risk;
Firm Specific Risk;Unique Risk
n
In a large portfolio the variance terms are effectively
diversified away, but the covariance terms are not.
Thus diversification can eliminate some, but not all of the risk of
individual securities.
Portfolio risk
1-106Risk Diversification: Systematic &Unsystematic Risk
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Asystematic riskis any risk that affects a large number of assets,
each to a greater or lesser degree.
It arises on account of economy wide uncertainties and the
tendency of individual securities to move together with changes
in the market. It is also known as Market risk.
Examples of systematic risk include uncertainty about general
economic conditions, such as GNP, interest rates or inflation.
This part of risk cannot be reduced through diversification.
1-107Risk Diversification: Systematic &Unsystematic Risk
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An unsystematic riskis a risk that specifically affects a single
asset or small group of assets.
It arises from the unique uncertainties of individual securities. It
is also called unique risk.
These uncertainties are diversifiable if a large number ofsecurities are combined to form well-diversified portfolios. Thus
unsystematic risk can be totally reduced through diversification.
Announcements specific to a company, such as a gold miningcompany striking gold, the government increases custom duty,
are examples of unsystematic risk.
Unsystematic Risk
1-108Relationship between Risk andExpected Return (CAPM)
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p ( )
Expected Return on the Market:
Expected return on an individual security:
PremiumRiskMarket+=F
M RR
)( FMiFi RRRR +=
Market Risk Premium
This applies to individual securities held within well-diversified portfolios.
1-109Expecte Return on an In v uaSecurity
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This formula is called the Capital Asset PricingModel (CAPM)
)( FMiFi RRRR +=
Assume i = 0, then the expected return isRF. Assume i = 1, then Mi RR =
Expectedreturn on
a security
=Risk-
free rate+
Beta of the
security
Market risk
premium
1-110Capital Asset Pricing Model (CAPM):Assumptions
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Market efficiency: The Capital Market efficiency implies that
share prices reflect all available information. Also, individual arenot able to effect the prices of securities. This means that there
are large number of investors holding small amount of wealth.
Risk aversion and mean-variance optimization: Investors are
risk-averse. They evaluate a securitys return and risk in terms of
expected return and variance or standard deviation respectively.
They prefer the highest expected returns for a given level of
risks. This implies that investors are mean-variance and they
form efficient portfolios.
1-111
CAPM Assumptions contd.
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Homogeneous Expectations: All investors have the
same expectations about the expected returns andrisk of securities.
Single Time period: All investors decisions arebased on single time period.
Risk-free rate: All investors can lend and borrow at
a risk-free rate of interest. They form portfoliosfrom publicly traded securities like shares and
bonds.
1-112
Capital Market Line
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The capital market (securities markets) is the market for securities
The capital market includes the stock market and the bond market.
CML is used to illustrate all of the efficient portfolio combinations
available to investors.
The CML is derived by drawing a tangent line from the intercept
point on the efficient frontier to the point where the expected return
equals the risk-free rate of return.
1-113
Capital Market Line
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The Capital Market Line
Expected Return onthe Portfolio
Standard Deviation of thePortfolio
0%
0% 10%
4%
8%
20% 30% 40%
12%
Risk-freerate
Capital
MarketLine
1-114
Capital Market Line
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The Capital Market Line and Iso Utility Curves
Expected Return onthe Portfolio
Standard Deviation of thePortfolio
0%
0% 10%
4%
8%
20% 30% 40%
12%
Risk-freerate
CapitalMarket
Line
HighlyRisk
AverseInvestor
A risk-taker
1-115
The Security Market Line
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Portfolio E(R) Beta
Risk-free asset Rf 0
Market portfolio E(Rm) 1
Consider a portfolio composed of the following two assets:
An asset that pays a risk-free return Rf, , and
A market portfolio that contains some of every risky asset inthe market.
Security market line: the line connecting the risk-free
asset and the market portfolio
1-116
The Security Market Line
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The Security Market Line shows how an investor can construct a
portfolio of T-bills and the market portfolio to achieve the
desired level of risk and return.
1-117
The Security Market Line
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In equilibrium, all assets lie on this line.
If individual stock or portfolio lies above the line:
Expected return is too high stock is undervalued.
Investors bid up price until expected return falls.
If individual stock or portfolio lies below SML:
Expected return is too low stock is overvalued.
Investors sell stock driving down price until expected
return rises.
Plots relationship between expected return and betas.
1-118
The Security Market Line
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i
E(RP)
RF
SML
Slope = (y2-y1) / (x2-x1)
= [E(RM) R
F] / (M-0)
= [E(RM) RF] / (1-0)
= E(RM) RF
= Market Risk Premium
A - Undervalued
RM
M =1.0
B
A
B - Overvalued
1-119
Capital Market Line v/sSecurity Market Line
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The capital market line (CML) is a line used in the capital asset
pricing model to illustrate the rates of return for efficient whilethe security market line (SML) is a line that graphs the
systematic, or market, risk versus return of the whole market at
a certain time and shows all risky marketable securities.
The CML is derived by drawing a tangent line from the
intercept point on the efficient frontier to the point where theexpected return equals the risk-free rate of return while the
SML essentially graphs the results from the capital asset
pricing model (CAPM) formula. The x-axis represents the risk
(beta), and the y-axis represents the expected return. Themarket risk premium is determined from the slope of the SML.
1-120
Capital Market Line v/sSecurity Market Line
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What is plotted CML plots efficient portfolios, i.e. combinations
of the risky portfolio and the risk-free asset (it is
not valid for individual assets)
SML plots individual assets and portfolios
Measure of risk
for CML standard deviation (because welldiversified portfolios)
f SML b (b i di id l )