5. introduction to risk and return

8/3/2019 5. Introduction to Risk and Return

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Financial Management I

5. Introduction to Risk and Return



Course Content - Syllabus

Sr Title ICMR Ch. PC Ch. IMP Ch.

1 Introduction to Financial Management 1* 1 1

2 Overview of Financial Markets 2* 2 -

3 Sources of Long-Term Finance 10* 17 20, 21

4 Raising Long-term Finance - 18* 20, 21, 23

5 Introduction to Risk and Return 4* 8, 9 4, 5

6 Time Value of Money

7 Valuation of Securities

8 Cost of Capital

9 Basics of Capital Expenditure Decisions

10 Analysis of Project Cash Flows

11 Risk Analysis and Optimal Capital

Expenditure Decision2 / 59



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Introduction to Risk and Return

Reference Books

1. Financial Management, ICMR Book, Chapter 4

2. Financial Management, Prasanna Chandra, 7th

Edition, Chapter 8, 9

3. Financial Management, I. M. Pandey, 9th Edition,



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Syllabus – Introduction to Risk and Return

1. Risk and Return Concepts

2. Risk in a Portfolio Context

3. Relationship between Risk and Return



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Introduction

•

While making the decisions regarding financing andinvestment, the finance manager seeks to achieve the

right balance between risk and return, in order to

optimize the value of the firm.

• Return and risk go together in investments.

• Every investor wants minimum or no risk. Government

bonds are risk-free but offer less returns.



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• Objective of any investor is to maximize expected returns

from his investments, with minimum risk.

• Importance of returns as follows

• It enables investors to compare alternative

investments possible

• Measurement of historical returns show the past



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• Historical Returns (Realized returns): Also called as ex-

post (after the fact) returns.• Expected Returns (Future returns): Also called as ex-

ante or anticipated returns. The expected returns are

subjected to uncertainty or risk hence the component of

probability is attached to it.• Com onents of Returns



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• Historical Returns (Realized returns): Also called as ex-

post (after the fact) returns.

Rate of Return = Dividend yield + Capital Gain Yield

1t

1tt1

P)P(PDk

−

−−+=

∑==

n

1i

iik pk



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Illustration 1

• The price of ACC share on Feb 8, 2008 was Rs 3580 and

it has increase to Rs 3800 in Feb 9, 2009 and dividend

paid was Rs 35. Calculate the rate of return.

• Solution:

1t

1tt1

P

)P(PDk

−

−−+=

3580)3580(380035 −+

=

7.12%or 0.0712=



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Illustration 2

• If a14%, Rs 1000 ICICI debenture purchased at 1350

and price is Rs 1500 at the end of the year, what is the

rate of return.

• Solution:

1t

1tt1

P

)P(PDk

−

−−+=

1350)1350(1500140 −+

=

21.48%or 0.2148=



11 / 59

Probabilities and Rates of Return

Probability is a number that describes the chances of an

event taking place. Probabilities are governed by five

rules and range from 0 to 1.•

The probability can never be larger than 1 (i.e.maximum probability of an event taking place is 100%)

• The sum total of probabilities must be equal to 1.• The probability can never be a negative number.• If an outcome is certain to occur, it is assigned a



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Illustration 3

• The probability distribution and corresponding rates of return of Alpha Company are shown below

•

Possible Outcome (i) Probability of Occurrence(Pi)

Rate of return (%)(Ki)

1 0.10 50

2 0.20 303 0.40 10

4 0.20 -10

5 0.10 -30

Total = 1.00

∑=

=n

1i

iik pk



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Risk

• Risk and return go hand in hand in investment and

finance. Investment decisions always involve a trade-off

between risk and return.

• Risk can be defined as the chance that the actual

outcome from an investment will differ from the



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Risk

Where to invest out of following two stocks ?

•

Both the stocks have same average returns, but the

Returns %Average

Returns %Standard

Deviation %

Stock M 30 28 34 32 31 31 2.236

Stock N 26 13 48 11 57 31 20.700



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Risk and Expected Rate of Return

• Width of a probability distribution of rates of return is a

measure of risk.• The wider the probability distribution, greater is the

risk. Greater the variability of return, greater the

variance.



Illustration

Pi Ki(%)

1 0.05 38

2 0.20 23

3 0.50 8

4 0.20 -7

5 0.05 -22

1.00

Pi Ki(%)

1 0.10 90

2 0.25 50

3 0.30 20

4 0.25 -10

5 0.10 -50

1.00

Beta Company Gamma Company

%8= K %20= K

0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 10

0.1

0.2

0.3

0.4

0.5

Probability

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

Probability

Return Return16 / 59



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Illustration

0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1

0

0.1

0.2

0.3

0.4

0.5

Probability

0 0.2 0.4 0.6 0.8 1

0

0.1

0.2

0.3

0.4

0.5

Probability

Return Return

Beta Company Gamma Company



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Sources of Risk

What are the sources of risk? What are the factors which

make any financial asset risky? They are as follows.

•

Interest Rate Risk • Market Risk

• Inflation Risk

• Business Risk



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Measurement of Total Risk

• Risk is associated with the dispersion in the likely

outcome.

• Dispersion refers to variability.

• If the assets return has no variability, it has no risk.

i



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Variance

• The variance of an asset’s rate of return can be found as

the sum of the squared deviation of each possible rate of

return from the expected rate of return multiplied by the

probability that rate of return occurs.

2n

1i

ii )k (k pVAR(k) ∑=

−=

S d d D i i



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Standard Deviation

• The most popular way of measuring variability of return

is standard deviation.

• The standard deviation is denoted by σ is simply square

root of variance.

2σ σ =

VAR(k)=

2n

1i

)k -(ki pi∑=

=

Ri k i f R



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Risk per unit of Return

• The risk per unit of return is calculate using the

coefficient of variance.

• Coefficient of Variance =

•

k σcov =



• Calculate the variance and standard deviation for Alpha

Company’s rates of return.

Illustration

Possible

Outcome

ki(%) pi

1 50 40 1600 0.10 160

2 30 20 400 0.20 80

3 10 0 0 0.40 0

4 -10 -20 400 0.20 80

5 -30 -40 1600 0.10 160

Variance =

k k i − ( )2k k i −2)( k k p ii −

∑ =− 480)( 2k k p ii

2/1

2

1

)()(

−== ∑

=

n

i

ii k k pk VARσ

21.9%480 == 23 /59

Ill t ti



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Illustration

Calculate the risk of stocks of following company

Solution:

Scenario Chance pi Return %ri pi x ri Deviation

(ri - E)Deviation2

(ri - E)2pi x Deviation2i.e. pi(ri - E)2

1 0.25 36 9 11 121 30.25

2 0.5 26 13 1 1 0.50

3 0.25 12 3 -13 169 42.25

E = 25 Sum = 73

Scenario Chance p Returns %

1 0.25 36

2 0.50 26

3 0.25 12



• What is portfolio? An investment portfolio refers to

group of assets that owned by the investor.• Generally, investing in a one security is riskier than

investing in portfolio.

•

In order to reduce the risk, investor hold a diversifiedportfolio consisting of equity, bonds, real estate, saving

in banks, and or bullion.

•

It is possible to construct a portfolio in such a way thattotal risk of such portfolio is less than risk of individual

assets.

• The saying, don’t put all eggs in a single basket.

2. Risk in a Portfolio Context

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•

Portfolio diversification is the investment in several

different asset classes or sectors

• Diversification is not just holding a lot of assets

§ For example, if you own 50 Internet stocks, you are

not diversified

§ However, if you own 50 stocks that span 20 different

industries, then you are diversified

Diversification

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Ri k i P tf li C t t



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Risk in a Portfolio Context

Example of investment in two companies

Returns %in summer (hot

season)

Returns % inwinter (cold

season)

AverageReturns %

Risk i.e.Standard

deviation %

Ice Cream Co. 30 10 20 10

Coffee Co. 10 30 20 10

Investment in bothcompanies 20 20 20 0

Di ifi bl d N di ifi bl Ri k



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Diversifiable and Non-diversifiable Risk

•

Returns on stocks do not move in perfect tandem means

that risk can be reduced by diversification.

• There is some positive correlation means that risk can

never be reduced to zero.

C l ti C ffi i t



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Correlation Coefficient ρ

• Movement of security returns is studied by correlation

coefficient•

If two returns move exactly in same direction, thencorrelation coefficient is +1

• If two returns move exactly opposite to each other, then

correlation coefficient is -1•

If two returns are entirely unrelated, then correlationcoefficient is 0

• Positive correlation coefficient , up to +1 indicates that

two returns move in same direction but not in same value•

Negative correlation coefficient , up to -1 indicates that

N b f St k i th P tf li



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Number of Stocks in the Portfolio

•

Risk reduction by diversification depends on the numberof stocks in the portfolio.

• As the number of stocks increase, the diversifying effect

of each additional stock diminishes as shown in figure

below.

Number of Stocks in10 20 30 40 200

Diversifiable Risk or

Unsystematic Risk

Non-diversifiable Risk or Market Risk orSystematic Risk

Total Risk of aportfolio

R i s k




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• Major benefits of diversification are obtained with the

first 10 to 12 stocks, provided they are drawn fromindustries that are not closely related.

• As the number of securities in a portfolio increases, say

up to 20 or 25, diversification reduces the portfolio risk

rapidly.

Diversifiable and Non diversifiable Risk



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•

Risk of any individual stock can be separated into twocomponents: diversifiable risk and non-diversifiable risk.

• Non-diversifiable risk is related to the general economy

or the stock market as a whole and hence can not be

eliminated by diversification. Non-diversifiable risk is

also called as market risk or systematic risk.

•

Diversifiable risk is specific to the company or industry

Diversifiable and Non diversifiable Risk



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• Risks are classified as systematic and unsystematic risks.• Some risk factors may affect an industry as a whole,

while some risk factors affect only a specific firm. Forexample monsoon may affect agro industry whereas raw

material cost may affect a specific firm• Systematic risk factors affect the entire market and such

risks can not be diversified or non-diversifiable

Non diversifiable or Market Risk or



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Non-diversifiable or Market Risk orSystematic Risk Factors

They are dependent on an economic environment or

system as a whole

• Major changes in the tax rates

• War and other calamities

• An increase or decrease in inflation rates

•

Diversifiable or Specific Risk or Unsystematic



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Diversifiable or Specific Risk or UnsystematicRisk Factors

They are dependent on specific company or industry

•

Company strike

• Bankruptcy of a major supplier

•

Death of a key company officer

Returns and Risk of a Portfolio



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Returns and Risk of a Portfolio

• Portfolio is a combination of two or more securities.

• Portfolio Returns

Returns and Risk in Two Asset Portfolio Case



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Returns and Risk in Two Asset Portfolio Case

•

A two asset portfolio is a situation in which theinvestment is in only two assets.

• Expected Returns from the portfolio:

2,121

2

2

2

2

2

1

2

1

2 2 σ σ σ σ wwww p ++=

212,121

2

2

2

2

2

1

2

1

2 2 σ σ ρ σ σ σ wwww p ++=21

1,21,2

σσ

σρ =

Example



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Example

Calculate the expected return, variance and standard

deviation for a portfolio containing stocks 1 and 2 with

correlation coefficient 0.75 and following information.

Security Returns % StandardDeviation %

Proportion of investments

1 12 10 2/3

2 18 26 1/3

Solution



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Solution

Expected portfolio returns:

= W1E1 + W2E2 + W3E3+…+WnEn

= 2/3 x 0.12 + 1/3 x 0.18

= 0.14 or 14%

Variance of a portfolio:

∑=

=n

1i

ii p EW)E(r



40 /59

σp2 = W12σ12 + W22 σ22+ 2W1W2 ρ1,2 σ1σ2

= (2/3)2 x 0.12 + (1/3)2 x 0.22 + 2 x 2/3 x 1/3 x 0.75

x0.1x0.2

Example



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Example

A portfolio of two securities x & y is with following

information. Evaluate the impact of diversification on

expected risk and returns for three different values of

correlation coefficients 1, 0.5 and -1.

Security Returns % StandardDeviation %

Proportion of investments %

X 20 10 40

y 30 16 60

Solution



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Solution

Expected portfolio returns:

= W1E1 + W2E2 + W3E3+…+WnEn

= 0.20 x 0.40 + 0.30 x 0.60

= 0.08 + 0.18

= 0.26 or 26%

Case 1: With ρ1,2 = 1

∑==

n

1i

ii p EW)E(r



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Case 2: With ρ1,2 = 0.5

σp2 = W12σ12 + W22 σ22+ 2W1W2 ρ1,2 σ1σ2

= 0.42 x 0.12 + 0.62 x 0.162 + 2 x 0.4 x 0.6 x 0.5 x 0.1 x

0.16

= 0.014656

σp = 0.121 or 12.1 %

Case 3: With ρ1,2 = -1

σp2 = W12σ12 + W22 σ22+ 2W1W2 ρ1,2 σ1σ2

= 0.42 x 0.12 + 0.62 x 0.162 + 2 x 0.4 x 0.6 x (-1) x 0.1 x

0.16



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Summary of results

Portfoliocomponents

x y x & y

ρ1,2 = 1

x & y

ρ1,2 = 0.5

x & y

ρ1,2 = -1

Mean Returns % 20 30 26 26 26

Risk σ % 10 16 13.6 12.1 5.6

Risk of Stocks in a Portfolio



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Risk of Stocks in a Portfolio

• In the portfolio context, variance is not the relevant risk

measure

• Riskiness of security when held in isolation is not the

same as the riskiness of a portfolio of securities, when

that security is included in the portfolio

•

It may be useful to regard risk or variability to factors

specific to an industry and a firm.

3 Relation between Risk and Return



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3. Relation between Risk and Return

Beta (β)

•

Modern Portfolio Theory defines the riskiness of a

security measured by beta (β), the sensitivity of returns

of security w.r.t the market returns.

• Beta measures the kind of risk which is non-diversifiable.

Higher the value of beta, higher the riskiness of the

security

Estimating the Beta (β) values



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• Simple linear regression method

•

General form of the regression modely = a + b x + ε

• Particular form of regression model

ri = α + β rm + ε …(1)

From this β = σi,m/σm2 …(2)

• Market return is defined as




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Regression (Characteristic) line

intercept

slope

S e c u r i t y

r e t u r n

Market return

Estimating Beta (β) values



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Estimating Beta (β) values

•

Beta for a portfolio is a weighted average of the betas of

individual securities

• Three methods of estimating betas

1. Based on historical returns data

2. Based on expected probability distribution

3. Estimating betas by adjusting historical betas,

Historical Betas



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Historical Betas

Historical betas are calculated based on covariance and

standard deviation values as

β = σi,m/σm2

Adjusted beta are calculated based on historical betas,

adjusting for factors causing change in future for

4 C i A i i



•

We have seen that the most used measure of risk orvariability in finance is standard deviation.

• Unique risk stems from firm specific features, where as

market risk emanates from economy wide features.

• Portfolio diversification washes away unique risk but

not market risk.

• Hence the risk of a fully diversified portfolio is its

market risk.

4. Capital Asset Pricing Model

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C i l A P i i M d l



•

The contribution of a security to the risk of a fullydiversified portfolio is measured by its Beta, which

reflects the sensitivity to the general market movement.

• The question arises what is the rationality between the

risk of the security measured by beta and its expected

return.

• The answer is given in a model known as Capital Asset

Pricing Model. (CAPM)

Capital Asset Pricing Model

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C i l A P i i M d l



• CAPM is represented as

Kj = Rf + βj(Km-Rf)Where

Kj = Expected return on security J.

Rf= Risk Free rate of return.

βj= Beta Coefficient of the security j.

Km= Expected Return on Market portfolio.

• Required rate of Return = Risk free rate + Risk Premium


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C it l A t P i i M d l



• Required rate of Return = Risk free rate + Risk Premium

Kj = Rf + βj(Km-Rf)

• The CAPM provides an explicit measure of therisk premium. It is the product of beta for a

particular security j and the market risk premium.


Risk free rate Risk Premium

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C it l A t P i i M d l




• Suppose you have the following information:Rf = 3.5% Km=8.5% βril=0.75

•

What should Kril be?

Answer:

• Kril = 0.035+ 0.75(0.085-0.035)

= 7.25%

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S it M k t Li



Security Market Line

• All risky securities are expected to form part of

market portfolio (M) and be properly represented

by SML. Stand alone securities do not provide

diversification.

•

Investors investing in single security will becompensated only for the systematic risk borne by

them and not for the unsystematic risk.

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S it M k t Li




• Hence the risk premium provided for anundiversified portfolio is in proportion to the risk premium provided for completely diversifiedmarket portfolio.

( )

−+= f mi f i R R R R E

_

β

2

,,

m

mi

m

mi

iVar

Cov

σ

σ β ==

57 /59




58 /59

y

The SML represents the average or normal, trade-off

between risk and return for a group of securities

SML

A

v e r a g e r e t u r n

f o r

g

r o u p o f s e c u r i

t i e s

r

i

Betas for different securities, risk

Below normal expected returns

Above normal expected returns

Applications of Security Market Line



pp y

Historical SML:

1.

Evaluating performance of portfolio manager2. Tests asset pricing theories such as CAPM

3. Tests market efficiency

Ex-ante SMLs

1. Identifying undervalued securities

2. Determining consensus, ‘price of risk’ in current

5. introduction to risk and return

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