Risk Return PPT

5-1

RISKRISK && RETURNRETURNRISKRISK && RETURNRETURN

Trade-OffTrade-OffMr. Rohan S.Mr. Rohan S.Ms. Shobhna M.Ms. Shobhna M.Mr. Prasad D.Mr. Prasad D.

5-2

Defining RiskDefining RiskDefining RiskDefining Risk

The variability of returns from The variability of returns from those that are expected.those that are expected.

The variability of returns from The variability of returns from those that are expected.those that are expected.

The chance of financial The chance of financial lossloss or or more formally the variability of more formally the variability of returns associated with a given returns associated with a given asset.asset.

5-3

Defining ReturnDefining ReturnDefining ReturnDefining Return

Income received Income received on an investment plus any change in market pricechange in market price, usually expressed as a percent of the beginning market price beginning market price of the

investment.

Income received Income received on an investment plus any change in market pricechange in market price, usually expressed as a percent of the beginning market price beginning market price of the

investment.

The total gain or loss experienced on an investment over a given

period of time.

5-4

CCtt + (PPtt - - PPt-1t-1 )

PPt-1t-1

Rt =

Calculation of ReturnCalculation of Return

Ct = Cash flow received from the asset investment in the time period t-1 to t

Pt = Price (value) of asset at time t.

Pt-1 = Price (value) of asset at time t-1.

Rt = Actual, expected or required rate of return during the period t

5-5

Return ExampleReturn ExampleReturn ExampleReturn Example

The stock price for Stock A was $10$10 per share 1 year ago. The stock is currently

trading at $9.50$9.50 per share, and shareholders just received a $1 dividend$1 dividend.

What return was earned over the past year?




5-6

Return ExampleReturn ExampleReturn ExampleReturn Example







$1.00 $1.00 + ($9.50$9.50 - $10.00$10.00 )$10.00$10.00RR = = 5%5%

5-7

Types of RiskTypes of Risk

5-8

Firm Specific RiskFirm Specific Risk

Business Risk: The chance that the firm will be unable to cover its OPERATING COSTS.

Financial Risk: The chance that the firm will be unable to cover its FINANCIAL OBLIGATIONS.

5-9

Shareholder-Specific RisksShareholder-Specific Risks

Interest rate risk: The chance that the changes in interest rates will adversely affect the value of an investment. Most investments lose value when the interest rate rises & increases in value when it falls.

Liquidity risk: The chance that an investment cannot be easily liquidated at a reasonable price. Liquidity is significantly affected by the size & depth of the market in which an investment is customarily traded.

5-10

Continued…

Market risk: The chance that the value of an investment will decline because of market factors that are independent of the investment(such as economic, political & social events). In general, the more a given investment’s value responds to the market, the greater its risk & vice versa.

5-11

Firm & Shareholder RisksFirm & Shareholder Risks

Event Risk: The chance that a totally unexpected event will have a significant effect on the value of the firm or a specific investment. These infrequent events such as Govt. mandated withdrawal of a popular prescription drug, typically affect a small group of firms or investments.

Continued…

5-12

Exchange rate risk: The exposure of future expected cash flows to fluctuations in the currency exchange rate. The greater the chance of undesirable exchange rate fluctuations, the greater the risk of the cash flows & therefore the lower the value of the firm or investment.

Continued…

5-13

Purchasing-Power risk: The chance that changing price levels caused by inflation or deflation in the economy will adversely affect the firm’s or investment’s cash flows & value.

Typically, firms or investments with cash flows that move with general price levels have a low purchasing-power risk & vice versa.

Continued…

5-14

Tax risk: The chance that unfavorable changes in tax laws will occur. Firms & investments with values that are sensitive to tax changes are more risky.

5-15

Issuer Specific RiskIssuer Specific Risk

Default risk: The possibility that the issuer of debt will not pay the contractual interest or principal as scheduled.

Maturity risk: The fact that the longer the maturity, the more the value of the security will change in response to a given change in interest rates.

Contractual provision risk: Conditions that are often included in a debt agreement or a stock issue.

5-16

Risk PreferencesRisk Preferences

Feelings about risk differ among managers/firms. Thus it is important to specify a generally acceptable level of risk. The 3 basic risk preference behaviors are:

(1) Risk-Indifferent

(2) Risk-Averse

(3) Risk-Seeking

5-17

Risk-Indifferent:

The attitude toward risk in which no change in return would be required for an increase in risk.

Risk-Averse:

The attitude toward risk in which an increased return would be required for an increase in risk.

Risk-Seeking:

The attitude toward risk in which a decreased return would be required for an increase in risk.

5-18

Indifferent

Averse

Seeking

X1 X2

RiskAverse

RiskIndifferent

RiskSeeking

Risk

5-19

Types of Assets/SecuritiesTypes of Assets/Securities

Single Asset:Assets are economic resources. Anything tangible or intangible that

is capable of being owned or controlled to produce value and that is held to have positive economic value is considered an asset.

Simply stated, assets represent ownership of value that can be converted into cash (although cash itself is also considered an asset)

Portfolio: A collection or group of assets created or developed to minimize

risk in order to maximize returns.

OR

A combination of two or more securities/assets.

5-20

Sensitivity Analysis:Sensitivity Analysis:

An approach for assessing risk that uses several possible return estimates to obtain a sense of the variability[uncertainty] among outcomes.

RANGE:RANGE:

A measure of an asset’s risk which is found by subtracting the pessimistic(worst) outcome from the optimistic(best) outcome.

5-21

Probability:Probability:

The chance that a given outcome will occur.

Probability Distribution:Probability Distribution:

A model that relates probabilities to the associated outcomes.

5-22

Probability Distribution

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-15% -3% 9% 21% 33%

Discrete Continuous

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

-50%

-41%

-32%

-23%

-14% -5

% 4%13

%22

%31

%40

%49

%58

%67

%

Returns

5-23

Determining Expected Determining Expected Return (Discrete Dist.)Return (Discrete Dist.)Determining Expected Determining Expected Return (Discrete Dist.)Return (Discrete Dist.)

R = ( Ri )( Pi )

R is the expected return for the asset,

Ri is the return for the ith possibility,

Pi is the probability of that return occurring,

n is the total number of possibilities.

R = ( Ri )( Pi )


Ri is the return for the ith possibility,

Pi is the probability of that return occurring,

n is the total number of possibilities.

n

i=1

5-24

How to Determine the Expected How to Determine the Expected Return and Standard DeviationReturn and Standard DeviationHow to Determine the Expected How to Determine the Expected Return and Standard DeviationReturn and Standard Deviation

Stock BW Ri Pi (Ri)(Pi)

-.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 0.090.090

Stock BW Ri Pi (Ri)(Pi)

-.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 0.090.090

The expected return, R, for Stock BW is .09

or 9%

5-25

Determining Standard Determining Standard Deviation (Risk Measure)Deviation (Risk Measure)Determining Standard Determining Standard Deviation (Risk Measure)Deviation (Risk Measure)

= ( Ri - R )2( Pi )

Standard DeviationStandard Deviation, , is a statistical measure of the variability of a distribution

around its expected return.

It is the square root of variance.

Note, this is for a Discrete Distribution.

= ( Ri - R )2( Pi )

Standard DeviationStandard Deviation, , is a statistical measure of the variability of a distribution

around its expected return.

It is the square root of variance.

Note, this is for a Discrete Distribution.

n

i=1

5-26

Determining Expected Determining Expected Return (Continuous Dist.)Return (Continuous Dist.)Determining Expected Determining Expected Return (Continuous Dist.)Return (Continuous Dist.)

R = ( Ri ) / ( n )


Ri is the return for the ith observation,

n is the total number of observations.

Probability is assumed to be equal

R = ( Ri ) / ( n )


Ri is the return for the ith observation,

n is the total number of observations.


n

i=1

5-27


n

i=1 = ( Ri - R )2

( n - 1)

Note, this is for a continuous distribution where the distribution is for a

population. R represents the population mean in this example.


= ( Ri - R )2

( n - 1)

Note, this is for a continuous distribution where the distribution is for a

population. R represents the population mean in this example.


5-28

How to Determine the Expected How to Determine the Expected Return and Standard DeviationReturn and Standard DeviationHow to Determine the Expected How to Determine the Expected Return and Standard DeviationReturn and Standard Deviation

Stock BW Ri Pi (Ri)(Pi) (Ri - R )2(Pi)

-.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042 .00288 .33 .10 .033 .00576 Sum 1.00 .090.090 .01728.01728

Stock BW Ri Pi (Ri)(Pi) (Ri - R )2(Pi)

-.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042 .00288 .33 .10 .033 .00576 Sum 1.00 .090.090 .01728.01728

5-29


= ( Ri - R )2( Pi )

= .01728

= .1315.1315 or 13.15%13.15%

= ( Ri - R )2( Pi )

= .01728

= .1315.1315 or 13.15%13.15%

n

i=1

5-30

Coefficient of Variation [CV]Coefficient of Variation [CV]Coefficient of Variation [CV]Coefficient of Variation [CV]

The ratio of the standard deviation standard deviation of a distribution to the Expected Rate of

Return of that distribution.

It is a measure of RELATIVERELATIVE dispersion that is used in comparing

the risks of assets with differing Expected Rate of Return.

CV = / RR

The ratio of the standard deviation standard deviation of a distribution to the Expected Rate of

Return of that distribution.

It is a measure of RELATIVERELATIVE dispersion that is used in comparing

the risks of assets with differing Expected Rate of Return.

CV = / RR

5-31

Coefficient of Variation [CV]Coefficient of Variation [CV]Coefficient of Variation [CV]Coefficient of Variation [CV]

It is a measure of RELATIVERELATIVE risk.

CV = / RR

CV of BW = .1315.1315 / .09.09 = 1.46

It is a measure of RELATIVERELATIVE risk.

CV = / RR

CV of BW = .1315.1315 / .09.09 = 1.46

Higher CV, the greater the risk & therefore the higher expected return of rate

5-32

SBI ICICI

Returns (Ri) [%]

Probability (Pi) [%]

Returns (Ri) [%]


22 0.05 12 0.05

16 0.15 8 0.08

12 0.25 6 0.10

6 0.45 -5 0.50-8 0.10 - 10 0.27

June 2010 Q7June 2010 Q7Find out Expected Rate of Return Find out Expected Rate of Return [[RR]] & & Standard Deviation Standard Deviation [[] ]

5-33

Expected Rate of Return Expected Rate of Return [[RR] ] for SBIfor SBI

Returns (Ri) [%]


Weighted Value R = (Ri)(Pi)

22 0.05 1.1

16 0.15 2.4

12 0.25 3.0

6 0.45 2.7-8 0.10 - 0.8

1.0 R = 8.4%

5-34

Expected Rate of Return Expected Rate of Return [[RR]] for ICICIfor ICICI

Returns (Ri) [%]


Weighted Value R = (Ri)(Pi)

12 0.05 0.60

8 0.08 0.64

6 0.10 0.60-5 0.50 - 2.50

- 10 0.27 - 2.70

1.0 R = - 3.36%

5-35

Standard Deviation Standard Deviation [[]] of of SBISBI

Returns (Ri)

Expected Return [R]

(Ri - R ) (Ri - R )2 Probability

(Pi) (Ri - R )2 * (Pi)

22 8.4% 13.6 184.96 0.05 9.248

16 8.4% 7.6 57.76 0.15 8.664

12 8.4% 3.6 12.96 0.25 3.24

6 8.4% - 2.4 5.76 0.45 2.592-8 8.4% - 16.4 268.96 0.10 26.896

1.0

5-36

Standard Deviation Standard Deviation [[]] of of ICICIICICI

Returns (Ri)

Expected Return [R]

(Ri - R ) (Ri - R )2 Probability (Pi)

(Ri - R )2 * (Pi)

12 - 3.36% 15.36 235.93 0.05 11.79

8 - 3.36% 11.36 129.05 0.08 10.32

6 - 3.36% 9.36 87.61 0.10 8.76-5 - 3.36% - 1.64 2.69 0.50 1.34

- 10 - 3.36% - 6.64 44.09 0.27 11.90

1.0

5-37

Continuous Continuous Distribution ProblemDistribution Problem

Assume that the following list represents the continuous distribution of population returns for a particular investment (even though there are only 10 returns).

9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5%

Calculate the Expected Return and Standard Deviation for the population assuming a continuous distribution.

5-38

Expected rate of return is 9% for the 10 observations.

Population SD is 13.32%

5-39

RP = ( Wj )( Rj )

RP is the expected return for the portfolio,

Wj is the weight (investment proportion) for the jth asset in the portfolio,

Rj is the expected return of the jth asset,

m is the total number of assets in the portfolio.

RP = ( Wj )( Rj )

RP is the expected return for the portfolio,

Wj is the weight (investment proportion) for the jth asset in the portfolio,

Rj is the expected return of the jth asset,

m is the total number of assets in the portfolio.

Determining PortfolioDetermining PortfolioExpected ReturnExpected ReturnDetermining PortfolioDetermining PortfolioExpected ReturnExpected Return

m

j=1

5-40

Determining Portfolio Determining Portfolio Standard DeviationStandard DeviationDetermining Portfolio Determining Portfolio Standard DeviationStandard Deviation

=p

p is the SD for portfolio.

W1 is the weight (investment proportion) for the 1st asset in the portfolio,.. W2

1 is the SD for the 1st asset in the portfolio

r1,2 is the correlation coefficient between 2 assets

p is the SD for portfolio.

W1 is the weight (investment proportion) for the 1st asset in the portfolio,.. W2

1 is the SD for the 1st asset in the portfolio

r1,2 is the correlation coefficient between 2 assets

W1+W22W1 W2 r1,2+1 2

2 2

5-45

Stock C Stock D Portfolio

ReturnReturn 9.00% 8.00% 8.64%

Stand.Stand.Dev.Dev. 13.15% 10.65% 10.91%

CVCV 1.46 1.33 1.26

The portfolio has the LOWEST coefficient of variation due to diversification.

Stock C Stock D Portfolio

ReturnReturn 9.00% 8.00% 8.64%

Stand.Stand.Dev.Dev. 13.15% 10.65% 10.91%

CVCV 1.46 1.33 1.26

The portfolio has the LOWEST coefficient of variation due to diversification.

Summary of the Portfolio Summary of the Portfolio Return and Risk CalculationReturn and Risk CalculationSummary of the Portfolio Summary of the Portfolio Return and Risk CalculationReturn and Risk Calculation

5-46

Correlation CoefficientCorrelation CoefficientCorrelation CoefficientCorrelation Coefficient

A standardized statistical measure of the linear relationship between

two variables.

Its range is from -1.0 -1.0 (perfect negative correlation), through 00 (no correlation), to +1.0 +1.0 (perfect

positive correlation).

A standardized statistical measure of the linear relationship between

two variables.

Its range is from -1.0 -1.0 (perfect negative correlation), through 00 (no correlation), to +1.0 +1.0 (perfect

positive correlation).

5-47

Perfectly Negatively CorrelatedIN

VE

ST

ME

NT

RE

TU

RN

TIME

Series-P

Series-Q

5-48

Perfectly Positively CorrelatedIN

VE

ST

ME

NT

RE

TU

RN

TIME

Series-P

Series-Q

5-49

Combining securities that are not perfectly, positively correlated reduces risk.

Combining securities that are not perfectly, positively correlated reduces risk.

Diversification and the Diversification and the Correlation CoefficientCorrelation CoefficientDiversification and the Diversification and the Correlation CoefficientCorrelation CoefficientIN

VE

ST

ME

NT

RE

TU

RN

TIME TIMETIME

SECURITY ESECURITY E SECURITY FSECURITY FCombinationCombination

E and FE and F

5-50

Systematic Risk [nondiversifiable or unavoidable] Systematic Risk [nondiversifiable or unavoidable] is the variability of return on stocks or portfolios associated with changes in return on the market

as a whole.

Unsystematic Risk [diversifiable or avoidable]Unsystematic Risk [diversifiable or avoidable] is the variability of return on stocks or portfolios not

explained by general market movements. It is avoidable through diversification.

Systematic Risk [nondiversifiable or unavoidable] Systematic Risk [nondiversifiable or unavoidable] is the variability of return on stocks or portfolios associated with changes in return on the market

as a whole.

Unsystematic Risk [diversifiable or avoidable]Unsystematic Risk [diversifiable or avoidable] is the variability of return on stocks or portfolios not

explained by general market movements. It is avoidable through diversification.

Total Risk = Systematic Total Risk = Systematic Risk + Unsystematic RiskRisk + Unsystematic RiskTotal Risk = Systematic Total Risk = Systematic Risk + Unsystematic RiskRisk + Unsystematic Risk

Total Risk Total Risk = SystematicSystematic RiskRisk + UnsystematicUnsystematic RiskRisk

5-51


TotalTotalRiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

ST

D D

EV

OF

PO

RT

FO

LIO

RE

TU

RN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors such as changes in nation’s economy, tax reform by the Congress,or a change in the world situation.

5-52


TotalTotalRiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

ST

D D

EV

OF

PO

RT

FO

LIO

RE

TU

RN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors unique to a particular companyor industry. For example, the death of akey executive or loss of a governmentaldefense contract.

5-53

William Sharpe in 1960

CAPM is a model that describes the relationship between risk and expected

(required) return; in this model, a security’s expected (required) return is the risk-free rate risk-free rate plus a premium a premium based on the systematic risk systematic risk of the security.

William Sharpe in 1960

CAPM is a model that describes the relationship between risk and expected

(required) return; in this model, a security’s expected (required) return is the risk-free rate risk-free rate plus a premium a premium based on the systematic risk systematic risk of the security.

Capital Asset Capital Asset Pricing Model (CAPM)Pricing Model (CAPM)Capital Asset Capital Asset Pricing Model (CAPM)Pricing Model (CAPM)

5-54

1. Capital markets are efficient.

2. Homogeneous investor expectations over a given period.

3. Risk-freeRisk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy).

4. Market portfolio contains only systematic risk systematic risk (use BSE, NSE Indexor similar as a proxy).

1. Capital markets are efficient.

2. Homogeneous investor expectations over a given period.

3. Risk-freeRisk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy).

4. Market portfolio contains only systematic risk systematic risk (use BSE, NSE Indexor similar as a proxy).

CAPM AssumptionsCAPM AssumptionsCAPM AssumptionsCAPM Assumptions

5-55

An index of systematic risk systematic risk [nondiversifiable risk][nondiversifiable risk].

It measures the sensitivity of a stock’s returns to changes in returns

on the market portfolio.

The betabeta for a portfolio is simply a weighted average of the individual

stock betas in the portfolio.

An index of systematic risk systematic risk [nondiversifiable risk][nondiversifiable risk].

It measures the sensitivity of a stock’s returns to changes in returns

on the market portfolio.

The betabeta for a portfolio is simply a weighted average of the individual

stock betas in the portfolio.

What is Beta?What is Beta?What is Beta?What is Beta?

5-56

Beta Coefficients & their Beta Coefficients & their InterpretationsInterpretations

Beta Interpretation Comments

2.0 Twice as responsive as the market Move in sameDirection as

Market 1.0 Same response as the market

0.5 Only half as responsive as the market

0 Unaffected by market movements

- 0.5 Only half as responsive as the market Move in opposite Direction to

Market- 1.0 Same response as the market

- 2.0 Twice as responsive as the market

5-57

Characteristic Line [a+bx]Characteristic Line [a+bx]Characteristic Line [a+bx]Characteristic Line [a+bx]EXCESS RETURN

ON STOCK

EXCESS RETURNON MARKET PORTFOLIO

BetaBeta =YY XX

Narrower spreadNarrower spreadis higher correlationis higher correlation

Characteristic LineCharacteristic Line

Data Points > DispersionData Points > DispersionWide Dispersion > Low Correlation > High Unsystematic riskWide Dispersion > Low Correlation > High Unsystematic riskNarrow Dispersion > High Correlation > Low Unsystematic risk Narrow Dispersion > High Correlation > Low Unsystematic risk

5-58

Characteristic Lines Characteristic Lines and Different Betasand Different BetasCharacteristic Lines Characteristic Lines and Different Betasand Different Betas

EXCESS RETURNON STOCK

EXCESS RETURNON MARKET PORTFOLIO

Beta < 1Beta < 1(Defensive)(Defensive)

Beta = 1Beta = 1

Beta > 1Beta > 1(Aggressive)(Aggressive)

Each characteristic characteristic line line has a

different slope.

Beta > 1 = More Systematic riskBeta > 1 = More Systematic riskMore proportion than MPMore proportion than MP

Beta < 1 = Less systematic riskLess proportion than MP

5-59

RRjj is the required rate of return for stock j,

RRff is the risk-free rate of return,

jj is the beta of stock j (measures systematic risk of stock j),

RRMM is the expected return for the market portfolio.

RRjj is the required rate of return for stock j,

RRff is the risk-free rate of return,

jj is the beta of stock j (measures systematic risk of stock j),

RRMM is the expected return for the market portfolio.

Security Market LineSecurity Market LineSecurity Market LineSecurity Market Line

RRjj = RRff + j(RRMM - RRff)

5-60

Security Market LineSecurity Market LineSecurity Market LineSecurity Market Line

RRjj = RRff + j(RRMM - RRff)

MM = 1.01.0

Systematic Risk (Beta)

RRff

RRMM

Req

uir

ed R

etu

rnR

equ

ired

Ret

urn

RiskRiskPremiumPremium

Risk-freeRisk-freeReturnReturn

5-61

Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is

using a 6% R6% Rff and a long-term market market

expected rate of return expected rate of return of 10%10%. A stock analyst following the firm has calculated

that the firm betabeta is 1.21.2. What is the required rate of returnrequired rate of return on the stock of

Basket Wonders?

Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is

using a 6% R6% Rff and a long-term market market

expected rate of return expected rate of return of 10%10%. A stock analyst following the firm has calculated

that the firm betabeta is 1.21.2. What is the required rate of returnrequired rate of return on the stock of

Basket Wonders?

Determination of the Determination of the Required Rate of ReturnRequired Rate of ReturnDetermination of the Determination of the Required Rate of ReturnRequired Rate of Return

5-62

RRBWBW = RRff + j(RRMM - RRff)

RRBWBW = 6%6% + 1.21.2(10%10% - 6%6%)

RRBWBW = 10.8%10.8%

The required rate of return exceeds the market rate of return as BW’s

beta exceeds the market beta (1.0).

RRBWBW = RRff + j(RRMM - RRff)

RRBWBW = 6%6% + 1.21.2(10%10% - 6%6%)

RRBWBW = 10.8%10.8%

The required rate of return exceeds the market rate of return as BW’s

beta exceeds the market beta (1.0).

BWs Required BWs Required Rate of ReturnRate of ReturnBWs Required BWs Required Rate of ReturnRate of Return

5-63

June 2010 Q7June 2010 Q7Using CAPM find out Required rate of Using CAPM find out Required rate of return return [[RRjj ] ]

Situation Expected return on Market

portfolio [%] [RRMM]

Risk Free Rate [%]

[RRff]]

Beta [bbj]

1 15 10 1.00

2 18 14 0.70

3 15 8 1.20

4 17 11 0.80

5 16 10 1.90

5-64

Situation Required Rate of Return RRjj = RRff + [bbj(RRMM - RRff)]

1 R1 = 10 + [1*(15 – 10)] = 10 + [1 * 5] R1 = 15%

2 R2 = 14 + [0.70*(18 – 14)] = 14 + [0.70 * 4] R2 = 16.8%

3 R3 = 8 + [1.2*(15 – 8)] = 8 + [1.2 * 7] R3 = 16.4%

4 R4 = 11 + [0.80*(17 – 11)] = 11 + [0.80 * 6] R4 = 15.8%

5 R5 = 10 + [1.90*(16 – 10)] = 10 + [1.90* 6] R5 = 21.4%

5-65

The common stocks of companies A & B have the expected returns & SD given below; the expected correlation coefficient between the 2 stocks is – 0.35

June 2009 Q4June 2009 Q4Using CAPM find out return Using CAPM find out return [[RRpp ]] &&

riskrisk [[PP]]

Company/Stock RRpp P

A 0.10 0.05

B 0.06 0.04

Compute the risk & return for a portfolio comprising60% invested in the stock A & 40% invested in stock B

5-66

RRpp = (0.60)(0.10) + (0.40) (0.06)

RRpp = 8.4%

(0.60) (0.05) + (0.4) (0.04) + 2(0.60)(0.40)(- 0.35) (0.05)(0.04)

P2 2 2 2=

P = 0.00082 = 2.86%

Solution:-

5-67

Intrinsic value Intrinsic value of a security is the true of a security is the true Economic Value.Economic Value.

It is also frequently called Fundamental ValueFundamental Value.

It is calculated by summing the future income generated by the asset, and discounting it to the Present Value.

Simply put, it is the Actual Value of a Security as opposed

to the Market or Book Value.

Intrinsic value Intrinsic value of a security is the true of a security is the true Economic Value.Economic Value.

It is also frequently called Fundamental ValueFundamental Value.

It is calculated by summing the future income generated by the asset, and discounting it to the Present Value.

Simply put, it is the Actual Value of a Security as opposed

to the Market or Book Value.

Determination of the Determination of the Intrinsic ValueIntrinsic ValueDetermination of the Determination of the Intrinsic ValueIntrinsic Value

5-68

IntrinsicIntrinsicValueValue

=Div next periodDiv next period

RRpp G-


Total Net Total Net Current AssetsCurrent Assets

No. of O/S No. of O/S Common SharesCommon Shares

=<CurrentCurrentMarketMarketPricePrice

of Common of Common ShareShare

Margin of Safety to Purchase Equity SharesMargin of Safety to Purchase Equity Shares

5-69

Lisa Miller at BW is also attempting to determine the intrinsic value intrinsic value of the stock. She is using the constant growth model.

Lisa estimates that the dividend next period dividend next period will be $0.50$0.50 and that BW will growgrow at a

constant rate of 5.8%5.8%. The stock is currently selling for $15.

What is the intrinsic value intrinsic value of the stock? Is the stock overover or underpricedunderpriced?

Lisa Miller at BW is also attempting to determine the intrinsic value intrinsic value of the stock. She is using the constant growth model.

Lisa estimates that the dividend next period dividend next period will be $0.50$0.50 and that BW will growgrow at a

constant rate of 5.8%5.8%. The stock is currently selling for $15.

What is the intrinsic value intrinsic value of the stock? Is the stock overover or underpricedunderpriced?

Determination of the Determination of the Intrinsic Value of BWIntrinsic Value of BWDetermination of the Determination of the Intrinsic Value of BWIntrinsic Value of BW

5-70

The stock is OVERVALUED as the market price ($15) exceeds

the intrinsic value intrinsic value ($10$10).

The stock is OVERVALUED as the market price ($15) exceeds

the intrinsic value intrinsic value ($10$10).

Determination of the Determination of the Intrinsic Value of BWIntrinsic Value of BWDetermination of the Determination of the Intrinsic Value of BWIntrinsic Value of BW

$0.50$0.5010.8%10.8% - 5.8%5.8%


=

= $10$10

5-71

Rule No.1: Never Lose Money.

Rule No.2: Never Forget Rule No.1. ...

5-72

Risk Return PPT

Documents