risk return concept

8/7/2019 Risk Return Concept

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The expected return is the uncertain futurereturn that an investor expects to get from his

investment.

The released return, on the contrary, is certainreturn that an investor has actually obtained

from his investment at the end of the holdingperiod.


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Risk is expressed in terms of variability ofreturn.

An investor before investing in securities mustproperly analyze the risks associated withthese securities.

There are two types of risks:

Systematic riskUnsystematic risk


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It is the risk that is caused by external factorssuch as economic, political and sociologicalconditions.

The factors that are external to a company andeffect a large number of securitiessimultaneously.

They are of three types:

Market risk Interest rate risk

Purchasing power risk


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Market risk as that portion of the total variability of returnsthat is caused by the alternating forces of bull(upward) and

bear(down) markets. When the stock market moves upwards, it is known as bull

market. On the other hand, when the stock market movesdownwards, then it is known as bear market.

The two forces that affect the market are:

Tangible events: Earthquake, war, political uncertainty and decrease inthe value of money are some of the examples of tangible events.

Intangible events: It is related to market psychology. Political unrestor fall of government affects the market sentiments.


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It is the risk caused by the variations in the marketinterest rates.

Prices of debentures, bonds, etc. are mainly affected

by the interest rate risk.The causes of interest rate risk are as follows:

Changes in the governments monetary policy

Changes in the interest rate of treasury bills

Changes in the interest rate of government bonds


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Variations in returns are caused by the loss of purchasingpower of currency.

There are mainly two types of inflation:

Demand-pull inflation: The demand for goods andservices remains higher than the supply.

Cost-push inflation: There is a rise in price due to theincrease in the cost of production.

Real future value =

Real Rate of Return =

where r = rate of returnIR = Inflation Rate

1.0 r 1.0

1.0 IR

+

+

Nominal future value

1.0 Inflation Rate+


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It is a type of risk which is unique, specificand related to a particular industry.

Managerial inefficiency, changes inpreferences of the consumers, availability ofraw material, labour problems, etc. are someof the causes of unsystematic risk.

It arises from two sources; a) the operatingenvironment b) financing pattern


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It is the risk that is caused by the inefficiency of acompany to manage its growth or stability ofearnings.

Fixed Cost and Variable Cost It can be classified as: Internal business risk: It is the risk that is associated with

the operational efficiency of a company.

External business risk: It is the risk that is the result ofoperating conditions imposed on the firm by the external

environment.


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It is associated with the capital structure of thecompany, which consists of equity and borrowedfunds.

The presence of debt in the capital structure causesfixed payment in the form of interest.

The financial risk considers the risk on EPS.

The payment of interest affects the eventual earningsof the company.


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Income receivedIncome received on an investment plus any changechangein market pricein market price, usually expressed as a percent

of thebeginning market pricebeginning market price of the investment.

Income receivedIncome received on an investment plus any changechangein market pricein market price, usually expressed as a percent

of thebeginning market pricebeginning market price of the investment.

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

PPt-1t-1R =


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The stock price for Stock A was $10$10 per share 1year ago. The stock is currently trading at $9.50$9.50

per share, and shareholders just received a $1$1dividenddividend. What return was earned over the past

year?

The stock price for Stock A was $10$10 per share 1year ago. The stock is currently trading at $9.50$9.50

per share, and shareholders just received a $1$1dividenddividend. What return was earned over the past

year?


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The stock price for Stock A was 1010 per share 1 yearago. The stock is currently trading at 9.509.50 per

share, and shareholders just received a 1 dividend1 dividend.What return was earned over the past year?

The stock price for Stock A was 1010 per share 1 yearago. The stock is currently trading at 9.509.50 per

share, and shareholders just received a 1 dividend1 dividend.What return was earned over the past year?

1.001.00 + (9.509.50 - 10.0010.00)

10.0010.00RR = = 5%5%


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R = (Ri)(P

i)

R is the expected return for the asset,R

iis the return for the ith possibility,

Piis the probability of that return occurring,

n is the total number of possibilities.

R= (Ri)(P

i)

Ris the expected return for the asset,R

iis the return for the ith possibility,

Piis the probability of that return occurring,

n is the total number of possibilities.

n

i=1


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Stock BW

Ri

Pi

(Ri)(P

i)

-.15 .10 -.015

-.03 .20 -.006

.09 .40 .036

.21 .20 .042

.33 .10 .033

Sum 1.00 .090.090

Stock BW

Ri

Pi

(Ri)(P

i)

-.15 .10 -.015

-.03 .20 -.006

.09 .40 .036

.21 .20 .042

.33 .10 .033

Sum 1.00 .090.090

Theexpected

return, R,

for Stock

BW is .09or 9%


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= (Ri- R )2(P

i)

Standard DeviationStandard Deviation, , is a statistical measure ofthe variability of a distribution around its mean.

It is the square root of variance.

= (Ri- R)2(P

i)

Standard DeviationStandard Deviation, , is a statistical measure ofthe variability of a distribution around its mean.

It is the square root of variance.

n

i=1


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Possible returns Xi Probability of occurrenceP(Xi)

30 0.10

40 0.30

50 0.40

60 0.10

70 0.10


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Possible returns Xi Probability ofoccurrence P(Xi)

Xi p(Xi)

30 0.10 3

40 0.30 12

50 0.40 20

60 0.10 6

70 0.10 7

Expected Return 48


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Possible returnsXi

Probability ofoccurrenceP(Xi)

Deviation(Xi - X)

DeviationSquared(Xi - X)22

Product

30 0.10 -18 324 32.4

40 0.30 -8 64 19.2

50 0.40 2 4 1.6

60 0.10 12 144 14.4

70 0.10 22 484 48.4

116.0


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is the 116. Standard deviation is the square root of the variance

and is represented as So is square root of 116 is 10.77


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n

i=1 = (R

i- R )2

( n )

Note, this is when probability is not given

= (Ri- R)2

( n )

Note, this is when probability is not given


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The average rate of return is the sum of thevarious one-period rates of return divided by thenumber of period.

Formula for the average rate of return is asfollows:

1 2

= 1

1 1= [ ]

n

n t

t

R R R Rn n

+ + + =L


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The ratio of thestandard deviationstandard deviation of adistribution to the meanmean of that distribution.It is a measure ofRELATIVERELATIVErisk.

CV = / RR

CV of BW = .1315.1315 / .09.09 = 1.46

The ratio of thestandard deviationstandard deviation of adistribution to the meanmean of that distribution.It is a measure ofRELATIVERELATIVErisk.

CV = / RR

CV of BW = .1315.1315 / .09.09 = 1.46


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Security A gives a return of 10% with a

dispersion of 3.5%, while security B gives a

return of 20% with a dispersion of 5%. Whichsecurity is more risky?


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Coefficient of Variation for Security A =

(3.5/10) = 0.35 or 35% and

Coefficient of Variation for Security B =(5/20) = 0.25 or 25%. Therefore, theSecurity A is more risky in relation to its

return.


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Systematic RiskSystematic Riskis the variability of return on stocksor portfolios associated with changes in return on the

market as a whole.

Unsystematic RiskUnsystematic Riskis the variability of return onstocks or portfolios not explained by general marketmovements. It is avoidable through diversification.

Systematic RiskSystematic Riskis the variability of return on stocksor portfolios associated with changes in return on the

market as a whole.

Unsystematic RiskUnsystematic Riskis the variability of return onstocks or portfolios not explained by general marketmovements. It is avoidable through diversification.

Total RiskTotal Risk= SystematicSystematicRiskRisk+UnsystematicUnsystematicRiskRisk


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TotalTotal

RiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

STD

DE

V

OFP

ORTFOLIO

RE

TURN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors such as changes in nations

economy, tax reform by the Congress,

or a change in the world situation.


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TotalTotal

RiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

STD

DE

V

OFP

ORTFOLIO

RE

TURN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors unique to a particular company

or industry. For example, the death of a

key executive or loss of a governmental

defense contract.

risk return concept

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