2. Return and Risk

8/7/2019 2. Return and Risk

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4/11/20114/11/2011 2. Return and Risk2. Return and Risk 11

2. Return and Risk2. Return and Risk

Alok KumarAlok Kumar


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What we did in last classWhat we did in last class


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WeWe covered in last classcovered in last class

Why people invest?

What they want from their investment?

Where all they can invest and what parameters they

adopt to invest?


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InvestmentInvestment

ReturnReturn

Historical

HPR

(Holding Period Return)

HPY

(Holding Period Yield)

Expected

RiskRisk

HistoricalHistorical

Variance and StandardVariance and StandardDeviationDeviation

Coefficient of VarianceCoefficient of Variance

ExpectedExpected

Variance and StandardVariance and Standard

DeviationDeviation

Coefficient of VarianceCoefficient of Variance


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How do we measure return?How do we measure return?

HPR- When we invest, we defer current consumption in order to add our wealth so

that we can consume more in future, hence return is change in wealth resulting from

investment. Ifyou commit Rs 1000 at the beginning of the period and you get back

Rs 1200 at the end of the period, return is Holding Period Return (HPR) calculated as

follows HPR = (Ending Value ofInvestment)/(beginning value ofInvestment) = 1200/1000 = 1.20

HPY conversion to percentage return, we calculate this as follows,

HPY = HPR-1 = 1.20-1.00 = 0.20 = 20%

AnnualHPR= (HPR)1/n = (1.2) , = 1.0954, if n is 2 years.

AnnualHPY = Annual HPR1 = 1.0954 1 = 0.0954 = 9.54%


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Computing Mean Historical ReturnComputing Mean Historical Return

Over a number ofyears, a single investments will likely to giveOver a number ofyears, a single investments will likely to give

high rates of return during some years and low rates of return, orhigh rates of return during some years and low rates of return, or

possibly negative rates of return, during others. We canpossibly negative rates of return, during others. We can

summarised the returns by computing the mean annual rate ofsummarised the returns by computing the mean annual rate ofreturn for this investment over some period of time.return for this investment over some period of time.

There are two measures of mean, Arithmetic Mean and GeometricThere are two measures of mean, Arithmetic Mean and Geometric

Mean.Mean.

Arithmetic Mean = HPY/nArithmetic Mean = HPY/n

Geometric Mean = [{(HPRGeometric Mean = [{(HPR11)) X (HPRX (HPR22) X (HPR) X (HPR33)})}1/n -1]


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How AM is different to GMHow AM is different to GM

Year

Beginning

Value

Ending

Value HPR HPY

1 1000 1150 1.15 0.15

2 1150 1380 1.2 0.2

3 1380 1104 0.8 -0.2

AM = [(0.15) + (0.20) + (-0.20)]/3 = 5%

GM = [(1.15) X (1.20) X (0.80)] 1/3 1 = 3.35%


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How AM is different to GMHow AM is different to GM

Year

Beginning

Value

Ending

Value HPR HPY

1 100 200 2.0 1.0

2 200 100 0.5 -0.5

AM = [(1.0) + (-0.50)]/2 = 0.50/2 = 0.25 = 25%

GM = [(2.0) X (0.50)] 1/2 1 = 0.00%


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How do we Calculate Expected ReturnHow do we Calculate Expected Return

Expected Return = RExpected Return = RiiPPii,,

where i varies from 0 to nwhere i varies from 0 to n

R denotes return from the security in i outcomeR denotes return from the security in i outcome

P denotes probability of occurrence of i outcomeP denotes probability of occurrence of i outcome

Economy Growth Probability of Occurrence

Deep Recession 5%

Mild Recession 20%Average Economy 50%

Mild Boom 20%

Strong Boom 5%


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How do we Calculate Expected ReturnHow do we Calculate Expected Return

Economy

Growth

Probability of

Occurrence T-Bills

Corporate

Bonds

Equity

A

Equity

B

Deep

Recession 5% 8% 12% -3% -2%

Mild Recession 20% 8% 10% 6% 9%

Average

Economy 50% 8% 9% 11% 12%

Mild Boom 20% 8% 8.50% 14% 15%

Strong Boom 5% 8% 8% 19% 26%

100%

Expected Rate

of Return 8.00% 9.20% 10.30% 12.00%


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Probability Distribution of ReturnProbability Distribution of Return

Probability Distribution of Equity "A"

0%

10%

20%

30%

40%

50%

60%

Dispersion from Expected Return

Probability

Series1

Series1 5% 20% 50% 20% 5%

-13.300% -4.300% 0.700% 3.700% 8.700%


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Probability Distribution of ReturnProbability Distribution of Return


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So there is a risk of earning moreSo there is a risk of earning more

than one return or uncertainty inthan one return or uncertainty inreturnreturn


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What is RiskWhat is Risk

WebsterWebster define it as a hazard; as a peril ; as adefine it as a hazard; as a peril ; as aexposure to loss or injury.exposure to loss or injury.

Chinese definitionChinese definition

Means its a threat but at the same time its anMeans its a threat but at the same time its an

opportunityopportunity

So what is in practicerisk meansto us?So what is in practicerisk meansto us?


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What is RiskWhat is Risk

ActualActual returnreturn cancan varyvary fromfrom ourour expectedexpected return,return,ii..ee.. wewe cancan earnearn eithereither moremore thanthan ourour expectedexpectedreturnreturn oror lessless thanthan ourour expectedexpected returnreturn oror nonodeviationdeviation fromfrom ourour expectedexpected returnreturn..

RiskRisk relatesrelates toto thethe probabilityprobability ofof earningearning aa returnreturnlessless thanthan thethe expectedexpected return,return, andand probabilityprobabilitydistributiondistribution provideprovide thethe foundationfoundation forfor riskrisk

measurementmeasurement..


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Risk Measures forHistorical ReturnsRisk Measures forHistorical Returns

VarianceVariance isis aa measuremeasure ofof thethe dispersiondispersion ofof actualactual outcomesoutcomesaroundaround thethe mean,mean, largerlarger thethe variance,variance, thethe greatergreater thethedispersiondispersion..

VarianceVariance == (HPY(HPYii AM)AM)22 // (n)(n)

wherewhere ii variesvaries fromfrom 11 toto nn..

VarianceVariance isis measuredmeasured inin thethe samesame unitsunits asas thethe outcomesoutcomes..

StandardStandard DeviationDeviation largerlarger thethe SS..D,D, thethe greatergreater thethe dispersiondispersionandand hencehence greatergreater thethe riskrisk..

CoefficientCoefficient ofofVariationVariation riskrisk perper unitunit ofof return,return,

== SS..D/MeanD/Mean ReturnReturn


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Risk Measurement forExpected ReturnRisk Measurement forExpected Return

VarianceVariance isis aa measuremeasure ofof thethe dispersiondispersion ofof possiblepossibleoutcomesoutcomes aroundaround thethe expectedexpected value,value, largerlarger thethe variance,variance,thethe greatergreater thethe dispersiondispersion..

VarianceVariance == (k(kii k)k)22 (P(Pii))

wherewhere ii variesvaries fromfrom 11 toto nn..

VarianceVariance isis measuredmeasured inin thethe samesame unitsunits asas thethe outcomesoutcomes..

StandardStandard DeviationDeviation largerlarger thethe SS..D,D, thethe greatergreater thethedispersiondispersion andand hencehence greatergreater standstand alonealone riskrisk..

CoefficientCoefficient ofofVariationVariation riskrisk perper unitunit ofof return,return,

== SS..D/ExpectedD/Expected ReturnReturn


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Return and Risk MeasurementReturn and Risk Measurement

Expected Return or Risk

Measure T-Bills

Corporate

Bonds Equity A Equity B

Expected return 8% 9.20% 10.30% 12.00%

Variance 0% 0.71% 19.31% 23.20%

Standard Deviation 0% 0.84% 4.39% 4.82%

Coefficient of Variation 0% 0.09% 0.43% 0.40%

Semi variance 0.00% 0.19% 12.54% 11.60%


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Things to look Measuring RiskThings to look Measuring Risk

Variance and Standard DeviationThe spread of the actual returns around the expected return; The greater the

deviation of the actual returns from expected returns, the greater the variance

SkewnessThe biasness towards positive or negative returns;

KurtosisThe shape of the tails of the distribution ; fatter tails lead to higher kurtosis


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Skewness and KurtosisSkewness and Kurtosis


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So How Return and Risk shouldSo How Return and Risk should

be related..be related..next classnext class


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End of Lecture 2End of Lecture 2Thank You!!!Thank You!!!

2. Return and Risk

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