2. Risk and Return
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09/04/0809/04/08 2. Return and Risk2. Return and Risk 11
2. Return and Risk2. Return and Risk
Alok KumarAlok Kumar
09/04/0809/04/08 2. Return and Risk2. Return and Risk 22
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 Standard Variance and Standard
DeviationDeviation
�� Coefficient of VarianceCoefficient of Variance
•• ExpectedExpected
�� Variance and Standard Variance 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. If you 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 of Investment)/(beginning value of Investment) = 1200/1000 = 1.20
• HPY – conversion to percentage return, we calculate this as follows,
� HPY = HPR-1 = 1.20-1.00 = 0.20 = 20%
• Annual HPR = (HPR)1/n = (1.2) ½, = 1.0954, if n is 2 years.
• Annual HPY = Annual HPR – 1 = 1.0954 – 1 = 0.0954 = 9.54%
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Computing Mean Historical ReturnComputing Mean Historical Return
�� Over a number of years, a single investments will likely to giveOver a number of years, a single investments will likely to give
high rates of return during some years and low rates of return, high rates of return during some years and low rates of return, or or
possibly negative rates of return, during others. We can possibly negative rates of return, during others. We can
summarised the returns by computing the mean annual rate of summarised the returns by computing the mean annual rate of
return 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 Geometric There are two measures of mean, Arithmetic Mean and Geometric
Mean.Mean.
�� Arithmetic Mean = Arithmetic Mean = ∑∑HPY/nHPY/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
-0.20.8110413803
0.21.2138011502
0.151.15115010001
HPYHPR
Ending
Value
Beginning
ValueYear
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
-0.50.51002002
1.02.02001001
HPYHPR
Ending
Value
Beginning
ValueYear
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 = Expected Return = ∑∑RRiiPPii,,
•• 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
5%Strong Boom
20%Mild Boom
50%Average Economy
20%Mild Recession
5%Deep Recession
Probability of OccurrenceEconomy Growth
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How do we Calculate Expected ReturnHow do we Calculate Expected Return
12.00%10.30%9.20%8.00%
Expected Rate
of Return
100%
26%19%8%8%5%Strong Boom
15%14%8.50%8%20%Mild Boom
12%11%9%8%50%
Average
Economy
9%6%10%8%20%Mild Recession
-2%-3%12%8%5%
Deep
Recession
Equity
B
Equity
A
Corporate
BondsT-Bills
Probability of
Occurrence
Economy
Growth
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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
Pro
bability
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 more So there is a risk of earning more
than one return or uncertainty in than one return or uncertainty in
returnreturn
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What is RiskWhat is Risk
�� WebsterWebster define it as a hazard; as a peril ; as a define it as a hazard; as a peril ; as a
exposure to loss or injury.exposure to loss or injury.
�� Chinese definition Chinese definition ––
Means its a threat but at the same time its an Means its a threat but at the same time its an
opportunityopportunity
So what is in practice risk means to us?So what is in practice risk means to us?
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What is RiskWhat is Risk
�� Actual return can vary from our expected return, Actual return can vary from our expected return,
i.e. we can earn either more than our expected i.e. we can earn either more than our expected
return or less than our expected return or no return or less than our expected return or no
deviation from our expected return.deviation from our expected return.
�� Risk relates to the probability of earning a return Risk relates to the probability of earning a return
less than the expected return, and probability less than the expected return, and probability
distribution provide the foundation for risk distribution provide the foundation for risk
measurement.measurement.
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Risk Measures for Historical ReturnsRisk Measures for Historical Returns
�� VarianceVariance –– is a measure of the dispersion of actual outcomes is a measure of the dispersion of actual outcomes around the mean, larger the variance, the greater the around the mean, larger the variance, the greater the dispersion.dispersion.
Variance = Variance = ∑∑((HPYHPYii –– AM)AM)22 / / (n)(n)
where i varies from 1 to n.where i varies from 1 to n.
Variance is measured in the same units as the outcomes.Variance is measured in the same units as the outcomes.
�� Standard DeviationStandard Deviation –– larger the S.D, the greater the dispersion larger the S.D, the greater the dispersion and hence greater the risk.and hence greater the risk.
�� Coefficient of VariationCoefficient of Variation –– risk per unit of return, risk per unit of return,
= S.D/Mean Return= S.D/Mean Return
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Risk Measurement for Expected Return Risk Measurement for Expected Return
�� VarianceVariance –– is a measure of the is a measure of the
dispersion of possible outcomes dispersion of possible outcomes
around the expected value, larger around the expected value, larger
the variance, the greater the the variance, the greater the
dispersion.dispersion.
Variance = Variance = ∑∑((kkii –– k)k)2 2 (P(Pii))
where i varies from 1 to n.where i varies from 1 to n.
Variance is measured in the same Variance is measured in the same
units as the outcomes.units as the outcomes.
Standard Deviation – larger the S.D,
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Return and Risk MeasurementReturn and Risk Measurement
11.60%12.54%0.19%0.00%Semi variance
0.40%0.43%0.09%0%Coefficient of Variation
4.82%4.39%0.84%0%Standard Deviation
23.20%19.31%0.71%0%Variance
12.00%10.30%9.20%8%Expected return
Equity BEquity A
Corporate
BondsT-Bills
Expected Return or Risk
Measure
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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 should So How Return and Risk should
be relatedbe related……....next classnext class