2. risk and return

09/04/0809/04/08 2. Return and Risk2. Return and Risk 11

2. Return and Risk2. Return and Risk

Alok KumarAlok Kumar


What we did in last classWhat we did in last class……


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?


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


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%


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]


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%


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%


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


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


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%


Probability Distribution of ReturnProbability Distribution of Return


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


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?


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.


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


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,


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


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


Skewness and KurtosisSkewness and Kurtosis


So How Return and Risk should So How Return and Risk should

be relatedbe related……....next classnext class


End of Lecture 2End of Lecture 2

Thank You!!!Thank You!!!

2. risk and return

Documents