2. Risk And Return

2. Return and Risk Alok Kumar

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What we did in last class…

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We covered 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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Investment Return




•




Risk

Historical





• Historical

HPR




(Holding Period Return)

Variance and Standard Deviation




Coefficient of Variance

HPY

• Expected

(Holding Period Yield)

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Variance and Standard Deviation




Coefficient of Variance

Expected 2. Return and Risk

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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 Return


Over a number of years, a single investments will likely to give high rates of return during some years and low rates of return, or possibly negative rates of return, during others. We can summarised the returns by computing the mean annual rate of return for this investment over some period of time.




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




Arithmetic Mean = ∑HPY/n




Geometric Mean = [{(HPR1) X (HPR2) X (HPR3)}1/n -1]

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How 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 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 Return Expected Return = ∑RiPi, • where i varies from 0 to n • R denotes return from the security in i outcome • P denotes probability of occurrence of i outcome

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Economy Growth

Probability of Occurrence

Deep Recession

5%

Mild Recession

20%

Average Economy

50%

Mild Boom

20%

Strong Boom

5% 2. Return and Risk

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How do we Calculate Expected Return Economy Growth

T-Bills

Corporate Bonds

Equity A

Equity B

5%

8%

12%

-3%

-2%

20%

8%

10%

6%

9%

50%

8%

9%

11%

12%

Mild Boom

20%

8%

8.50%

14%

15%

Strong Boom

5%

8%

8%

19%

26%

8.00%

9.20%

10.30%

12.00%

Deep Recession Mild Recession Average Economy

Probability of Occurrence

100% Expected Rate of Return 09/04/08

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Probability Distribution of Return Probability Distribution of Equity "A" 60% P r oba bility

50% 40% 30%

Series1

20% 10% 0% Series1

-13.300%

-4.300%

0.700%

3.700%

8.700%

5%

20%

50%

20%

5%

Dispersion from Expected Return

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Probability Distribution of Return

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So there is a risk of earning more than one return or uncertainty in return

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What is Risk





Webster define it as a hazard; as a peril ; as a exposure to loss or injury. Chinese definition –

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

So what is in practice risk means to us? 09/04/08

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What is Risk





Actual return can vary from our expected return, i.e. we can earn either more than our expected return or less than our expected return or no deviation from our expected return. Risk relates to the probability of earning a return less than the expected return, and probability distribution provide the foundation for risk measurement.

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Risk Measures for Historical Returns


Variance – is a measure of the dispersion of actual outcomes around the mean, larger the variance, the greater the dispersion. Variance = ∑(HPYi – AM)2 / (n) where i varies from 1 to n.

Variance is measured in the same units as the outcomes.





Standard Deviation – larger the S.D, the greater the dispersion and hence greater the risk. Coefficient of Variation – risk per unit of return, = S.D/Mean Return

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Risk Measurement for Expected Return


Variance – is a measure of the dispersion of possible outcomes around the expected value, larger the variance, the greater the dispersion. Variance = ∑(ki – k)2 (Pi) where i varies from 1 to n.

Variance is measured in the same units as the outcomes. 09/04/08

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Standard Deviation – larger the S.D,

Return and Risk Measurement Expected Return or Risk Measure

T-Bills

Corporate Bonds

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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Equity A Equity B

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Things to look Measuring Risk • Variance and Standard Deviation The spread of the actual returns around the expected return; The greater the deviation of the actual returns from expected returns, the greater the variance

• Skewness The biasness towards positive or negative returns;

• Kurtosis The shape of the tails of the distribution ; fatter tails lead to higher kurtosis

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Skewness and Kurtosis

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So How Return and Risk should be related…..next class

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End of Lecture 2 Thank You!!!

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