introduction to risk and return


TOPICS COVERED

Over a Century of Capital Market History

Measuring Portfolio Risk

Calculating Portfolio Risk

How Individual Securities Affect Portfolio Risk

Diversification & Value ‘Additivity’


$1

$10

$100

$1,000

$10,000

$100,000

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Start of Year

Dol

lars

(log

sca

le)

Common Stock

US Govt Bonds

T-Bills

14,276

24171

2008

THE VALUE OF AN INVESTMENT OF $1 IN 1900

$1

$10

$100

$1,000

1900

1909

1919

1929

1939

1949

1959

1969

1979

1989

1999

Start of Year

Dol

lars

(log

sca

le)

Equities

Bonds

Bills

581

9.85

2.87

2008

Real Returns

The Value of an Investment of $1 in 1900

Investment of Rs.100 over the period 1978 – 2011


AVERAGE MARKET RISK PREMIA (BY COUNTRY)

4.29 4.69 5.05 5.43 5.5 5.61 5.67 6.04 6.29 6.94 7.137.94 8.34 8.4 8.74 9.1 9.61 10.21

0123456789

1011

Den

mar

k

Bel

giu

m

Sw

itze

rlan

d

Irel

and

Sp

ain

Nor

way

Can

ada

U.K

.

Net

her

lan

ds

Ave

rage

U.S

.

Sw

eden

Au

stra

lia

Sou

th A

fric

a

Ger

man

y

Fra

nce

Jap

an

Ital

y

Risk premium, %

Country


MARKET RISK PREMIUM IN INDIA


DIVIDEND YIELD

Dividend yields in the U.S.A. 1900–2008


DIVIDEND YIELD ON SENSEX

Rates of Return 1900-2008

Source: Ibbotson Associates Year

Per

cent

age

Ret

urn

Stock Market Index Returns

Rates of Return for Sensex: 1980 - 2011


MEASURING RISK

1 24

11 11

21

17

24

13

32

0

4

8

12

16

20

24

-50

to -

40

-40

to -

30

-30

to -

20

-20

to -

10

-10

to 0

0 to

10

10 t

o 20

20 t

o 30

30 t

o 40

40 t

o 50

50 t

o 60

Return %

# of Years

Histogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns

(1900-2008)(1900-2008)


MEASURING RISK

Variance - Average value of squared deviations from mean. A measure of volatility.

Standard Deviation - Average value of squared deviations from mean. A measure of volatility.


MEASURING RISK

Coin Toss Game-calculating variance and standard deviation


MEASURING RISK


EQUITY MARKET RISK (BY COUNTRY)

17.02 18.45 19.22 20.16 21.83 22.05 22.99 23.23 23.42 23.51 23.98 24.09 25.2828.32 29.57

33.93 34.3

0

5

10

15

20

25

30

35

40

Can

ada

Au

stra

lia

Sw

itze

rlan

d

U.S

.

U.K

.

Den

mar

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Sp

ain

Net

her

lan

ds

Sou

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fric

a

Irel

and

Sw

eden

Bel

giu

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Fra

nce

Nor

way

Jap

an

Ital

y

Ger

man

y

Sta

ndar

d D

evia

tion

of A

nnua

l Ret

urns

, %

Average Risk (1900-2008)


DOW JONES RISK

Annualized Standard Deviation of the DJIA over the preceding 52 weeks

(1900 – 2008)

Years

Sta

ndar

d D

evia

tion

(%

)


SENSEX RISK


MEASURING RISK

Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.

Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”

Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”


COMPARING RETURNS


MEASURING RISK

05 10 15

Number of Securities

Po

rtf

oli

o s

tan

dard

devia

tio

n


MEASURING RISK

05 10 15

Number of Securities

Po

rtfo

lio

sta

nd

ard

dev

iati

on

Market risk

Uniquerisk


PORTFOLIO RISK

22

22

211221

1221

211221

122121

21

σxσσρxx

σxx2Stock

σσρxx

σxxσx1Stock

2Stock 1Stock


PORTFOLIO RISK


PORTFOLIO RISK Example

Suppose you invest 62% of your portfolio in Bharti Airtel and 38% in Tata Motors. The expected dollar return on your Bharti Airtel stock is 14% and on Tata Motors is 17%. The standard deviation of their annualized daily returns are 33.5% and 54.8%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.


PORTFOLIO RISK


PORTFOLIO RISK

%12)1540(.)1060(. ReturnExpected

Another Example

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is:


PORTFOLIO RISK

2222

22

211221

2112212221

21

)3.27()40(.σx3.272.181

60.40.σσρxxCola-Coca

3.272.181

60.40.σσρxx)2.18()60(.σxMobil-Exxon

Cola-CocaMobil-Exxon

Another Example

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.


PORTFOLIO RISKAnother Example

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.

% 21.8 0.477 DeviationStandard

0.47718.2x27.3)2(.40x.60x

]x(27.3)[(.40)

]x(18.2)[(.60) Variance Portfolio22

22


PORTFOLIO RISK

)rx()r(x Return PortfolioExpected 2211

)σσρxx(2σxσxVariance Portfolio 21122122

22

21

21


PORTFOLIO RISK

Example

Stocks % of Portfolio Avg Return

ABC Corp 28 60% 15%

Big Corp 42 40% 21%

Correlation Coefficient = .4

Standard Deviation = weighted avg. = 33.6

Standard Deviation = Portfolio = 28.1

Real Standard Deviation: = (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4) = 28.1 CORRECT

Return : r = (15%)(.60) + (21%)(.4) = 17.4%


PORTFOLIO RISK

Example Correlation Coefficient = .4

Standard Deviation = weighted avg = 33.6

Standard Deviation = Portfolio = 28.1

Return = weighted avg = Portfolio = 17.4%

Let’s Add stock New Corp to the portfolio

Stocks σ % of Portfolio

Average Return

ABC Corp 28 60% 15%

Big Corp 42 40% 21%


PORTFOLIO RISK

Example Correlation Coefficient = .3

NEW Standard Deviation = weighted average = 31.80

NEW Standard Deviation = Portfolio = 23.43

NEW Return = weighted average = Portfolio = 18.20%

NOTE: Higher return & Lower risk

How did we do that? DIVERSIFICATION

Stocks σ % of Portfolio

Average Return

Portfolio 28.1 50% 17.4%

New Corp 30 50% 19%

The shaded boxes contain variance terms; the remainder contain covariance terms.

1

2

3

4

5

6

N

1 2 3 4 5 6 N

STOCK

STOCK

To calculate portfolio variance add up the boxes

Variance

Covariance

It is the average covariance that constitutes the bedrock of risk remaining after diversification has done its work. The risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio.


PORTFOLIO RISK

Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the Sensex, is used to represent the market.

Beta - Sensitivity of a stock’s return to the return on the market portfolio.


PORTFOLIO RISK

The return on Tata Steel stock changes on average by 1.77% for each additional 1% change in the market return. Beta is therefore 1.77.


PORTFOLIO RISK


PORTFOLIO RISK

Covariance with the market

Variance of the market


BETA

(1) (2) (3) (4) (5) (6) (7)Product of

Deviation Squared deviationsDeviation from average deviation from average

Market Anchovy Q from average Anchovy Q from average returnsMonth return return market return return market return (cols 4 x 5)

1 -8% -11% -10% -13% 100 1302 4 8 2 6 4 123 12 19 10 17 100 1704 -6 -13 -8 -15 64 1205 2 3 0 1 0 06 8 6 6 4 36 24

Average 2 2 Total 304 456

Variance = σm2 = 304/6 = 50.67

Covariance = σim = 736/6 = 76

Beta (β) = σim/σm2 = 76/50.67 = 1.5

Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of

the variance to the covariance (i.e., β = σim/σm2)


ANNOUNCEMENTS, SURPRISES,AND EXPECTED RETURNS

41


ANNOUNCEMENTS AND NEWS

42


SYSTEMATIC AND UNSYSTEMATIC RISK

43


THE PRINCIPLE OF DIVERSIFICATION The process of spreading an investment across assets (and thereby forming a portfolio) is called diversification.

The principle of diversification tells us that spreading an investment across many assets will eliminate some of the risk.

45


DIVERSIFICATION

Unsystematic risk

Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets has almost no unsystematic risk.

Also called diversifiable risk, unique risk, or asset-specific risk.

Systematic risk

systematic risk affects almost all assets to some degree, so no matter how many assets we put into a portfolio, the systematic risk doesn’t go away.

The terms systematic risk and non-diversifiable risk are hence used interchangeably.

46


SYSTEMATIC RISK AND BETA

THE SYSTEMATIC RISK PRINCIPLE

The systematic risk principle states that the reward for bearing risk depends only on the systematic risk of an investment.

Because unsystematic risk can be eliminated by diversifying, there is no reward for bearing it, the market does not reward risks that are borne unnecessarily.

The expected return on an asset depends only on that asset’s systematic risk.

No matter how much total risk an asset has, only the systematic portion is relevant in determining the expected return (and the risk premium) on that asset.

47



MEASURING SYSTEMATIC RISK

The amount of systematic risk present in a particular risky asset relative to that in an average risky asset.

An average asset has a beta of 1.0 relative to itself. An asset with a beta of .50, therefore, has half as much systematic risk as an average asset; an asset with a beta of 2.0 has twice as much.

Assets with larger betas have greater systematic risks, they will have greater expected returns.

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PORTFOLIO BETAS

A portfolio beta, can be calculated, just like a portfolio expected return.

49



50


THE SECURITY MARKET LINE

51



52



54


THE SECURITY MARKET LINE OF B

55


SECURITY MARKET LINES

56

investors would be attracted to Asset A and away from Asset B. As a result, Asset A’s price would rise and Asset B’s price would fall.The reward-to-risk ratio must be the same for all the assets in the market.


SECURITY MARKET LINE

58


THE CAPITAL ASSET PRICING MODEL

59

introduction to risk and return

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