Unit II - Risk and Return Tradeoff

8/8/2019 Unit II - Risk and Return Tradeoff

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Measuring RiskPortfolio Risk Portfolio theory

Beta and Unique Risk Security MarketLineDiversification

Capital Asset Pricing Model (CAPM)


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Rate of return = (Annual Income + Endingprice - Beginning price) / Beginning price

Eg., Price at the beginning of the year =Rs.60

Dividend paid at the end of the year =Rs.2.40

Price at the end of the year = Rs.69Hence, ROR = 19%.


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Current yield = annualincome/beginning priceCapital gains yield = ending price-beginning price/beginning priceRoR = current yield +capital gains yield


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The probability of an event representsthe likelihood of its occurrence

State of theeconomy

Probabilityof occurrence

Company A(RoR %)

Company B(RoR %)

Boom 0.30 16 40

Normal 0.50 11 10

recession 0.20 6 -20


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The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

0.1

10

1000

1925 1940 1955 1970 1985 2000

S&PSmall CapCorp BondsLong BondT Bill

Index

Year End

1

6402

2587

64.1

48.9

16.6


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Rates of Return 1926-2000: US Economy

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

2 6 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 2 0

0 0

Common StocksLong T-BondsT-Bills

Year

Percen tageR eturn


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4.35.1 6 6.1 6 .1

6.5 6.7 7.17.5 8

8.5 9.9 9.9 10 11

0

12

3

45

6

78

9

10

11

D e n B

e l

C a n

S w

i

S p a

U K I r

e

N e t h

U S A

S w e

A u s

G e r

F r a

J a p I t

Risk premium, %

Country


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Variance - Average value of squareddeviations from mean. A measure of volatility.

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


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Coin Toss Game-calculating variance andstandard deviation

(1) (2) (3)

Percent Rate of Return Deviation from Mean Squared Deviation

+ 40 + 30 900

+ 10 0 0

+ 10 0 0

- 20 - 30 900

Variance = average of squared deviations = 1800 / 4 = 450Standard deviation = square of root variance = 450 = 21.2%


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Diversification - Strategy designed to reducerisk by spreading the portfolio across manyinvestments.

Unique Risk - Risk factors affecting only thatfirm. Also called diversifiable risk.Market Risk - Economy-wide sources of risk

that affect the overall stock market. Alsocalled systematic risk.


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Portfolio rate

of return=

fraction of portfolio

in first assetx

rate of return

on first asset

+fraction of portfolio

in second assetx

rate of return

on second asset

((

((

))

))


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0

5 10 15

Number of Securities

P o r t

f o l i o

s t a n

d a r d

d e v

i a t i o n

Market risk

Uniquerisk


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beta

Expected

return

Expectedmarketreturn

10%10%- +

-10%+10%

stock

pyright 1996 by The McGraw-Hill Companies, Inc

-10%

1. Total risk =diversifiable risk +market risk 2. Market risk ismeasured by beta,

the sensitivity tomarket changes


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Market Portfolio - Portfolio of allassets in the economy. In practicea broad stock market index, suchas the S&P Composite, is used torepresent the market.

Beta - Sensitivity of a stocks returnto the return on the marketportfolio.


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2m

imi

B

=


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2

m

im

i B

=

Covariance with the

market

Variance of the market


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E (Rj) = Rf +j [E (Rm) - Rf]Where,E (Rj) = expected return on security jRf = risk-free returnj = beta of security jE (Rm) = expected return on market portfolio

Risk premium = j [E (Rm) - Rf]


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Markowitz Portfolio TheoryRisk and Return Relationship

Testing the CAPM


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Combining stocks into portfolios can reducestandard deviation, below the level obtainedfrom a simple weighted average calculation.

Correlation coefficients make this possible. The various weighted combinations of stocksthat create this standard deviationsconstitute the set of efficient portfoliosefficient portfolios .


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Price changes vs. Normal distribution

Microsoft - Daily % change 1990-2001

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


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Standard Deviation VS. Expected ReturnInvestment A

0

2

4

6

8

10

12

14

16

18

20

-50 0 50


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Standard Deviation VS. Expected Return

Investment B

0

2

4

6

8

10

12

14

16

18

20

-50 0 50


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Expected Returns and Standard Deviations vary givendifferent weighted combinations of the stocks

Expected Return(%)

StandardDeviation

Goal is to move up andleft.

WHY?


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Each half egg shell represents the possible weightedcombinations for two stocks.

The composite of all stock sets constitutes the efficient frontier


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Example Correlation Coefficient = .4

Stocks

% of Portfolio Avg ReturnABC Corp 28 60% 15%

Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6

Standard Deviation = Portfolio = 28.1

Return = weighted avg = Portfolio = 17.4%


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Lets Add stock New Corp to the portfolioExample Correlation Coefficient = .3Stocks % of Portfolio Avg

ReturnPortfolio 28.1 50% 17.4%New CorpNew Corp 3030 50%50% 19%19%

NEW Standard Deviation = weighted avg = 31.80NEW Standard Deviation = Portfolio = 23.43NEW Return = weighted avg = Portfolio = 18.20


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Example Correlation Coefficient = .3Stocks % of Portfolio Avg ReturnPortfolio 28.1 50% 17.4%New Corp 30 50% 19%

NEW Standard Deviation = weighted avg = 31.80NEW Standard Deviation = Portfolio = 23.43NEW Return = weighted avg = Portfolio = 18.20%

NOTE: Higher return & Lower riskHow did we do that? DIVERSIFICATION


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SML Equation = r f + B ( r m - r f )

Capital Asset Pricing Model

R = r f + B ( r m -

r f )


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Unit II - Risk and Return Tradeoff

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