Lecture3 Risk,Return,and The Opportunity Cost of Capital(高级金

Advanced Financial Management

Lecture 3Risk, Return, and The Opportunity Cost of Capital Professor Yuanlue FuCenter for Accounting Studies of Xiamen University 2007

Sub-topics Covered Over a Century of Capital Market History Measuring Portfolio Risk Calculating Portfolio Risk Beta and Unique Risk Diversification& Value Additivity Markowitz Portfolio Theory Risk and Return Relationship Validity and the Role of the CAPM Some Alternative Theories

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1.The Value of an Investment of$1 in 1900$100,000$10,000Common Stock US Govt Bonds T-Bills

15,578

Dollars

$1,000$100$10$119 00 19 10 19 20 19 30 19 40 19 50 19 60 19 70 19 80 19 90 20 00

147 61

Start of YearXiamen University– Advanced Financial Management

2004

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1.The Value of an Investment of$1 in 1900Real Returns$1,000 719Equities Bonds Bills

$100

Dollars$10

6.81 2.80

$119 40 19 30 19 20 19 00 19 10 19 50 19 60 19 70 19 80 19 90 20 00

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2004

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2.Average Market Risk Premia (by country)Risk premium,%11 10 9 8 7 6 5 4 3 2 1 0

4.3

4.7

5.1

5.3

5.8

5.9

5.9

6.3

6.4

6.6

7.6

8.1

8.2

8.6

9.3

10

10.7

Switzerland

Germany

Average

Belgium

Denmark

Ireland

Sweden

South Africa

Australia

Spain

Canada

Country

Netherlands

France

Japan

Italy

USA

UK

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2.Average Market Risk Premium---Rates of Return 1900-2003 Stock Market Index Returns80%

Percentage Return

60% 40% 20% 0% -20% 1900 -40% -60%

1920

1940

1960

1980

2000

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Source: Ibbotson AssociatesXiamen University– Advanced Financial Management

3.Measuring RiskHistogram of Annual Stock Market Returns# of Years24 20 16 12 8 4 0

24 19 12 15 13

10 4 1-50 to -40

1-10 to 0 0 to 10 10 to 20 20 to 30 30 to 40 -40 to -30 -30 to -20 -20 to -10

340 to 50

2Return%50 to 60

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3.Measuring RiskVariance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation– square root of variance. A measure of volatility.

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3.Measuring RiskCoin Toss Game-calculating variance and standard 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= 450 Standard deviation= square of root variance= 450= 21.2%

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3.Measuring RiskDiversification - 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 call

ed“systematic risk.”

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3.Measuring Riskfraction of portfolio Portfolio rate x= in first asset of return

rate of return fraction of portfolio x+ on second asset in second asset

( (

)( )(

rate of return on first asset

) )

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3.Measuring RiskPortfolio standard deviation

0 5 10 15 Number of Securities

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3.Measuring RiskPortfolio standard deviation

Unique risk Market risk

0 5 10 15 Number of Securities

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4.Portfolio RiskThe variance of a two stock portfolio is the sum of these four boxes

Stock 1 Stock 1 Stock 22 2 x1σ1

Stock 2 x 1x 2σ 12= x 1x 2ρ 12σ 1σ 22 x2σ 2 2

x 1x 2σ 12= x 1x 2ρ 12σ 1σ 2

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4. Portfolio RiskExample 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:

Expected Return= (. 60× 10 )+ (. 40× 15 )= 12%Xiamen University– Advanced Financial Management

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4.Portfolio RiskExample 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.

Exxon - Mobil2 2 Exxon - Mobil x1σ1= (.60) 2× (18.2) 2

Coca - Cola x1x 2ρ12σ1σ 2= .40× .60× 1× 18.2× 27.32 2 2 x2σ= (. 40 )× ( 27 . 3 ) 2 2

Coca - Cola

x1x 2ρ12σ1σ 2= .40× .60× 1× 18.2× 27.3

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