issues

• 1. Portfolio: mean-variance model

• 2. Measuring risk

• 3. Equilibrium in a Market for Risky Asset

--CAPM

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投資者偏好• 兩商品• 報酬率 : mean return

• 風險 : 標準差

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2.1 Measuring risk for holdingMany risky assets

Examples:

• Consider two risky assets :1. A :0.5 gets 10 and 0.5 gets -5 the expected return of A is 2.5 ; the standard deviation of A is 7.52. B: 0.5 gets 10 and 0.5 gets -5 the expected return of B is 2.5 ; the standard deviation of B is 7.5

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Examples:

• Consider two risky assets :1. A :0.5 gets 10 and 0.5 gets -5 the expected return of A is 2.5

the standard deviation of A is (10-2.5) 2. B: 0.5 gets 10 and 0.5 gets -53. When A is worth 10, B is worth -5. 4. When A is worth -5, B is worth 10. ? What is the risk of buying 0.5A

asset with 0.5 B asset ?

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2.1 Measuring risk for holdingMany risky assets

• If there are many risky assets, the standard deviation is not an appropriate measure for the amount of risk in an asset.

Correlation

• The value of an asset depends on much more on the correlation of its return with other assets than its own variation

Two types of Risks

• Symmetric (non-divisible ) risk: 如未預期之總體經濟變數 ( 通膨 ) , 天災 , 人禍 (

政治 ,…), each risky asset 都會 more or less 被波及• Divisible risk (un-symmetric) risk , 個別公司獨特風

險 ,. 只會波及個別公司或產業~ 分散風險 via 多檔 (1) 負相關 (2) 無相關 risky asset • 參考

圖 21.7 可分散風險與不可分散風險

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個股之不可分散風險 :Beta 係數

• 大盤漲跌時 , 有些股漲跌少 , 有些漲股跌多

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Beta

• Beta is the covariance of the return on the stock with the market return divided by the variance of the market return

• 參考, 參考

3. Equilibrium

in a Market for risky assets• All assets, after

adjusting for risk, have earn the same rate of return

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CAPM

Problem for CAPM

• CAPM 算法

How Returns Adjust?

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Question 1

• If the risk-free rate of return is 6%, and if a risky asset is available with a return of 9% and a standard deviation of 3%,

• what is the maximum rate of return you can achieve if you are willing to accept a standard deviation of 2% ?

• What percentage of your wealth would have to be invested in the risky asset ?

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Question 2:What is the price of risk in the above

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Question 3

• If a stock has a beta of 1.5, the return on the market is 10%, and the risk-free rate is 5%,

• what expected rate of return should this stock offer according to the Capital Asset Price Model ?

• If the expected value of the stock is $100, what price should the stock be selling for today ?

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CAPM