1. issues 1. Portfolio: mean-variance model 2. Measuring risk 3. Equilibrium in a Market for Risky Asset --CAPM

2. Consider a risk-free asset, which always pays a fixed rate of return and a risky asset with state s=1,..S

3. X ratio in the risky asset and 1-x in the risk-free asset

4. 投資者偏好 兩商品 報酬率 : mean return 風險 : 標準差

5. Fig. 13.2

6. Budget line of portfolio

7. Preference

8. Optimal portfolio

9. 2.1 Measuring risk for holding Many risky assets

10. 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 7.5 2. 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

11. Examples: What is the risk of buying o.5 A asset with 0.5 B asset ?

12. 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 -5 3. 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 ?

13. 2.1 Measuring risk for holding Many risky assets If there are many risky assets, the standard deviation is not an appropriate measure for the amount of risk in an asset.

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

15. 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

16. 圖 21.7 可分散風險與不可分散風險

17. 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

18. 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 參考

19. 3. Equilibrium in a Market for risky assets All assets, after adjusting for risk, have earn the same rate of return

20. CAPM ~Capital Asset Pricing Model

21. Problem for CAPM CAPM 算法CAPM 算法

22. How Returns Adjust?

23. 練習例子 定存 =2.5% 某電子類股票 Beta=1.17 大盤報酬率之機率密 度函數 ~

24. 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 ?

25. Answer

26. Question 2: What is the price of risk in the above exercise (question 1) ?

27. 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 ?

28. Answer