資本資產定價模型 CAPMPPT學習教案

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1、會計學12第1頁/共73頁3第2頁/共73頁4NE(r) = p(s)r(s)s=12E(r) - srsp N1=s = 2)()(離差平方離差平方離差平方第3頁/共73頁5%11)(%)28(31%)12(31%)7(31)(SSrErE離差平方離差平方第4頁/共73頁6%7)(%)3(31%)7(31%)17(31)(BBrErE離差平方離差平方第5頁/共73頁72(11%( 7%)3.24% 離差平方離差平方第6頁/共73頁8%01.%)12%11(2離差平方離差平方第7頁/共73頁9%89. 2%)28%11(2離差平方離差平方第8頁/共73頁10%)89. 2%01. 0%24.

2、3(31%05. 2離差平方離差平方第9頁/共73頁110205. 0%3 .14離差平方離差平方第10頁/共73頁12第11頁/共73頁13注意到股票的收益率和風險都比債券的高。讓我們考慮一個風險收益權衡的組合：一半由股票構成、一半由債券構成。第12頁/共73頁14組合的收益率等于組合中的股票和債券收益率的加權平均值。SSBBPrwrwr%)17(%50%)7(%50%5第13頁/共73頁15組合的收益率等于組合中的股票和債券收益率的加權平均值。%)7(%50%)12(%50%5 . 9SSBBPrwrwr第14頁/共73頁16組合的收益率等于組合中的股票和債券收益率的加權平均值。%)3(%

3、50%)28(%50%5 .12SSBBPrwrwr第15頁/共73頁17組合的期望收益率是組合中各個證期望收益率的加權平均。%)7(%50%)11(%50%9)()()(SSBBPrEwrEwrE第16頁/共73頁18有兩個風險證券組成的組合的方差是：BSSSBB2SS2BB2P)(w2(w)(w)(w其中BS 是股票基金和債券基金收益率的相關系數。第17頁/共73頁19注意到分散化使得風險下降。由一半股票和一半債券構成的組合風險比組合中的股票或者債券的風險都小。第18頁/共73頁20p(w11+w22)第19頁/共73頁21第20頁/共73頁22第21頁/共73頁23第22頁/共73頁24

4、經濟狀況經濟狀況發(fā)生概率發(fā)生概率股票股票A 報酬率報酬率股票股票B報酬率報酬率蕭條蕭條0.200.150.20正常正常0.500.200.30景氣景氣0.300.600.40第23頁/共73頁25第24頁/共73頁26第25頁/共73頁27第26頁/共73頁28第27頁/共73頁29我們可以考慮除了50%股票和50%債券組合方式之外的情況100% 債券100% 股票第28頁/共73頁30我們可以考慮除了50%股票和50%債券組合方式之外的情況100% bonds100% stocks% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15

5、%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%

6、8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%5

7、0%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4

8、%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.

9、2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10

10、.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Retur

11、n0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8

12、%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%

13、35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.

14、1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6

15、%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85

16、%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%1

17、00%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8

18、.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6

19、%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0

20、.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.

21、0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%

22、7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%第29頁/共73頁31100% stocks100% bonds注意到一些組合優(yōu)于其他的組合，因為他們在同等的風險水平下收益比較高。這些有效的組合構成的集合在圖中稱為有效前沿。第30頁/共73頁32100% 債券收益100% 股票 = 0.2 = 1.0 = -1.0第31頁/共73頁33第32頁/共73頁ijjiNjNiiNiiPwww11212222211111,NNNiijiijijNN 其中1 N組合方差平均方差11N

23、平均協方差隨著N增大，組合的方差趨向于平均協方差。第33頁/共73頁35不可分散風險; 系統風險; 市場風險可分散風險; 非系統風險; 具體企業(yè)風險; 特有風險n組合證券數量大的情況下，方差項被有效地分散掉，但是協方差項不能分散掉。因此，分散化可以消除單個證券一部分風險，而不是全部的風險。組合風險第34頁/共73頁36nf. 最高法院的一項裁決顯著地擴最高法院的一項裁決顯著地擴大了生產者對產品使用者所造大了生產者對產品使用者所造成傷害的責任。成傷害的責任。第35頁/共73頁37收益P單個資產第36頁/共73頁38收益P最小方差組合單個資產第37頁/共73頁39收益P最小風險組合有效前沿單個證券

24、第38頁/共73頁40100% 債券100% 股票rf收益第39頁/共73頁41標準差 = (.5 x 0)2+ (.5 x .16)2 + (2 x .5 x .5 x 0 x .16 x 0).5 = .5 x .16 = .08 or 8%第40頁/共73頁42第41頁/共73頁43SE(收益)rf = 7.5%15% 16% 第42頁/共73頁44100% 債券100% 股票rf收益平衡基金CML第43頁/共73頁45收益P有效前沿rfCML第44頁/共73頁46收益P有效前沿rfMCML第45頁/共73頁47收益P有效前沿rfMCML第46頁/共73頁48收益P有效前沿rfMCML第

25、47頁/共73頁49100% 債券100% 股票rf收益平衡基金CML第48頁/共73頁50100% 債券100% 股票rf收益最優(yōu)風險組合CML第49頁/共73頁51100% 債券100% 股票rf收益最優(yōu)風險組合CML第50頁/共73頁52100% 債券100% 股票收益第一最優(yōu)風險組合第二最優(yōu)風險組合CML0CML10fr1fr第51頁/共73頁53第52頁/共73頁54第53頁/共73頁55收益率進行回歸，回歸線的斜率是對貝塔的統計估計。)(2),(MRMRiRCovi第54頁/共73頁56第55頁/共73頁57股票股票貝塔貝塔Bank of America1.55Borland In

26、ternational2.35Travelers, Inc.1.65Du Pont1.00Kimberly-Clark Corp.0.90Microsoft1.05Green Mountain Power0.55Homestake Mining0.20Oracle, Inc.0.49第56頁/共73頁58)()(2,MMiiRRRCov明顯地，你對貝塔的估計取決于你所選擇的市場組合。第57頁/共73頁59單個證券的期望收益:MFRR市場風險溢價)(FMiFiRRRR市場風險溢價這個公式對多元化組合中的單個證券也適用。第58頁/共73頁60第59頁/共73頁61)(FMiFiRRRR假設 i =

27、 0, 則期望收益率是 RF.假設 i = 1, 則MiRR 證券的期望收益=無風險利率+證券貝塔市場風險溢價第60頁/共73頁62第61頁/共73頁63第62頁/共73頁64期望收益)(FMiFiRRRRFR1.0MR)(FMiFiRRRR第63頁/共73頁65期望收益%3FR%31.5%5 .135 . 1 i%10MR%5 .13%)3%10(5 . 1%3iR第64頁/共73頁)(FRMRBristolFRBristolR%4 .12%)4 . 8 x 81(.%6 . 5BristolR第65頁/共73頁貝塔期望收益0Rf = 5.6% 1.0Rm = 14%1.5.8112.4%B

28、ristol Myers SquibbRR第66頁/共73頁68第67頁/共73頁69產收益率與市場收益率的敏感產收益率與市場收益率的敏感度度) 第68頁/共73頁70第69頁/共73頁71ABAABB2BB2AA2P)(w2(w)(w)(w)()()(BBAAPrEwrEwrE通過改變wA, 我們就可以得到組合的有效集合。我們以兩個資產為例子畫出有效前沿，有效前沿的彎曲程度反映了多元化的效應：兩證券的相關程度越低，多元化的效應越大。兩個證券有效組合的曲線形狀和多個證券的形狀是一致的。第70頁/共73頁72收益P有效前沿rfMCML通過借貸，投資者可以選擇資本市場線上的一點（他所偏好的那一點）。第71頁/共73頁73CAPM認為，證券的期望收益率和證券的貝塔正相關：)()(2,MMiiRRRCov)(FMiFiRRRR第72頁/共73頁