4-风险和回报10.ppt

1、Chapter 4,Risk and Return,1,没有免费的午餐收益总伴随着风险,收益和风险存在内在的关联性吗？ 请阅读中债日评,2,A股市场上证综指走势图,3,美国各种证券的Average Returns,4,假定1924年投资1元，不同证券的收益率,5,不同证券 的收益率波动风险,6,收益,假定资产不分红。资产在t期的价格为Pt。 单周期简单收益率： 若从第t-1天到第t天（一个周期）持有某种资产，则收益率为： 1+Rt=Pt/Pt-1 即Pt=Pt-1(1+Rt) 相应的净收益率为：Rt=Pt/Pt-11,7,收益,多周期简单收益率： 若从第t-k天到第t天（k个周期）内持有某种资

2、产，则k周期收益率为： 1+Rtk=Pt/Pt-k=Pt/Pt-1Pt-1/Pt-2. Pt-k+1/Pt-k=(1+Rt)( 1+Rt-1)( 1+Rt-k+1)= 即k个单周期收益率的乘积，即复合收益率,8,收益,年化收益率： 若持有资产k年，每年的平均收益率为： 这是由所包含的k个周期简单收益率几何平均得到的。,9,收益,计算几何平均数：,10,收益,复合收益法：计算连续复合收益率 多期情形：,11,Expected Returns,Expected returns are based on the probabilities of possible outcomes In this c

3、ontext, “expected” means average if the process is repeated many times The “expected” return does not even have to be a possible return,12,Example: Expected Returns,Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?

4、State Probability RC RT Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession 0.2 0.02 0.01 E(RC) = .3(.15) + .5(.10) + .2(.02) = .099 = 9.90% E(RT) = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%,13,Variance and Standard Deviation,Variance and standard deviation still measure the volatility of returns Usi

5、ng the associated probabilities for the entire range of possibilities Weighted average of squared deviations, where the probabilities are the weights:,14,Example: Variance and Standard Deviation,Consider the previous example. What are the variance and standard deviation for each stock? Stock C 2 = .

6、3(.15-.099)2 + .5(.1-.099)2 + .2(.02-.099)2 = .002029 = .045 Stock T 2 = .3(.25-.177)2 + .5(.2-.177)2 + .2(.01-.177)2 = .007441 = .0863,15,Another Example,Consider the following information: StateProbabilityRate of Return Boom.25.15 Normal.50.08 Slowdown.15.04 Recession.10-.03 What is the expected r

7、eturn? (Verify: 8.05%) What is the variance? (Verify: 002675) What is the standard deviation? (Verify: 5.17%),16,Portfolios,A portfolio is a collection of assets A constituent assets risk and return is important in how it affects the risk and return of the portfolio The risk-return trade-off for a p

8、ortfolio is measured by the portfolio expected return and standard deviation, just as with individual assets,17,Using the previous example with stock C and T,Suppose a portfolio with stock C and T is formed with weights of 0.6 in C and 0.4 in T respectively The return of the portfolio in each state

9、is the weighted return of the two assets in that state, as follows:,18,Return of Portfolio with Stock C (60%) and T (40%),19,Portfolio Expected Return and Variance,Expected Return = 0.3(0.19) + 0.5(0.14) + 0.2(0.016) =0.1302 (or 13.02%) Variance = 0.3(0.19-0.1302)2 + 0.5(0.14-0.1302)2 + 0.2(0.016-0.

10、1302)2 = 0.0037 Standard Deviation = 0.0611 = 6.11%,资产组合的风险与收益,两项资产构成的资产组合的风险与收益 1.期望收益 2.方差,资产组合的风险与收益,例：设有G、H两项资产，相关参数为： E(Rg)=20%, g=40%, E(Rh)=12%, h=13.3%，相关系数为gh Wg=0.25, Wh=0.75 组合的期望值与标准差分别为： E(Rp)=0.2520%+0.7512%=14%,资产组合的风险与收益,从上述计算可以看出，资产组合的期望收益与资产收益率之间的相关关系无关，而标准差的大小则与相关系数的大小有关。因此，资产组合的风险的大小，不仅与每个单项资产各自的风险大小（标准差的大小）有关，而且与资产间收益率变化的相互影响、相互联系有关。