Example with incremental IRR.
Incremental IRR is the IRR on the incremental investment from choosing the large project instead of the small one.
Furthermore, we can calculate the NPV for incremental Cash Flows.
In review, we can handle this example (or any mutually exclusive example) in one of three ways:
1. Compare the NPVs of the two choices.
2. Compare the incremental NPV from making the large-budget picture instead of the small-budget picture.
3. Compare the incremental IRR to the discount rate.
(2).The Timing Problem
We can select the better project with one of three different methods: 1. Compare NPVs of the two projects
2. Compare incremental IRR to discount rate. 3. Calculate NPV on incremental cash flows.
The IRR probably survives because it fills a need that the NPV does not. People seem to want a rule that summarizes the information about a project in a single rate of return.
To their credit, however, companies that employ the IRR approach seem to understand its deficiencies.
6.8 The Practice of Capital Budgeting
1.IRR 2.NPV 3.Payback
第10章
1Individual Securities(单个证券):
1.The characteristics of Individual Securities（单个证券的特点） ①return（期望收益） ②risk（风险）
10.2Expected Return,Variance,and Covariance（期望收益、方差、协方差）
1.Expected Return（期望收益）：Arithmetic mean of historical return（算术平均的
历史回归）
2. Variance and standard Deviation（方差与标准差）
Var(R)?ExpectedSD(R)?Var(R)
valueof(R?R)2
3. Covariance and Correlation（协方差和相关系数）
?AB?Cov(RA.RB)?Expectedvalueof[(RA?RA)?(RB?RB)]
?AB?Corr(RA.RB)?Cov(RA.RB)
?A??B
10.3 The Return and Risk for Portfolios
1. The expected return on a portfolio is simply a weighted average of the expected returns on the individual securities.(组合的期望收益是构成组合的各个证券的期望收益的简单加权平均) Expected return on portfolio(组合的期望收益)=XARA+XBRB=RP 2. The variance of the portfolio(投资组合的方差)
Var(portfolio)=X2A?2A+2XAXB?A,B+XB?B
22
3. The diversification effect Variance
of
super,slow+Xslow?22portfolio’s
slow
return=X2super?2super+2XsuperXslow?super,slow?As long as ?<1,the standard deviation of a portfolio of two securities is less than the weighted average of the standard deviations of the individual securities.(当由两种证券构成投资组合时，只要?AB<1，组合的标准差就小于这两种证券
各自的标准差的加权平均数)
10.4
The efficient set for two assets两种资产组合的有效集
图：1.Portfolio1 is composed of 90 percent slowpoke and 10 percent supertech.(p=-0.1639).
2. Portfolio2 is composed of 50 percent slowpoke and 50
percent supertech.(p=-0.1639)
3. Portfolio3 is composed of 10 percent slowpoke and 90 percent supertech.(p=-0.1639)
P<=0,backward bending always occurs(会出现后弯)；p>0, backward bending may or may not occur(可能出现也有可能不出现后弯)。
4.nonsystematic risk can be diversified away (非系统性风险可以消除)；systematic risk can not be delimitated (系统性风险不可以消除)。
10.5：The Efficient Set for Many Securities 多种资产组合的有效集 1、
无限多种组合但所有只能是落在有效区域内。 2、多种资产组合的期望收益。 3、投资组合方差的矩阵计算表。
10.6 Diversification:An Example
1.Variance portfolio=N?(
1111?varvarcov)+N(N-1)()=()+(1-)cov 22NNNNof
2.Variance of portfolio(when N??)=cov
10.7 Riskless Borrowing and lending 无风险的借和贷
1.由一种风险资产和一种无风险资产构成的投资组合的收益率：是两种资产收益的加权平均数。
2. 由一种风险资产和一种无风险资产构成的投资组合的风险：X2risky?risky 3. 35% in risk assets(风险资产)，65% in risk-free assets(无风险资产)
4.该图说明了一个要点：通过按照无风险利率进行接入或贷出，任何投资者持有的风险资产的投资组合都将是点A。无论投资者的风险厌恶程度如何，他绝不会选择风险资产有效集中的其他点，也绝不会选择可行集内部的任何点。
10.8：Market Equilibrium市场均衡
在一个具有共同期望的世界中，所有的投资者都会持有A点所代表的风险资产组合。 10.9Relationship between Risk and Expected Return (CAPM) 期望收益与风险之间的关系：资本定价模型 1Beta
1)Beta measures the responsiveness of a security to movements in the market portfolio 贝塔系数是度量一种证券对于市场组合变动的反应程度的指标 2)The actual definition of beta is
2?i?Cov(Ri，RM)?(R2M)
其中分子是第i种证券的收益与市场组合收益之间的协方差，分母是市场组合收益的方差 3）①One usefull property is that the average beta across all securities,when weighted by the proportion of each securiy’s market value to that the market portfolio,is 1.That is,即证券市场的一般证券的贝塔系数为1
②增加一个一个贝塔系数大于1的股票，将增加投资组合的风险
?X?i?1iNi?1
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