Deviation from mean离均差 Deviation fromSquared Example: YearRate of ReturnAverage ReturnDeviation
1999 23.7 19.52 381.03 2000 (10.9) (15.08) 227.41 2001 (11.0) (15.18) 230.432002 (20.9) (25.08) 629.01
2003 31.6 27.42 751.86
2004 12.6 8.42 70.90
Total25.1 2,290.63 Average rate of return = 25.1/6=4.18% Variance = average of squared deviations = 2290.63/6=381.77Standard deviation = squared root of variance = 19.54%
Risk and Diversification
Diversification: Building a Portfolio
A portfolio’s rate of return is the weighted sum of each asset’s rate of return. Two Asset Case:
?fraction of portfolio??rate of return? Portfolio Rate of Return=??x???in first asset??on first asset?
?fraction of portfolio??rate of return?+??x?? ?in second asset??on second asset? Example:Consider the following portfolio:
Stock IBM Starbucks Walmart
Weight Wibm=50% Wsbux=25% Ww=25% Rate of Return Ribm=8.3% Rsbux=12.5% Rw=4.7% Portfolio Rate of Return = ?wIBM?rIBM???wSBUX?rSBUX???wW?rW?? (50%?8.3%)??25%?12.5%???25%?4.7%??8.45%? Return of portfolio (with project A and B)
‘Rp = WA’RA + WB’RB
? Risk of portfolio
σp =√WA2σA2+WB2σB2+2WAWBσAσBρAB
? e.g.
project A Project B
Expected return 14% 17% Proportion of inv. 3500 6500 Standard deviation 0.09 0.09 Weight of inv. 35% 65%
?R = 0.35 (14%) + 0.65 (17%) = 15.95%
? σp=√(.35)2(.09)2+(.65)2(.09)2+2(.35)(.65)
(.09)(.09)(1) = 0.09
? σp=√(.35)2(.09)2+(.65)2(.09)2+2(.35)(.65)
(.09)(.09)(0.5) = 0.0791
? σp =√(.35)2(.09)2+(.65)2(.09)2+2(.35)(.65)
(.09)(.09)(-0.5) = 0.0507
Chapter 12
Beta
Sensitivity of a stock?s return to the return on the market portfolio. A measure of a stock?s risk relative to the risk of the market portfolio.
Example: The Fosterhouse Gourmet Foods corporation has the following % returns on its stock, relative to the listed changes in the % return on the market portfolio. Its beta (β) can be derived from this information. Month*Market Return %Fosterhouse Return %
123456+1-1+1+1-1-1+1.8+1.6+0.2-0.8+0.0-2.8? When the market was up 1%, Fosterhouse Corporation?s average percent change was +.4%.
? When the market was down 1%, Fosterhouse Corporation?s average percent change was -.4%.
? The change of .8% (-.4% to .4%) divided by the 2% (-1.0% to 1.0%) change in the market produces a beta of .4. .4%?(?.4%).8%
????.41%?(?1%)2%
Portfolio Beta
投资组合的贝塔系数=（第一只股票在投资组合中的比例x第一只股票的贝塔系数）+（。。。。）+（。。。。。）+。。。。。
Measuring Market Risk:The Market Risk Premium
Risk premium of market portfolio; the difference between the market return and the return on risk-free Treasury bills.
Example:
14
12
Let,10
8rf? 4% 6rm?12%4
2Market Risk Premium = 8%
0
Capital Asset Pricing Model (CAPM) 资本资产定价模型
Market risk premium?rm-rfLet r = expected return on any asset
Risk premium on any asset?r-rf
r?rf???(rm?rf)
or,*
r?rf???(rm?rf)
Example:
Let,Suppose ??1.2
rf? Risk-free rate of return
According to CAPM, the expected return on the asset isrm?Market Return
Market Risk Premium = rm?rfr?rf???(rm?rf)?4%?1.2?(8%)?13.6%
证券市场线（SML）
ExpectedReturn (%)0.20.40.60.80Beta1
某公司股票的系数为2，无风险利率为5%，市场上所有股票的平均报酬率为10%。利用资本资产定价模型计算该公司的股票成本。 CAPM定价模型的公式
R=Rf+β（Rm-Rf） 请问题目里的 所有股票的平均报酬率体现在公式哪里？是R么，但是这个R不是单一资产期望收益率么？ 另外如何计算股票成本呢？ 谢谢！ R=Rf+β（Rm-Rf）=5%+2*(10%-5%)=15% 注意：Rm表示市场上所有股票的平均报酬率。
R表示单个股票的期望报酬率（即该股票的资本成本）
β表示某个单个股票相对于整个股票市场的风险变动倍数（一般假设整个股票市场的风险变动系数为1）
根据题目的信息，所谓的股票成本应该是该股票筹资的资本成本。
Chapter 13加权平均成本WACC，会算WACC（公式债务利息要扣税）会算free cash flow，公司评估P313页 D??E?cost of capital 一个用百分比表示公 rassets??? r?? rdebtequity?????V??V?司资本预算计划要求的最低回报率
weighted-average cost of capital (WACC)加权平均成本
Example: Macrosoft, Inc. has issued long-term bonds with a present value of $25 million and a yield of 8%. It currently has 12 million shares outstanding, trading at $20 each, offering an expected return of 14%. What is the firm?s cost of capital?
E?12,000,000?$20?$240million
The WACC provides a firm’s after-tax cost of capital. ?D??E?WACC=?? (1-Tc)?rdebt?+?? requity? ?V??V?Where: Tc = The firm?s average tax rate
WACC (加权平均资本成本)，英文Weighted Average Cost of Capital的缩写。WACC代表公司整体平均资金成本，可用来衡量一个项目是否值得投资——项目的回报必须不低于WACC。
Calculating WACC
? firm?s WACC is calculated in 3 steps:
1. Calculate the value of each security as a proportion of firm value. 2. Determine the required rate of return on each security.
3. Calculate a weighted average of the after-tax return on the debt and return on the equity.
Example: What is the WACC for a firm with $30 million in outstanding debt with a required return of 8%, 8 million in equity shares outstanding trading at $15 each with a required return of 12%, and a tax rate of 35%?
If there are 3 (or more) sources of financing, simply calculate the weighted-average after-tax return of each security type.
?D??E??P?? If the firm issues preferred stock: WACC=?? (1-Tc)rdebt?+?? requity?+?? rPreferred??V??V??V?
(When estimating WACC, use market values, not book values.) Calculating Expected Returns
To calculate the WACC, we must first calculate the rates of return that investors expect from each security.
? Expected returns on bonds
The risk of bankruptcy aside, the yield to maturity represents an investor’s expected return on a firm’s bonds.
? Expected returns on common stock Estimating requity using CAPM:
Example: A firm’s beta is 1.5, Treasury bills currently yield 4%, and the long-run market
risk premium is 8%. What is the firm’s cost of equity?