最新投资学第5章利率史与风险溢价1 student精品ppt课件学习资料

1、投资学第5章利率史与风险溢价1 student2本章主要内容 利率水平的确定 - Interest Rate Determinants 期望收益与波动性 Expected Return and its Variance 风险价值 Value at Risk6 5.1.3 名义利率均衡 - Equilibrium Nominal Rate of Interest费雪方程(Fisher equation)含义：名义利率应该随预期通胀率的增加而增加 As the inflation rate increases, investors will demand higher nominal rates

2、of return If E(i) denotes current expectations of inflation, then we get the Fisher Equation: Nominal rate = real rate + inflation forecast)(iErR75.1.4 税收与实际利率 着通胀率的上升而下降可见：税后实际利率随税后真实利率为：则税后名义利率为，名义利率为记税率为ittritiritRtRRt)1 ()1)()1 ()1 (85.2 持有期收益率1/Tf(T)r1EAR1rate) annual effective(EAR,1)(100)()(，则

3、为：折为有效年利率益率为：则贴现债券的持有期收为买入价格，为持有期，若TPTrTPTfZero Coupon Bond, Par = $100, T=maturity, P=price, rf(T)=total risk free return9Example 5.2 Annualized Rates of Return10Equation 5.7 实际年利率 - EAR Effective annual rate definition: percentage increase in funds invested over a 1-year horizon TfTrEAR111115.2.1

4、年百分比利率TEARAPRAPRTTrTrEARAPRTTrTrnAPRTrTTTfnffff1)1(即：1)(1)(11更一般地，有：)(或)(，则有：)(期，每期利率为T1n一年为来表示，即若rate) percentage annual，(APR分比利率短期投资利率常用年百/1/112Equation 5.8 年百分比率 - APR TEARAPRT11 TfTrEAR11113Table 5.1 APR vs. EAR145.2.2 连续复利收益率 当T趋于无限小时，可得连续复利(continuous compounding)概念)1ln(1 1lim1/10EARreEAReAPRT

5、EARccrrTTcccc即：15Table 5.2 Statistics for T-Bill Rates, Inflation Rates and Real Rates, 1926-200916Figure 5.3 Interest Rates and Inflation, 1926-200917Figure 5.4 Nominal and Real Wealth Indexes for Investment in Treasury Bills, 1966-2005 185.4 风险和风险溢价risk premium 5.4.1 持有期收益 holding period return股票收

6、益包括两部分：红利收益(dividends)与资本利得(capital gains)持有期收益率(holding-period return)期初价格现金红利期初价格股票期末价格-HPR19Risk and Risk PremiumsPDPPHPR0101HPR = Holding Period ReturnP0 = Beginning priceP1 = Ending priceD1 = Dividend during period oneRates of Return: Single Period20Ending Price =110Beginning Price = 100Dividen

7、d = 4HPR = (110 - 100 + 4 )/ (100) = 14%Rates of Return: Single Period Example215.4.2 期望收益expected return与标准差 standard deviation：E-V方法 We are not sure about the eventual HPR, so we have to know the Probability Distribution of the future outcome.We will characterize PD in terms of their expected retu

8、rn E(r) and their standard deviation .22)()( )( )()()()()()(rEsrspsrsprErEHPRsrspsss则有：为标准差为期望收益，为各情形的为各情形的概率，记不确定情形的集合为22StateProb. of Stater in State Excellent.250.3100Good.450.1400Poor.25-0.0675Crash.05-0.5200E(r) = (.25)(.31) + (.45)(.14) + (.25)(-.0675) + (0.05)(-0.52)E(r) = .0976 or 9.76%Scena

9、rio Returns: Example23Variance (VAR):Variance and Standard Deviation22( )( )( )sp sr sE r2STDStandard Deviation (STD):24Scenario VAR and STD Example VAR calculation:2 = .25(.31 - 0.0976)2+.45(.14 - .0976)2 + .25(-0.0675 - 0.0976)2 + .05(-.52 - .0976)2 = .038 Example STD calculation:1949.038.25 例：假定投

10、资于某股票，初始价格1 0 0美元，持有期1年，现金红利为4美元，预期股票价格由如下三种可能，求其期望收益和方差。(1)(140 100 4)/10044%r26=4500.5=21.2132275.4.3 超额收益与风险溢价 Risk and Risk premiums Example: rf=6%, rstockA=14%, so what is 8% which equals to rstockA-rf? rstockA-rf=excess return, or excess return=actual return riskfree rate. The risk premium is

11、the expected value of the excess return, then E(r)-rf=risk premium. We measure the return of an investment with its E(r), we measure the risk of an investment with its risk premiums standard deviation.285.4.3 超额收益与风险溢价 Risk and Risk premiums 例：上例中我们得到股票的预期回报率E(r)为14，若无风险收益率为rf8。初始投资100元于股票，其风险溢价(E(r

12、)-rf)为6元，作为其承担风险（标准差为21.2元）的补偿。 投资者对风险资产投资的满意度取决于其风险厌恶(risk aversion)程度295.5 历史收益率时间序列分析5.5.1 时间序列与情景分析We do not know the PD of future outcomes, as well as their E(r) and . We must infer from its history or time series in order to estimate them.5.5.2 期望收益与算术平均收益率的算术平均数 arithmetic average of rates of

13、 return：nsnssrnsrsprE11)(1)()()(305.5.2 几何收益率Geometric Average ReturnTV = 投资终值投资终值(Terminal Value of the Investment)1/1TVgng= 几何平均收益率几何平均收益率(geometric average rate of return)1 ()1)(1 (21nnrrrTV315.5.4 方差与标准差 325.5.5 报酬-风险比率(夏普比率)The Reward-to-Volatility (Sharpe) RatioSharpe Ratio for Portfolios =Ris

14、k PremiumSD of Excess ReturnWe would like to know the trade-off between reward(the risk premium) and risk(as measured by standard deviation or SD)33 5.6 正态分布 - The Normal Distribution Investment management is easier when returns are normal.http:/ deviation is a good measure of risk when returns are

15、symmetric.If security returns are symmetric, portfolio returns will be, too.Future scenarios can be estimated using only the mean and the standard deviation.34 5.6 正态分布 - The Normal Distribution35Normality and Risk Measures What if excess returns are not normally distributed?Standard deviation is no

16、 longer a complete measure of riskSharpe ratio is not a complete measure of portfolio performanceNeed to consider skew and kurtosis365.7 偏离正态 偏度，亦称三阶矩(third-order moments)峰度：33)()(rEsrEskew3)()(44rEsrEkurtosis37图 5.5A 正态与偏度分布 (mean = 6% SD = 17%)38图5.5B 正态与厚尾分布 (mean = .1, SD =.2)39Value at Risk (Va

17、R) A measure of loss most frequently associated with extreme negative returns VaR is the quantile of a distribution below which lies q % of the possible values of that distributionThe 5% VaR , commonly estimated in practice, is the return at the 5th percentile when returns are sorted from high to lo

18、w.40Expected Shortfall (ES) Also called conditional tail expectation (CTE) More conservative measure of downside risk than VaRVaR takes the highest return from the worst casesES takes an average return of the worst cases41Covariance and Correlation Portfolio risk depends on the correlation between t

19、he returns of the assets in the portfolio Covariance and the correlation coefficient provide a measure of the way returns of two assets vary42Two-Security Portfolio: Return 43 = Variance of Security i = Variance of Security j = Covariance of returns for Security i and Security jTwo-Security Portfoli

20、o: RiskiijijjiirrCovwwww,222222p2j2ijirrCov,44 = Covariance of returns for Security i and Security jTwo-Security Portfolio: RiskjirrCov,iijijjiirrCovwwww,222222p 45Two-Security Portfolio: Risk 465.8 股权收益与长期债券收益的历史记录5.8.1 平均收益与标准差基本结论：高风险、高收益47表5.3 各个时期的资产历史收益率1926- 200548图5.6 1926-2005年历史收益率495.8.2 风险资产组合的其他统计量5.8.3 夏普比率5.8.4 时间序列相关性5.8.5 偏度与峰度5.8.6 历史风险溢价的估计5.8.7 全球历史数据50表5.4 资产的历史超额收益率1926- 200551图5.7 世界名义和实际股权收益率1900-200052图 5.8 世界股权和债券实际收益率的年标准差 1900-2000535.9 长期投资545.9.1 长期投资的风险与对数正态分布 连续复利的收益率若呈正态分布，则实际的持连续复利的