投资学第5章利率史与风险溢价1 student

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,#,投资学 第,5,章,历史数据中的收益与风险,Introduction to Risk, Return, and the Historical Record,2,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 Risk,3,5.1,利率水平的确定,利率水平的决定因素：,资金供给,(,居民,) -,Households,资金需求,(,企业,) -,Businesses,资金供求的外生影响,(,政府,) -,Governments Net Supply and/or Demand,Federal Reserve Actions,4,5.1.1,实际利率,(real interest rate),与名义利率,(nominal interest rate),消费者物价指数,(CPI,，,consumer price index),Nominal,interest rate(R): Growth rate of your money,Real,interest rate(r): Growth rate of your purchasing power,5,5.1.2,实际利率均衡,- Equilibrium Real Rate of Interest,四因素：供给、需求、政府行为和通胀率,资金,均衡资金借出,均衡的,真实利率,利率,E,E,需求,供给,利率,均衡的,真实利率,利率,均衡资金借出,均衡的,真实利率,利率,资金,均衡资金借出,均衡的,真实利率,利率,供给,资金,均衡资金借出,均衡的,真实利率,利率,6,5.1.3,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 of return,If,E,(,i,) denotes current expectations of inflation, then we get the Fisher Equation:,Nominal rate = real rate + inflation forecast,7,5.1.4,税收与实际利率,8,5.2,持有期收益率,Zero Coupon Bond, Par = $100, T=maturity, P=price,r,f,(T)=total risk free return,5-,9,Example 5.2 Annualized Rates of Return,5-,10,Equation 5.7,实际年利率,- EAR,Effective annual rate definition: percentage increase in funds invested over a 1-year horizon,11,5.2.1,年百分比利率,5-,12,Equation 5.8,年百分比率,- APR,5-,13,Table 5.1 APR vs. EAR,14,5.2.2,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,5-,15,Table 5.2 Statistics for T-Bill Rates, Inflation Rates and Real Rates, 1926-2009,5-,16,Figure 5.3 Interest Rates and Inflation, 1926-2009,17,Figure 5.4 Nominal and Real Wealth Indexes for Investment in Treasury Bills, 1966-2005,18,5.4,风险和风险溢价,risk premium,5.4.1,持有期收益,holding period return,股票收益包括两部分：,红利收益,(dividends),与,资本利得,(capital gains),持有期收益率,(holding-period return),5-,19,Risk and Risk Premiums,HPR,= Holding Period Return,P,0,= Beginning price,P,1,= Ending price,D,1,= Dividend during period one,Rates of Return: Single Period,5-,20,Ending Price =110,Beginning Price = 100,Dividend = 4,HPR,= (110 - 100 + 4 )/ (100) = 14%,Rates of Return: Single Period Example,21,5.4.2,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 return E(r) and their standard deviation,.,5-,22,State,Prob. of State,r,in State,Excellent.250.3100,Good.450.1400,Poor.25-0.0675,Crash.05-0.5200,E,(,r,) = (.25)(.31) + (.45)(.14) + (.25)(-.0675),+ (0.05)(-0.52),E,(,r,) = .0976 or 9.76%,Scenario Returns: Example,5-,23,Variance (VAR):,Variance and Standard Deviation,Standard Deviation (STD):,5-,24,Scenario 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:,25,例：假定投资于某股票，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。,26,=4500.5=21.2132,27,5.4.3,超额收益与风险溢价, Risk and Risk premiums,Example: r,f,=6%, r,stockA,=14%, so what is 8% which equals to r,stockA,-,r,f,?,r,stockA,-r,f,=excess return, or excess return=actual return riskfree rate.,The risk premium is the expected value of the excess return, then,E(r)-,r,f,=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.,28,5.4.3,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,r,f,8,。初始投资,100,元于股票，其风险溢价,(E(r,)-,r,f,),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,29,5.5,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 return,：,30,5.5.2,几何收益率,Geometric Average Return,TV =,投资终值,(,Terminal Value of the Investment),g=,几何平均收益率,(geometric average rate of return),31,5.5.4,方差与标准差,方差,=,期望值偏离的平方,(expected value of squared deviations),历史数据的方差估计：,无偏化处理：,32,5.5.5,报酬,-,风险比率,(,夏普比率,)The Reward-to-Volatility (Sharpe) Ratio,Sharpe Ratio for Portfolios =,Risk Premium,SD of Excess Return,We would like to know the trade-off between reward(the risk premium) and risk(as measured by standard deviation or SD),5-,33,5.6,正态分布,- The Normal Distribution,Investment management is easier when returns are normal., deviation is a good measure of risk when returns are 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 Distribution,5-,35,Normality and Risk Measures,What if excess returns are not normally distributed?,Standard deviation is no longer a complete measure of risk,Sharpe ratio is not a complete measure of portfolio performance,Need to consider skew and kurtosis,36,5.7,偏离正态,偏度，亦称三阶矩,(third-order moments),峰度：,37,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),5-,39,Value at Risk (VaR),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 distribution,The 5% VaR , commonly estimated in practice, is the return at the 5,th,percentile when returns are sorted from high to low,.,5-,40,Expected Shortfall (ES),Also called conditional tail expectation (CTE),More conservative measure of downside risk than VaR,VaR takes the highest return from the worst cases,ES takes an average return of the worst cases,7-,41,Covariance and Correlation,Portfolio risk depends on the correlation between the returns of the assets in the portfolio,Covariance and the correlation coefficient provide a measure of the way returns of two assets vary,7-,42,Two-Security Portfolio: Return,+,portfolio expected return,security i return,security j,return,security i expected return,security j,expected return,7-,43,=,Variance of Security,i,=,Variance of Security,j,=,Covariance of returns for,Security,i,and Security,j,Two-Security Portfolio: Risk,7-,44,=,Covariance of returns for,Security,i,and Security,j,Two-Security Portfolio: Risk,通用公式：,7-,45,Two-Security Portfolio: Risk,通用公式：,46,5.8,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- 2005,48,图,5.6 1926-2005,年历史收益率,49,5.8.2,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- 2005,51,图,5.7,世界名义和实际股权收益率,1900-2000,52,图,5.8,世界股权和债券实际收益率的年标准差,1900-2000,53,5.9,长期投资,54,5.9.1,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，则实际的持有期收益率为对数正态分布,终值为：,55,5.9.2,夏普比率回顾,夏普比率的时间维度,5.9.3,长期未来收益率模拟,5.9.4,长期预测,56,图,5.10 Annually Compounded, 25-Year HPRs from Bootstrapped History and A Normal Distribution (50,000,样本,),57,图,5.11 Annually Compounded, 25-Year HPRs from Bootstrapped History(50,000,Observation),58,图,5.12,Wealth Indexes of Selected Outcomes of Large Stock Portfolios and the Average T-bill Portfolio,59,5.10,非正态分布的风险度量,风险价值,(value at risk, VaR),分布的分位数,(,q,),，表示有,q,%,的值小于它,尾部条件期望,(conditional tail expectation, CTE),下偏标准差,(Lower partial standard deviation,LPSD),60,表,5.5 Risk Measures for Non-Normal Distributions,61,本章小结,实际利率与名义利率,证券均衡期望收益率,风险与收益的权衡,风险投资在长期看并不安全,非标准正态分布的风险度量,