Chap风险与收益.ppt

* * * * * * * * * * * * * * * * * * * * * * * * * * 5-* Figure 5.5A Normal and Skewed Distributions 正态与有偏分布 5-* Figure 5.5B Normal and Fat-Tailed Distributions (mean = .1, SD =.2)正态与厚尾分布 5-* Value at Risk (VaR)在险价值 A measure of loss most frequently associated with extreme negative returns度量一定概率下发生极端负值所造成的损失 VaR is the quantile of a distribution below which lies q % of the possible values of that distribution在险价值的另一个名字是分布的分位数 The 5% VaR , commonly estimated in practice, is the return at the 5th percentile when returns are sorted from high to low.通常估计的5%的VaR是指收益从高到底排列后的，有95%的收益都会好过的那一个值。 5-* Expected Shortfall (ES)预期损失 Also called conditional tail expectation (CTE)也叫做条件尾部期望 More conservative measure of downside risk than VaR比起在险价值是下侧风险更为保守的风险测度 VaR takes the highest return from the worst cases在险价值取所有最坏情况的最高值来表达风险 ES takes an average return of the worst cases预期损失取所有最坏情况的平均值 5-* Lower Partial Standard Deviation (LPSD)and the Sortino Ratio下标准偏差与Sortino比 Issues:分布不对称带来的问题 Need to consider negative deviations separately需要单独考察负值偏差 Need to consider deviations of returns from the risk-free rate.需要考察收益偏离无风险收益的水平 LPSD: similar to usual standard deviation, but uses only negative deviations from rf下标准和标准差的计算一样，不同的是它只用负收益为样本 Sortino Ratio replaces Sharpe Ratio在这种情况下我们用Sortino比率代替夏普比衡量风险收益比 5-* Historic Returns on Risky Portfolios风险组合的历史收益 Returns appear normally distributed收益通常是正态分布的 Returns are lower over the most recent half of the period (1986-2009)近年来收益降低了 SD for small stocks became smaller; SD for long-term bonds got bigger小型股的标准差变小，但是长期债券的标准差变大 5-* Historic Returns on Risky Portfolios风险组合的历史收益 Better diversified portfolios have higher Sharpe Ratios分散较好的组合有较高的夏普比 Negative skew右偏，或者说向负值偏斜 5-* Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-2000名义与真实收益 5-* Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-2000股票与债券真实收益的标准差 5-* Figure 5.9 Probability of Investment Outcomes After 25 Years with a Lognormal Distr