riskandreturngeznn精品.ppt

* * * * * * * * * Degree of freedom: the number of factors which you can choose freely. * * * * * Moment-generating function * skew to the left ? positive skewness skew to the right ? negative skewness * * Created by JP Morgan * * * * * * * * Figure 5.5B Normal and Fat-Tailed Distributions (mean = .1, SD =.2) * 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 5th percentile when returns are sorted from high to low. * 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 (so ES is usually worse than VaR) * Lower Partial Standard Deviation (LPSD)and the Sortino Ratio Issues: Need to consider negative deviations separately Need to consider deviations of returns from the risk-free rate. LPSD: similar to usual standard deviation, but uses only negative deviations from rf Sortino Ratio replaces Sharpe Ratio * History of Risk and Return Small stocks had the highest long-term returns, while T-Bills had the lowest long-term returns. Small stocks had the largest fluctuations in price, while T-Bills had the lowest. Higher risk requires a higher return. * * * * * Returns appear normally distributed Returns are lower over the most recent half of the period (1968-2009) (See Table 5.3) SD for small stocks became smaller; SD for long-term bonds got bigger (See Table 5.3) * * Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-2000 * Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-2000 * Figure 10.5 The Historical Tradeoff Between Risk and Return in Large Portfolios, 1926–2005 Source: CRSP, Morgan Stanley Capital International * * * * r = r* (