introduction to ris, return, and the historical record有关风险,回报和历史记录.ppt

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introduction to ris, return, and the historical record有关风险,回报和历史记录.ppt

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introduction to ris, return, and the historical record有关风险,回报和历史记录

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 5-* Scenario VAR and STD Example VAR calculation: σ2 = .25(.31 - 0.0976)2+.45(.14 - .0976)2 + .25(-0.0675 - 0.0976)2 + .05(-.52 - .0976)2 = .038 Example STD calculation: Hafiz Hoque 5-* Time Series Analysis of Past Rates of Return The Arithmetic Average of rate of return: Hafiz Hoque 5-* Geometric Average Return TV = Terminal Value of the Investment g= geometric average rate of return Hafiz Hoque 5-* Geometric Variance and Standard Deviation Formulas Estimated Variance = expected value of squared deviations Hafiz Hoque 5-* Geometric Variance and Standard Deviation Formulas When eliminating the bias, Variance and Standard Deviation become: Hafiz Hoque 5-* The Reward-to-Volatility (Sharpe) Ratio Sharpe Ratio for Portfolios: Hafiz Hoque 5-* The Normal Distribution Investment management is easier when returns are normal. Standard 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. Hafiz Hoque 5-* Figure 5.4 The Normal Distribution Hafiz Hoque 5-* 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 Hafiz Hoque 5-* Skew and Kurtosis Skew Equation 5.19 Kurtosis Equation 5.20 Hafiz Hoque 5-* Figure 5.5A Normal and Skewed Distributions Hafiz Hoque 5-* Figure 5.5B Normal and Fat-Tailed Distributions (mean = .1, SD =.2) Hafiz Hoque 5-* 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. Haf