tailieunhanh - Tài liệu tham khảo về Phân tích rủi ro

Tài liệu học Phân tích về Rủi ro | Fisher effect: Approximation R = r + i or r = R - i Example: r = 3%, i = 6% R = 9% = 3%+6% or r = 3% = 9%-6% Fisher effect: Exact Real vs. Nominal Rates or Numerically: HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one Rates of Return: Single Period Ending Price = 48 Beginning Price = 40 Dividend = 2 Rates of Return: Single Period Example 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2 Characteristics of Probability Distributions Symmetric distribution r . . Normal Distribution Subjective returns ‘s’ = number of scenarios considered pi = probability that scenario ‘i’ will occur ri = return if scenario ‘i’ occurs Measuring Mean: Scenario or Subjective Returns E(r) = (.1)()+(.2)(.05).+(.1)(.35) E(r) = .15 = 15% Numerical example: Scenario Distributions Scenario Probability Return 1 -5% 2 5% | Fisher effect: Approximation R = r + i or r = R - i Example: r = 3%, i = 6% R = 9% = 3%+6% or r = 3% = 9%-6% Fisher effect: Exact Real vs. Nominal Rates or Numerically: HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one Rates of Return: Single Period Ending Price = 48 Beginning Price = 40 Dividend = 2 Rates of Return: Single Period Example 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2 Characteristics of Probability Distributions Symmetric distribution r . . Normal Distribution Subjective returns ‘s’ = number of scenarios considered pi = probability that scenario ‘i’ will occur ri = return if scenario ‘i’ occurs Measuring Mean: Scenario or Subjective Returns E(r) = (.1)()+(.2)(.05).+(.1)(.35) E(r) = .15 = 15% Numerical example: Scenario Distributions Scenario Probability Return 1 -5% 2 5% 3 15% 4 25% 5 35% Using Our Example: s2=[(.1)()2+(.2)(.05- .15)2+ ] =.01199 s = [ .01199]1/2 = .1095 = Subjective or Scenario Distributions Measuring Variance or Dispersion of Returns Standard deviation = [variance]1/2 = s W = 100 W1 = 150; Profit = 50 p = .6 W2 = 80; Profit = -20 1-p = .4 E(W) = pW1 + (1-p)W2 = 122 s2 = p[W1 - E(W)]2 + (1-p) [W2 - E(W)]2 s2 = 1,176 and s = Risk - Uncertain Outcomes W1 = 150 Profit = 50 p = .6 W2 = 80 Profit = -20 1-p = .4 100 Risky Investment Risk Free T-bills Profit = 5 Risk Premium = 22-5 = 17 Risky Investments with Risk-Free Investment Investor’s view of risk Risk Averse Risk Neutral Risk Seeking Utility Utility Function U = E ( r ) – .005 A s 2 A measures the degree of risk aversion Risk Aversion & Utility Risk Aversion and Value: The Sample Investment U = E ( r ) - .005 A s 2 = 22% - .005 A (34%) 2 Risk Aversion A Utility High 5 3 Low 1 T-bill = 5% Dominance Principle 1 2 3 4 Expected Return .